Evolutionary possibilities of the emergence of economic calculation and money. The problem of the impossibility of socialism.

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Problem of the economic calculation is usually associated with the problem of the impossibility of the economic calculation in the socialist society and with impossibility to calculate without money. The monetary calculation is considered as the beginning of economic calculation in cardinal units, given the fact it sets the so-called common denominator of calculation. The authors active in this area typically resort to claims that before the emergence of money there had to be some form of ineffective type of calculation. This paper focuses on the critique of the current approaches to the economic calculation problem. It points out the logical errors of the Mises’s or Hayek’s interpretation of the problem. Nonetheless, it seeks the solution in a modified Hayek’s version of the interpretation of the problem defined as a knowledge problem. It proposes an alternative, evolutionary solution, consistent with other claims of the Austrian School of Economics. I present here not a superficial solution to the problem. The problem is solved in the context of the modified theory of the subjective value, value imputation problem, as well as the problem of the transition from the subjective evaluation of economic goods to objectively set values (prices) of such goods (appraisal problem). Modification of the approach enables the description of the problem of economic calculation in the non-monetary economy, and then also in the monetary one. On the basis of this line of reasoning it is possible also to explain the so-called problem of the objective exchange value of money, meaning the purchasing power of money. Furthermore, this argumentation also shows the options of the evolution of money (economic tool) also in accordance with different competitive approaches to the problem of money from the perspective of economic anthropology. It follows from the argumentation provided in this paper that the term ‘economic effectiveness’ has a relativistic character. The conclusions reached in this paper clearly show the possibility of the existence of economic calculation in the socialist society. In order to refuse socialism, there is a need for other forms of reasoning, based on the principles of personal freedom of each individual within the boundaries of the private property, which have the form of “absolute” social norms. I also claim that regardless of the fact that the term economic effectiveness has a relativistic character, socialist society has to be a less effective economic community by definition. This is due to the fact that socialism is applying anti-social (involuntary) standard of economic calculation leading to the weaker satisfaction of the ends of individuals as members of these societies compared with capitalism, or some forms of more free society where the calculation standard is chosen within the competitiveness process.

Key words

Theory of value, Pricing theory, economic calculation, socialism, money

1. Introduction

The problem of the economic calculation has generated numerous economic discussions. And I sincerely hope that this contribution will generate a new ones. Mainly, because It will be quite controversial. The problem of the economic calculation is usually associated with the problem of impossibility of the economic calculation in the socialist society. None of the works on the topic, however, focuses on the answering of the question related to the evolution of the emergence of the monetary economic calculation. The monetary calculation is considered either as a beginning of the possibility of any effective calculation in the cardinal units of common denominator of calculation, or the authors writing on this topic resort to the claims, that prior to that there had to be only some ineffective form of calculation (which is not worth a mention?) It is the background of the answers to the question of the evolution of the economic calculation phenomenon that shows that the perception so far is not correct. The order of my argument supporting the claim is chosen in the following manner:

We describe the problem of economic calculation, we present the critique of the current interpretation of the problem and we identify the valid parts of current interpretation. Within this context we make use as the basic texts Mises´s “Economic Calculation in the Socialist Commonwealth”[1] and Hayek´s “The Use of Knowledge in Society”[2]. Subsequently, we will criticize Mises and Hayek. As we shall see, the premises underlying the arguments of Mises and then Hayek, are logically inconsistent. However, Hayek’s interpretation of the problem of the economic calculation of socialist society, as well as the theory of cultural evolution, suggests a direction in which the identified problems could be eliminated (as we shall see, however, Hayek does not solve the identified problems completely). During the criticism we of course point out also the valid parts of the theories, whether Mises’s or Hayek’s. It is actually the valid parts of the arguments of both authors that will form the foundation for the reformulation of the solution. The offered solution to the problem focuses on the three areas of problems, namely the nature of the evaluation of economic goods and their subsequent pricing, the problem of the common denominator of the economic calculation (its gradual emergence) and placing the presented solution into the potential historical context. The reconstruction of the evolutionary emergence of economic calculation will obviously have a logical-formal character, meaning that it is not an exact reconstruction of the historical facts, but rather a possible interpretation of the motivations and logical framework. It will not, therefore, make a claim for an absolute truthfulness. It will seek to identify the principles. In the process I will also uncover my comments to the arguments related to the previous debate on the economic calculation of Austrian authors[3]  (in the alphabetical order): Boetke, P., Eshelman, L., Herbener, J., Hoppe, H., Hülsmann, J., Lavoi, D., Kirzner, I., Rothbard, M. Salerno, J. as well as the contribution of B. Caplan[4]. The paper follows my previously presented criticism of the Mises’s branch of the Austrian School and its interpretation of the problem of the purchasing power of money, the criticism of the regression theorem, or the revision of the Austrian approach to the interest rate, which are related to the problem of calculation, and thus I shall make references to my previous works[5].

The paper shall lead us to some quite controversial claims. I argue that the economic calculation in socialism is possible and so is socialism. It is just that socialism is by definition less effective and so is the economic calculation within the socialism. I will also address the importance of the property rights and I will state that the property rights are a condition for a higher efficiency. I describe the problem of organizational units (family, company, community,…) and the problem of economic calculation: I argue that the calculation is derived also from the determination of the accounting standard of the given organizational unit. I also focus on the contribution of Hayek and his so-called knowledge problem. I will claim that Hayek’s contribution to the discussion is valid and, conversely, it is the Mises’s interpretation that is actually incorrect, even though from the beginning of his thought process Mises explicitly suggests the solution. Nevertheless, he does not develop it leading his line of reasoning to logical difficulties. Finally, we show the answers to some new related questions related to the topic of economic calculation, which shall arise from the presented interpretation of the problem; for example, why capitalism and free society are more effective in the use of the scarce resources.

2. Problem of the economic calculation and the criticism of the existing approach of the Austrian school

The problem of the economic calculation is associated with a question of how it is possible to explain the existence of a calculating unit, which is identical for each person, if each person attributes value to economic goods subjectively. The problem stems from the fact that the subjective attribution of value to economic goods is not comparable. Each human subject has its own value scale, based on he/she perceives the reality around. The second problem stems from the fact that human subjects approach the evaluation of economic goods in different ways, so these economic goods have value-heterogeneous character. This means that the economic good – water – can be value-perceived differently by two different human subjects. If we include time frame, or time continuum, in the picture, the problem becomes all the more obvious even in the case of one person, not to mention more people. This is true given the point of view, that the water as economic good can be value-perceived by that same person at time t differently compare to the time t+1. We face, therefore, a very interesting problem of how human subjects can, based on these presumptions, economically calculate at all? The fact that they deal with this problem is obvious from the empirical reality, which we perceive around us, i.e. that people calculate and solved this issue. We must “only” describe how. 

In 1920 Mises proposes a solution, about which he claimed that it is consistent with the theory of subjective value. Mises realizes the problem of the subjective perception and subjective attribution of value to the economic goods. He proposes to solve the problem using exchange! Mises claims that the exchange of two economic goods, which is based on evaluating exchanged goods in question differently, creates however an objective exchange ratio of these economic goods; the price. The objective nature of this exchange ratio allows subsequently its perception not just by the two human subjects undertaking the exchange, but also by other humans. It is because the price is objective feature of reality. This way people mutually “communicate” subjectively perceived ends, which they satisfy through the exchanged means. Subjective and inverse evaluation of the two means by two human subjects creates in fact an objective feature of reality. The price is indeed an objective fact. On this topic Mises writes:

“In an exchange economy the objective exchange value of commodities enters as the unit of economic calculation. This entails a threefold advantage. In the first place, it renders it possible to base the calculation upon the valuations of all participants in trade. The subjective use value of each is not immediately comparable as a purely individual phenomenon with the subjective use value of other men. It only becomes so in exchange value, which arises out of the interplay of the subjective valuations of all who take part in exchange. But in that case calculation by exchange value furnishes a control over the appropriate employment of goods. Anyone who wishes to make calculations in regard to a complicated process of production will immediately notice whether he has worked more economically than others or not; if he finds, from reference to the exchange relations obtaining in the market, that he will not be able to produce profitably, this shows that others understand how to make a better use of the goods of higher order in question. Lastly, calculation by exchange value makes it possible to refer values back to a unit. For this purpose, since goods are mutually substitutable in accordance with the exchange relations obtaining in the market, any possible good can be chosen. In a monetary economy it is money that is so chosen.” (p. 10, Mises 1920)

This part is crucial with respect to our argument, both from the perspective of validity of Mises’s line of reasoning, as well as in terms of our criticism. That is why I have presented citation in full. Here Mises points out the possibility of mutual comparison of the activities of human subjects related to the economization of objects of reality. The comparison allows on one hand uncover the valuation of the second human subject associated with the evaluation of the object of reality, which he demands in the exchange, as well as on the other hand the valuation associated with that object of reality, which he offers in the exchange and vice versa from the point of view of the other one. Thus, we are setting some kind of mutual value benchmark. Valid here and now and valid for two given human subjects, however, the information is transferable also to other human subjects that are aware of the exchange. Literally this shows to the two sides of the exchange, as well as to others the mutual relation of the ascribing of value to the economic goods by the two human subjects during exchange. Mises cautions that the objective exchange value of the goods at the same time allows to calculate (re-calculate) our economic activity in some units. So far up to this point one cannot really criticize Mises as he presents a brilliant solution to the subjective nature of valuation of economic goods. Then, however, he follows with a part that seems logical: „since goods are mutually substitutable in accordance with the exchange relations obtaining in the market, any possible good can be chosen. In a monetary economy it is money that is so chosen.“ As we shall see, this is from Mises an unfortunate simplification of the problem, which in turn necessarily leads him to wrong logical conclusions and directs his argument to logically contradictory statements.

It is true that Mises describes the process of the transition from subjective valuation to calculation based on objective criteria. However, he talks about economic calculation primarily only as a monetary calculation. In essence, he cannot imagine a different one. When mentioning the non-monetary calculation, he refers to statements, that it is possible only with the economic goods of lower order. He mentions the example of a household, or a peasant who does not have to have any calculation problem, until economic goods of higher order enter the scene (capital goods, needed for the production of the consumer goods of lower order). He equally refers to Robinson Crusoe, saying that he does not necessarily need to have a calculation problem, insofar as the calculation focuses on the satisfaction of his ends (in kind calculation). His argumentation in the context of economic calculation in socialist society is quite the same. It is a developed economic community, which cannot exist without monetary calculation, given the fact that it is mainly the advanced production processes, in which the community needs the monetary economic calculation created in the free market in the context of individual property rights:

Calculation in natura, in an economy without exchange, can embrace consumption goods only; it completely fails when it comes to dealing with goods of a higher order. And as soon as one gives up the conception of a freely established monetary price for goods of a higher order, rational production becomes completely impossible. Every step that takes us away from private ownership of the means of production and from the use of money also takes us away from rational economics. [emphasis in original, p. 17. Mises 1920)]

However, the perception of the economic calculation as the monetary calculation puts Mises and his defenders to the mutually contradicting and illogical claims. I claim, that the main problem of this line of argument is in the derivation of the calculation from the past monetary exchange price. The problem is of course the past price. Whether monetary or non-monetary. The claim creates a three-way problem; the third one is the most serious one. The first problem is that our predecessor have not always had money. This is not denied by either Mises or his followers. However, what was then before our predecessors invented money? After all they had to conduct economic calculation and a successful one, even though in the context of (their mental) capacities. Without undertaking some form of “successful” economic calculation we would not be here and also there would be no way to create more complicated production structures, where Mises demands calculation and he even claims that it can only be monetary. Non-calculation simply cannot lead to calculation[6]. It appears that Mises was not in the mood to go deeper into the explanation of such answers associated with the means of calculation before the monetary economy. He circumvents the answer by the argument about the application of calculation for the so-called simple and complex economic processes. In case of the simple processes he claimed that it is actually simple to do the calculation. The estimates of the prices be undertaken by the mini community (individual, family, small community). Of course, based on the previous (barter) prices. This, nonetheless, creates a second problem. The empirical question of since when the monetary calculation is necessary and until what kind of process is not. Alternatively, the question is what kind of economic process is still simple and which one is already a complex one? The third problem, which is related to the two previous ones and which is the main problem (it is exactly this third problem that creates the first two problems), is the discord of the claim about the economic calculation based on the past prices in the context of future oriented activity. The past is given and “forgotten” history for new action. It is something what already happens based on something what was perceived in the past. This is not my claim; this is Mises proper claim. If the calculation process is based on previous prices and previous prices are also outcome of calculations, how then, however, is previous calculation even possible? The price (fact) is outcome of some calculation process and calculation process is based on past prices. This is the so-called contradictory regressus ad infinitum. In other words, how could we even, based on this logic, presented by Mises, ever start calculating? The presumption of the past price actually implies the existence of the past calculation[7]. Mises, however, claims that without the past price one cannot calculate. This is not some obscure argument in terms of Mises’s interpretation. This is the explicit position of the Misesians. They even explain it as a form of “Verstehen” of the situation that it is only this way that one can perceive previous conditions of the actions of the human subjects, based on which we can make further decisions and actions and calculation[8].

There are two ways to look at this issue. The first options is that we stay with Mises’s position, but then we necessarily have to get to the vicious argument cycle. Prices (whether monetary or non-monetary) are for Mises the prerequisite for any economic calculation, but at the same time a result of an exchange, which is inevitably the result of an activity including an element of calculation. The second option is to admit that Mises did not really explain the problem of economic calculation.

And as we can see, the fundamental question is how humans ever started to calculate under the assumptions set out above, i.e. there is no common denominator of economic calculation and there is a heterogeneity in the value perception of economic goods. How is than possible to calculate once there is no common denominator and there is value heterogeneity of goods? Both must be explained in the context of the validity of the theories, such as the subjective value theory and the marginal utility theory.

The problem we face here is of a twofold nature. First, it is necessary to explain how a common denominator for the economic calculation acquires its purchasing power – per se[9]. Yet on the other hand, we must also explain the principles of economic calculation itself.

Before we can proceed to the revision of Mises’ approach, let us introduce Hayek’s claims about the calculation problem. Hayek writes his work clearly in the reference to Mises – monetary calculation. He is, therefore, subject to identical criticism as Mises. Nonetheless, Hayek brings the discussion about the calculation problem to a slightly different level, which I consider in the context of this paper to be instructive and valid. Hayek calls this level “knowledge problem”, which the community solves through the price system. Hayek perceives the actual realization of the economic calculation only as a computing problem. This is, however, preceded in Hayek’s words by the problem of the input of data inaccessible to anyone (implies the existence of the central planner) on their own. He writes that the problem of economic allocation of resources lies in how to ensure the best use of scarce resources for the members of the community, as the members of the community exactly perceive those resources. Hayek focuses on the fact that information is of course necessary for the proper allocation of resources. He claims that there is, in principle, nothing that would happen in the world that would not affect people’s decision about the allocation of scarce resources. However, he emphasizes that it is a price system that, by condensing these scattered atomized information, makes it easier to decide about the right allocation of resources. And this is without the each individual having to deal with the causes related to what directly affects his/her interest. Hayek writes:

„It is indeed the great contribution of the pure logic of choice that it has demonstrated conclusively that even such a single mind could solve this kind of problem only by constructing and constantly using rates of equivalence (or “values,” or “marginal rates of substitution”), i.e., by attaching to each kind of scarce resource a numerical index which cannot be derived from any property possessed by that particular thing, but which reflects, or in which is condensed, its significance in view of the whole means-end structure. In any small change he will have to consider only these quantitative indices (or “values”) in which all the relevant information is concentrated; and, by adjusting the quantities one by one, he can appropriately rearrange his dispositions without having to solve the whole puzzle ab initio or without needing at any stage to survey it at once in all its ramifications.“  (part V, Hayek 1945)

Thus, Hayek understands the price system as a communication tool that society has spontaneously created. Hayek writes this passage in the context of the monetary pricing system. However, as we shall see below, the monetary price system is only a further step in the evolution of economic calculation. This Hayek’s claim needs to be anchored first in a community without a monetary unit, thus showing the more general validity of the given premises (for forgetting this step, Hayek must be criticized), and only then argue the monetary system is only a vital “communication extension tool” of the solution to the problem of the economic calculation. Then we will be able to point out that the institutionalized pricing system (e.g. today’s stock exchange system, impact of market-makers, today’s HFT technologies) is even another extension of this tool. It is even possible to speculate, whether the new technologies bringing the possibilities of the so-called triple-accounting (a double-entry cryptographic transaction-based confirmation based on decentralized blockchain technologies, or other data consensus-based technologies) are/will be the next technological evolutionary step, which will improve the price system-related tool to address the problem of economic calculation and price discovery. Although we will not explicitly discuss this topic. The fact that Hayek looks at the pricing system as an evolutionary tool can be seen in the following passage of his work:

„The price system is just one of those formations which man has learned to use (though he is still very far from having learned to make the best use of it) after he had stumbled upon it without understanding it.“ (bold added, part VI, Hayek 1945)

So let us go to the revision of the original Misesian concept of economic calculation and use vital parts of either Mises´s or Hayek’s arguments.

3. Revision of the economic calculation theory

Even though it does not appear so, based on the previous criticism, Mises actually hinted at the solution to the problem, but he never elaborated it. Whether the reasons was his method or something else, is for another discussion. Nonetheless Mises clearly shows, that the price is an objective feature of the reality, which makes it possible for it to be grasped by any subject. It is at the same time the price, meaning the exchange ratio of the two economic goods, which reveals the attribution of value to two economic goods inversely by two human subjects during the exchange. The problem faced by Mises is that the direct exchange (in particular time t) as soon as it is passes, it ends and becomes the past. Its conditions can be theoretically replicated, but this is not given and we should rather presuppose a constant change. The economic calculation in the context of barter or past monetary prices then must necessarily lead to logical problems. Economic calculation needs to be explained with reference to the future, without the past being relevant in any way.

Let us try for the beginning of our inquiry take the valid part of the Mises’s argument. In doing so we shall undertake a slight change in its interpretation, thus defining the basic positions, from which we can take the inquiry further. The problem can be solved by a small change of the perspective on the problem and by abandoning the exchange at the specific time t, which ends and becomes the past. We need to focus on the debt exchange, meaning the exchange at times t, when the creditor provides the debtor the economic good X and at time t+1 the debtor eliminates his/her obligation to the creditor in terms of the good Y. In this case the objects of the evaluation of the two human subjects is not the comparison of the past and present as it is within the exchange at particular time t. During the exchange at particular time t we exchange something that we have already previously created. We judge something that has already happened. For this type of calculation, we necessarily have to compare the price at time t and a different price at t – 1. However, as we have shown already, the reference to the past creates problems; we are comparing two situations, which have a different value context. The past is completely heterogenous compare to present. Without money we compare apples to oranges. Nonetheless, our goal is to explain such comparison without money.

The debt exchange, on the contrary, lasts into the future. It is a plan. It is a future elimination of debt through some units of economic good Y in exchange for the debtor earning X, which has already been made, earlier in time. I claim here that from the point of this exchange the economic calculation is the accounting standard[10] of the creditor in terms of the economic good Y, which he agreed with the debtor. It is at the same time a common standard of the creditor and the debtor given that even the debt exchange implies a mutual agreement of both human subjects. However, it is true that the standard is proposed more by the creditor in terms of the ratio Y/X, which is fulfilled later in time, because the exchange ratio X/Y is already realized at time t and becomes the past. The accounting standard (standard of economic calculation) is rather an agreement in terms of the elimination of the obligation in Y. Based on that the participants of the exchange can calculate their profits, which from the perspective of the creditor take the form of the promised economic good Y and from the perspective of debtor in the form of what he keeps, if he respects the obligation towards the creditor, meaning the remains of some economic goods, which are the result of his economic activity during the time period t à t+1, minus Y, by which the debtor eliminated the debt.

The change of the focus from the direct exchange (time t) to the debt exchange provides a number of qualitative changes. First, the debt exchange happens over time and at the given time the created accounting standard lasts. This makes the standard transferable also to other members of the economic community. Second, the economic calculation focuses on the future, which is completely in line with the claim that the human action always focuses on the future; that means that the calculation is not derived from the past prices, it is based on an objective ex ante agreement. Other prices of economic goods in the period of the duration of the obligation we derive from the activity of the debtor that tries to eliminate the debt in the form of Y. This means that in the period of the duration of the obligation the debtor exchanges the results of his economic activity for some part of Y so that by the end of the agreement, he will have repaid the entire obligation in Y. The ongoing exchange in Y is motivated by the effort to eliminate the obligation in t+1. The other prices thus generated during the duration of the obligation expressed in Y (the debtor demands Y in order to repay the obligation) have their future orientation as well. At the same time, it is irrelevant, whether the Y takes the form of money or any other economic good. It is an agreement about the debt exchange, which implies the objective standard of calculation between the creditor and the debtor expressed in Y, which is provided later in time for X, which is provided earlier in time. At the same time it is completely irrelevant, whether the given exchange concerns a simple or complicated production process. What is also essential is that the principle of the standard of economic calculation is applicable in the evolutionary development of the economic relations, meaning it is possible to describe its gradual creation from the debt exchange of two subjects, which create a sort of binary economic calculation standard (standard of the two human subjects) for any production process, up to any numerous community of human subjects, which in time create mutual economic-calculation standard (n-nary standard), which, as we shall see, logically collapses into the expression of economic calculation only in a certain number of economic goods, which the community uses for calculation in the form of several kinds of money.

At the same time the context of such line of reasoning is connectable to the Hayek’s argument about the price system as the tool of economic calculation. The economic good Y as the accounting standard of the two human subjects is transferable to other human subjects. Obviously only in the case that other human subjects agree to the given standard, meaning that it is beneficial for them to use the standard. It could become the part of the rules of the community and it could be formed in the primitive competitive environment among numerous economic goods used by the community. Subsequently the “price” system in a given community is also determined in units Y. The good Y could have started to serve as the basis for the further estimation of the acceptability and feasibility of the fulfilment of the subsequent debt exchanges of other members of the community. This means that in a simplified manner human subjects are beginning to address gradually the question of whether or not to accept the terms of the debt exchange, which is proposed in the given standard. This then influences the further development of the production structures and its potential expansion (also beyond the borders of the community) based on repetition of the process. The specialization of economic activities connected with the standardization of debt exchanges in Y are further developed in communities, which improve the determination of the purchasing power of Y (the emergence of money à primitive banking system à modern banking system) and on the other hand the price system itself is improving as well (first primitive exchanges beyond the border of community à first primitive standard market places à first stock markets à global financial system).

In the following subchapters we describe in detail this brief outline of the solution and give a deeper argumentation and its explanation. Indeed, we have to show how this theory can be linked to subjective value theory. Then we need to show how subjective valuations lead to prices and what their role is and how we calculate in non-monetary exchanges. Ultimately we focus on the processes standing behind the attribution of the purchasing power of the monetary calculation unit (money) and how this theory can be linked to other theories of the emergence of money.

3.1 Subjective theory of value

Economic calculation needs to be anchored in the context of the value theory and the associated problem, so-called value imputation problem. The method that we choose follow on the recent and very inspirational works of a Slovak social scientist Šimon Biľo. As Biľo shows, the value theory and the problem of the attribution of value to the so-called goods of higher order (in the context of the value imputation theory) was a topic basically unopened since 1930. Misesian, so-called ordinalistic approach to the valuation theory “defeated” the cardinalistic attempts to explain the valuation of economic goods of higher order present in the works of Böhm-Bawerk and Wieser[11]. While Böhm-Bawerk and Wieser try to solve the problem of the value imputation of economic goods of higher order through a cardinalistic approach, it is Čuhel-Mises’s solution of the given problem claims that in the context of the evaluation there is nothing more than the preference of a against b. That means no value calculation, just a comparison of what is better and what is worse. However, Mises’s solution still contains equation, meaning that the value of product equals the value of the overall combination of production factors necessary for its production. Biľo points out that it is professor Hülsmann who identified this point of Mises’s “legacy” inherited from other Austrian school authors[12]. This claim is, according to Hülsmann, not in line with Mises’s claims that the valuation can be based only on the ordinalistic principle, meaning the valuation is based only on the “preference a to b” principle, not “equals” principle. Professor Hülsmann, building on this finding, determines in the context of theory of interest that the interest originates from the value spread between ends and means, meaning that means have to be on the value scale always lower than their corresponding ends.

Šimon Biľo, however, provides an excellent critique of prof. Hülsmann ending in the claim that there is nothing like the existence of the value spread between ends and means. It is no coincidence that in doing so Biľo also presents his own solution to the valuation problem and the problem of value imputation. It is also a very inspirational solution. We shall first introduce the solution, and then I shall provide my own critical remarks of it.  Based on these remarks, I try to eliminate the identified errors, so that his valuation theory can sustain such criticisms. This way I shall introduce a new version of this theory, which can serve as an explanation of how our predecessors calculated even without money.

Biľo is a praxeologist, and so he begins his description by defining, what is action. He considers that an action has to be purposeful and requiring choice leading to the achievement of desired ends. He points out that the condition for action is the person’s feeling of uneasiness, the vision of a more satisfying state and the expectation that the action will causally leads to the removal or amelioration of the feeling of uneasiness. As he explains, the action is necessarily focused only on the future, the goal of the action is always so-called action-result category, assessed in the context of contra-factuality of the result of the action, meaning the potentially alternative state of what could happen in other circumstances, if the person did not take the action to remove the perceived uneasiness. Thus, it is not the present state of the perceived uneasiness that is important for the person, but rather the potential situations, which are “unacceptable” to us, if we do not act.

Biľo follows Mises, that it is an active man that transforms the things and makes them into economic means („acting man makes them – things – means“). Biľo further paraphrases Mises, that the means must always be scare at the same time, otherwise it would not make sense to act and the means would just be general conditions of human welfare. It is the decision (choice) between the different options, which represents the value, and the given alternatives are ordinary valued on the preferential scale. In the context of evolution of the value theory Biľo notices, that the ordinal evaluation can only take place at the level of ends and not on the level of means. He explicitly confronts the contradictory claim of professor Hülsmann who claims that the value is a trilateral relation between the subject and at least two economic goods. It is not. The use of means, or the decision on their acquisition, is derived from the ends and their valuation. The trilateral relation must exist only on the level of ends. This means that the valuation is a trilateral relation between end, contrafactual end and the human subject. The value can only be determined from the valuation of ends. Not from the valuation of economic goods.

From these foundations then follows the key point of his work – he identifies two kinds of value, or valuation. In doing so, he refers to Mises who specifies that the mind of a man imagines before taking action in reality two possible situations and decides between these two imagined situations in the sense of “which of them suits him better?” Based on this Biľo identifies the existence of so-called ex ante value. He claims that this ex ante value is a necessary condition for any action (it is a pre-action nexus), meaning that the value exists also “outside” of action (quotation marks are used by Biľo himself). From this it necessarily follows for Biľo that there must be two different kinds of valuation – ex ante and in action. At this point he very cleverly connects this finding with the Rothbard’s perception of the valuation, while in Biľo’s words Rothbard slightly deviates from his predecessors given that the basis of the Rothbard’s explanation of value is the transformation of the ordinal relationship between ends and means. This signifies that based on the ordinal valuation of ends, the ordinal valuation of means is achieved through transformation, by which Rothbard solves also the value imputation problem, meaning that the valuation of consumer and production goods is not interconnected, but rather is derived from the ends. Biľo cleverly uses Rothbard’s thinking and applies it to his conclusions – to the existence of ex-ante valuation and in action valuation. He introduces a so-called praxeological point. Biľo himself claims that it is an aid in the process of the imagining of the problem. He uses the praxeological point to divide ex-ante valuation and in-action valuation. The valuation is ex-ante attributed to ends and their corresponding ultimate ends; Biľo does not differentiate between the two. Consequently valuation is transformed into the valuation of the means through the valuation in-action, which, however is not a valuation per se, but a specific choice of the state of affairs, the state of means – economic goods, which satisfy the intended ends. It is clear the choice of means is thus completely influenced by ex-ante value of what should be satisfied by them. It is clearly not about the state of economic goods per se, it is all about the satisfaction of our ends through means! It is a very important point that has been inspired possibly by the work of professor Hülsmann who claims that if the person is able to satisfy his ends without having to choose any means for their fulfilment, he would do so. This way Biľo really solves the value imputation problem through fresh thinking in such a way that the (quasi) valuation of the ends directs always towards the satisfaction of ultimate ends and we transfer these value relations (ordinarily preferred) between the ends into reality and based on the subjective viewpoint we choose the best matching means of their satisfaction. He equally formulates[13] the following rules of value imputation:

„1. Every action is only action-result oriented – only action-result categories could be valued.

2. Only ultimate ends (= uneasiness = action-result desires) are really valued (“ex ante”), their quasi-ends are valued only derivatively. No choice could be thought of between these two (ends and their quasi ends) and also between consequent quasi-ends of the same end – choice represents taking and giving up, whereas these have to be either chosen or given up together from the nature of the choice.

3. Means in the role of conditions of relevant praxeological point are not valued at all, only ultimate ends and quasi-ends – action-result means, are valued, “ex ante” and “in action”, second one only “in action”. Means that in particular “praxeological point” represent our abilities just are. They are “given”, or they are the result of previous quasi-ends.“

Thus, we have in front of us a new theory of value and imputation formulated by Biľo. At the same time, it follows that the search for the interest in the spread between ends and means is not possible, therefore logically proving the invalidity of interest theory by professor Hülsmann. Biľo very elegantly connects the existing findings in the area of value theory, while connecting the older findings, which he improves by new insights[14].

Critique of Biľo’s theory

While, I am going to criticize Biľo’s approach, I shall nonetheless propose a solution addressing the identified problems. I see the problems in his theory on the following places. The first is the praxeological point, the second, related one is the following hierarchy of ends. And the third issue is that Biľo does not solve nor describe his theory in the time continuum.

Biľo claims that he use the praxeological point as an aid in the explanation process. The problem is that this is a key point of his work. It is exactly on the basis of this point that it is possible to differentiate between ex-ante and in-action valuation. It is not an aid. It is principle. Such a distinction, however, causes a problem. On such a foundation Biľo claims that the valuation exists also outside the action, namely before it. This is not a presumption on my part. Biľo is too explicit. It is, however, a clear objectification of the valuation. But the valuation must be, by definition, subjective. It has no way of existing outside the action, i.e. before it. In other words the action does not begin with it, or alternatively stated even the thinking about the hierarchy of ends is action. Biľo could still claim, that there are two kinds of action. One in the process of thinking and the second one in the context of conducting the action. This is, nonetheless, a logical nonsense. There is only one action. The problem is, however, that Biľo is, at the same time, right. The action does really need a state, from which it could take off. A praxeological presumption is necessary. This is the first area of problems that we must solve.

The second issue is the solution to the problem of value imputation. Biľo follows Rothbard’s work and explains that the problem of value imputation can be viewed only from the point of ends and their hierarchy. He claims that man realizes his valuation based on the choice of so-called ultimate ends and ends (ends are derived from ultimate ends). However, in the footnote he claims[15] that he does not differentiate between ultimate ends and ends, but then he claims that quasi-ends become in the valuation process the means to fulfil the ultimate-ends. From the above follows a clear hierarchisation of ends and the need to differentiate between them. It seems that here Biľo creates a similar hierarchisation, which was attempted by Böhm in solving the value imputation on the side of means. Biľo himself uses Mises’s argument that the organization of production goods and consumer goods is not at all important. The argument about ex-ante and in-action valuation, however, implies the hierarchisation of the ends. Does not Biľo commit the identical mistake, for which Mises criticizes Böhm?

At the same time, an attentive reader may have noticed that Biľo elegantly avoids the given problem of prof. Hülsmann who points out that Mises left in the imputation theory a problem of the value equality. Biľo following Rothbard talks about a transposition, or derivation of in-action from ex-ante valuation. The derivation, or deduction or transfer from ex-ante to in-action, however, implies either identical valuation, hence equality. Biľo himself claims that in in-action valuation it is not an actual valuation per se. It is not entirely clear, what he means by that. Based on the context I am inclined to say that with in-action we cannot use valuation at all. In – action valuation per se is then only about the choice of the state of economic goods –state of affairs in reality. This signifies that when it comes to the question of whether there is any kind of valuation of goods, he should answer that there is not any; we only valuate the ends. And from this it follows that it is not possible to consider any equaling of value nor any inclusion of means in the value scale of ends. So, the Mises’s problem is eliminated by Biľo per se. It does not exist in his system at all.

The last problem, which we can imply in his theory, is the problem of time continuum. He does not solve the above-noted description in time[16]. At the same time, he does not hesitate to claim that any economic good M, which the subject used for the satisfaction of ends in time “t”, is later in time a completely different good and from the praxeological viewpoint there is no value connection with M (regardless of the physical similarities). If this were to be true, however, the law of diminishing marginal utility would be by definition invalid, as the law claims that over time the later unit of economic good M satisfies ends less. We cannot even talk about some demand for the good M (there would be nothing like the demand, everything would be in time continuum praxeologically different goods) and we cannot even explain, how can a person prefer the ends, which should be satisfied by M more today, than tomorrow. Or we would have to claim that, when the human subject is demanding M, he does not change the valuation of the end, which the M should satisfy, which is very problematic in time, because we would have to presume either the constancy of the valuation of ends in time or admit that we know the future[17]. It is a pity, that Biľo did not pay attention to the problem of application of his theory in the time continuum. He left us only with estimates in this field.


The aim of this section is not the deny Biľo’s claims. Rather, I will try to describe the problem so as to eliminate all the above-mentioned reservations. Biľo’s theory is, thus, not problem-free. But which one is, right? The key problem is, however, in my opinion the above-identified problem – the ex-ante valuation and in-action valuation. And we have to remove it. By its removal we avoid the praxeological point and as we shall see we can also avoid the hierarchisation of ultimate ends and their corresponding ends. We have to equally present a solution applicable over the time continuum, so that the law of the diminishing marginal utility is valid. And, at the same time, we must answer the relation between the ends and means in the sense of Hülsmann’s critique of equality and Biľo’s avoiding of the problem. And to make matters more difficult, the general problems of the previous approaches, meaning not only that one of Biľo, is, in my opinion, also the argument about the perception of scarcity in the context of ends – means and action, which should equally be corrected[18].

The remedy needs to be obviously directed towards the main problem. Where the economic value comes from. To the problem of the valuation of goods, Menger writes[19]:

„The value of goods [i.e. means] arises from their relationship to our needs [i.e. ends], and is not inherent in the goods themselves. With changes in this relationship, value arises and disappears. “

Menger describes a causal relationship. The economic goods themselves have no value for him. The value is ascribed in the context of ends. The end-mean relationship at the same time creates in a way the two sides of the equation. On one side we have the ends, on the other side we have the means. This division has caused for example, that a part of Austrian scientists have addressed the problem of value on the side of the goods and searched how the value is imputed to the goods. Given that they “operated” on the side of economic goods, it is not a wonder that they search the solution in the cardinal expression of value[20]. The Čuhel-Mises ordinalistic solution eliminates problems of the cardinal calculation of value and it directs us much more to the valuation of ends, based on the baseline comparison of the a always being more suitable / preferred to b. At the same time Mises retains the consistency in the evaluation of ends and corresponding valuation of means. He omits the problem of the imputation and derives the mutual connection between the production and consumer goods only from the comparison, whether they satisfy defined ends. Hülsmann notices, however, that Mises maintains equality, which bothers Hülsmann, since it implies the mathematical comparison of the value between ends and means. He even seeks in the spread between ends and means the interest rate. Rothbard (together with Biľo) focus explicitly on the valuation of ends. It is, however, Biľo who is consistent and comes with a solution to the valuation only on the level of ends; means are for him just a chosen state of things (state of affairs), which is derived from the valuation of ends. This way, however, he ends in the vicious circle, where he has to claim that the subjective valuation during action is derived from the valuation before action, which implies either objective existence of valuation before action or existence of different kinds of action. What do we see? We see the intellectual discussion focusing on the value problem, which was identified by Menger in the context of the revelation of the causal ends-means relationship. In the beginning the discussion was focused on the side of means and later it moved to the side of ends. Both approaches, however, lead to problematic conclusions. So only one thing really remains. To focus on the relationship per se[21]. And I think this is the only feasible solution. Let us consider, e.g. Hülsmann’s remark, which Biľo also notes, that if a man could prefer the satisfaction of ends without the use of means, he would have done so. Hülsmann writes[22]:

„The end is what really counts for the acting person, whereas the means is merely the thing or the action that is in between his present state of affairs and the state of affairs in which his end is realized …. if an acting person could choose between either having his end realized or having the means to attain it, he would choose the end.“

According to him, if the means is chosen, then it is only because it satisfies the corresponding end[23]. It was this abstraction (probably) that has led Biľo to the realization that it is the ends, which we valuate, not the means. We choose the means. From here it is possible to divide the action into ex-ante and in-action. What is, however, important, we choose means only in the context of ends. There is no other context. As we know, the fact that something exists in reality, does not mean that it is automatically means. It is the acting agent that takes a thing and makes it into means.

„A thing becomes a means when human reason plans to employ it for the attainment of some end and human action really employs it for this purpose. Thinking man sees the serviceableness of things, i.e., their ability to minister to his ends, and acting man makes them means“[24].

Hülsmann’s abstraction in the sense that we could avoid the choice of means and directly satisfy ends, is incorrect[25]. It is a causal relation per se. Though one’s mind can define some end per se and this is the main focus for this person. However, subsequently the mind implies the question how to satisfy the defined end. This is why we seek means and the mind creates the causal relationship. From the point of view of rejecting Hülsmann’s thesis, this is not about a practical problem of scarcity and the fact that given our perception of scarcity we are forced to choose means, i.e. it is not possible just to choose ends by very nature of the reality around us. This is about the nature of causality created by mind, meaning the rules of the thought process. The scarcity is not a feature of the reality per se, not it is the precondition for action, as several authors within the Austrian school mistakenly believe.

The thesis that the scarcity is a necessary condition for any reasoning and argument regarding the human action is incorrect. It cannot be true both that a precondition for action is the scarcity of the reality and that only economic goods are scare, which can become economic goods solely based on action (…. Human action really employs it…”). Before that these are just things, or if they are not scarce, they are general conditions of human welfare[26]. Either things (reality) become economic goods based on the action, with the subsequent revelation that they are rare respectively it is realized that some part of reality is not rare and thus it is only a general condition of human welfare, or the scarcity of the reality is the precondition for action. Both claims cannot be valid at the same time. Reality is not scarce per se. It is scarce for the acting person. And it is scarce in the context of his ends[27]. That means that the scarcity is derived from the fact that we evaluate the reality. The scarcity then has to be revealed ex-post, after the subject identifies the relation end-mean. Let us focus on the Mises’s citation. „Thinking man sees the serviceableness of things, i.e., their ability to minister to his ends, and acting man makes them means“. The order of the explanation should be the following. In case that there is a form of abundant good (say I choose 2 apples and I find myself in the warehouse with a million of apples) or even unlimited good (I choose sunlight or air), then in the context of our ends it is still a mean, which we can call a kind of thing-mean[28]. Even such a thing satisfies our ends, subject can identify in such case an end-mean causality. Without us the given thing would be just part of reality. This way (with us) it is a part of general conditions of human welfare! If, however, it is a case of a limited good in the context of our ends, only then can the mind identify its relative scarcity; and only in such a case we can call it economic-mean, precisely for the reason that it must be used economically. Also, at the same time, let us note that the law of diminishing marginal utility[29] applies both in the case of thing-mean as well as in the case of economic-mean. The law results from the end-mean relation per se and from the relation among various potentially valuated relations of ends-means. These are then the mutually indivisibly perceived causal relations, which the mind categorizes and creates among them a preferential scale in the context of the perceived scarcity of the means[30].

Through the assessment of the relation end-mean as such or per se we can sustain the valid part of the Biľo’s argumentation without presupposing the valuation ex-ante and in-action at the same time. We “need” to describe the valuation only in-action. And we do this through the relationship. If we stop here and if we use traditional value scale, we would describe it as follows:

1st end-mean relationship

2nd end-mean relationship

Nth end-mean relationship

This is not correct. The end-mean relationship would not be possible to use in time continuum. It could always happen that it will be changed due to fact that action is future oriented what cause the change of the value context and reasonable action and preference scale has to be applicable in time. So, we “need” the explanation to be applicable in time and maintain the validity of the law of the diminishing marginal utility at the same time. We must then make further necessary adjustment, besides the application of the theory on the relationship per se.

The adjustment is not too radical. Actually, it is very simple one. We need to make a claim that the person does not value the particular relationship and some explicit scale in the sense:

1st end-mean

2nd end-mean

Nth end-mean relationship

We will claim, that the given relation must be viewed as the sum, i.e.. the person perceives ΣEnds which he tries to satisfied by ΣMeans (portfolio of goods)[31]. The perception of the ΣEnds → ΣMeans is necessary for the explanation of the problem of the valuation in the time continuum. Once we use ΣEnds → ΣMeans we can explain the functionality of relationship in time. Mathematical construct of sum of ends is satisfied by sum of means (portfolio of economic goods). Mathematical construct is a time invariant, so usable in time continuum and the relative position of goods within the portfolio enables to solve different subjective valuation context in time as we change our sum of ends to eliminate new and new uneasiness. So do we are able to describe preference scale in this way?

1st ΣEnds → ΣMeans,

2nd ΣEnds → ΣMeans,

N-th relationship ΣEnds → ΣMeans

As I was notified by Fratišek Chroustal[32], the use of such a modified albeit traditionally displayed preferential scale, would imply the following problems. First, some automatic creation and stable ends-mean relationship. Second problem of the classic display, which I originally did not realize, is that it implies always the existence of some actually existing mean for any thinkable end. However, it must be admitted that it is the ends, which are essential and primary. Only then the mind searches for the corresponding means and creates a relational structure of the mind. Nonetheless, sometimes the mind may not find any mean. It does not mean, however, that mind cannot formulate the vision of some end per se. The mind of a man can seamlessly, say, formulate an end, that it would be fine if I could do for example magic. He can equally “formulate” a corresponding mean in a form of magic wand or spell. Although, these things from their very nature do not exist. Equally, if automatic and stable formulation of the end-mean relationship exists, it would follow, that we would not be able to formulate new kinds of means, for example in the form of inventions or innovative discoveries of the satisfaction of ends. All of this forces us to refrain from traditional display of the preferential scale completely.

However, it is still true that the Čuhel-Mises’s solution of valuation in the context a is more preferred than b is valid. The scale must exist. However, Hayek’s description of the functioning of mind, which says that our mind is formulating mental maps and greatly simplifies the interpretation of reality, can be instructive in our proposed modification. We can be also inspired by interpreting the factual and counter-factual (hypothetical) part of human action[33]. A preview of the structure of the preferential scale can be seen in the following figure:

Figure no. 1: Illustrative preferential scale:

This approach brings multiple solutions. The Figure shows the vision of the preferential scale. The Ends part is divided into two basic categories – factual and counter-factual, or hypothetical. Hypothetical (counterfactual) is divided further into two categories – real and unreal (potential). Everything, to what we subordinate our current actions, is located on the level of the factual preferential scale. Everything that is non-priority and at the same time feasible in the context of means is in the real counterfactual level of the preferential scale. Everything that unrealizable in the context of means is in hypothetical – counterfactual level of the preferential scale. The preferential scale is, thus, relatively simple. It has two basic levels[34], which corresponds to Hayek’s claim that mind simplifies the interpretation of the reality. By focusing on the relationship ΣEnds → ΣMeans in the context of the preferential scale, we do not have to differentiate between the valuation ex-ante and in-action. In the specific action we choose from the totalities of the relationship ΣEnds → ΣMeans. By this adjustment we are able to explain valuation of ends in time and imputation of value to economic goods in time. ΣMeans = portfolio of means is demanded and hold by individual to satisfy factual and real-contra-factual ΣEnds.

When man acts, he is doing this or that in the context of current factually perceived ΣEnds. The idea should imply that the formulation of ends is, however, crucial. At the same time, it is implied that the mind is trying to match the corresponding combination of means to create relationship. On the factual level the corresponding combination of means is clearly identified; that is why it is illustrated by a fixed bond. This is what we see in-action when we chose current state of affairs. What is important to stress is that one of the need which is part of the factual ΣEnds could be focused also on the elimination of some contra-factual ends; meaning that we built portfolio of ΣMeans by our current action as diversify as possible which enable us to react to uncertain future[35].  

On the counterfactual level the corresponding combination of means is intended; thus it is illustrated by a non-fixed bond. At the same time the idea implies the possibility of the formulation of end without a corresponding combination of real means. The person can, then, formulate some idea of an end, for which he tries to identify the corresponding means, although it is not by the very nature of world of things possible. The extreme case can be the end of immortality (for now), or the ability to do magic, which the human mind can identify. It can even identify some idea of means, like the elixir of the immortality or some magic wand, which, nonetheless, do not exist in reality and the human mind cannot it materialize.

On this example we also show, that the formulation of ends is the main feature of the preferential scale. However, we also show that the mind tries to formulate the link to means and in doing so sometimes encounters a real impossibility of the satisfaction of the given end. If, at the same time the mind can identify in form of, say, some invention or innovation, the satisfaction of up till then only unrealistic ends, it is possible formally to incorporate the given ends to a lower, though still counterfactual level of ends. The counterfactual level of ends as a whole, however, expresses still what the part of current action isn’t. However it could be part of plan.

The reasons why the counterfactual level of ends is not fully realized by men are of twofold nature. This nature results on one hand from the prioritization of ends – factual ends have a higher priority as others combination of ends. On the other hand it is caused by the very fact that something is impossible to do by the nature of reality, or our limitations in terms of our available knowledge, means or savings[36].

In the sketch we defined, the decision about the factual or counterfactual nature of ends is influenced by the bond itself or by its evaluation with respect to means. The reason is that it is a relationship. It follows, that one could have desire the end to have a factual character in the context of considering it to be a priority and he put it among actual plans, nonetheless it still remains to be on the counterfactual level, since it cannot be fulfilled for some objective reasons, given the limited nature of means available to man. The first example can be a man in the dessert that given his thirst, desires water to extinguish his thirst as his most urgent factual end, which nonetheless does not imply that he can drink immediately. He may not find water and since his elimination of thirst is among actual plans and so in factual level of the scale, so happens that he exchanges diamond for camel to reach water more quickly. However, it does not mean that he will find water and eliminate thirst. The second example of the impact of means on ends can be the end of reaching some social status, which, however, will never be fulfilled given the limited access to the goods signaling a given social status. This is so not due to the fact that the person cannot prioritize the given end or that he would not want to, but due to the fact that he is not so skillful so as to obtain in his lifetime the goods, securing the end.

In the sketch we can also see two gray-colored fields. At the side of ends, an explicitly defined field of the concurrently perceived sum of factual ends is shown, in the context of which one is acting, and which are satisfied by a portion of the goods portfolio one owns. As we can see, the colored field at the side of means exceeds into the area of counterfactual ends. The reason is that the idea of a man in the time continuum also includes the awareness of the counterfactual ends. The fact that they are currently not preferred, does not mean that one ignores the given Σ Ends. On the contrary. The created Σ Means is in this way “ready” to satisfy the ends, which move into the factual Σ Ends according to the man’s decision and the currently perceived factual Σ Ends later in time. The man perceives himself in some time continuum. And it is exactly this expansion of Σ Means, which enables the person to better satisfy the perception of the changing current Σ Ends sometimes later in the future.

Thus, a man has some totally perceived ΣEnds → ΣMeans, which forms some form of “pool”, from which person chooses and just simply scales the currently perceived relationship – factual relationship – ΣEnds → ΣMeans against the counterfactual in the context of the perception of himself in some subjectively perceived time continuum. We do not have any other hierarchization of ends. We can imagine it in such a way that under some circumstances and the feeling of what Mises calls uneasiness, the person will perceive the current relationship ΣEnds → ΣMeans related to the satisfaction by food however it is affected also by a religious or cultural background of the given person (these factors enter the formulation of particular ΣEnds). This results in a specific mixture of goods (specific food), by which our man satisfies the complex of ends, meaning that, for example, he would demand that his food was kosher or he will not prefer the beef, so that it would suit the entire complex of ends. However, under different conditions, the religious perception is placed to the background and what prevails is the survival instinct (to which he subjects the ΣEnds). In case of such a radical change of the environment, such a part forming of ΣEnds, in the form of the religious or cultural background, will obviously not disappear, but It will be transferred to the counterfactual level and will not have any influence the factual side of the ends. Of course, even the extreme situation does not necessarily need to change the perception of ΣEnds, in the context of the religious or cultural perception of ends and one can still sacrifice one’s life (die of hunger) in the context of the end of his religious and cultural background.

It is not a specific and clearly hierarchized scale in the sense of ultimate ends vs. quasi-ends, as we see with Biľo. It is a created current scale of particular relationships ΣEnds → ΣMeans, which move from counterfactual to factual level and the other way depending on the kind of choice the person makes. From the point of view of the person, it is rather about different combinations of ends, which this person perceives and chooses from some pool of ends. Thus, it is not necessary to claim that some End is just a quasi-end (in Biľo’s interpretation it is Mean), which corresponds to the fulfilment of some ultimate end. The related Ends (say in the form of some complex business plan) are equally ΣEnds, while their mutual relationship is (flexibly) constructed already in the given and evaluated factual ΣEnds as some undertaken plan.

In some cases it can have a very specific and sometimes very vague form within the factual level of ΣEnds. An example of a vague ends can be the goal to live to the highest age possible. But a man does not know the place, time circumstances and his precise age related to the possible delay of death. He can, nonetheless, implicitly adjust ΣMeans, say, in the form of optimal diet, or physical exercise. Conversely, he can determine in some subjectively perceived time continuum a very specific ΣEnds, which can be related to, for example, a loss of weight to a target of 80 kilograms. At other time, he can indeed create some ΣEnds, which can fulfil the condition to be of an ultimate nature. For example, in a case of a life-threatening situation, when all of his action will be adjusted to this goal. Therefore, perhaps a best description of the scaling is a choice and formulation of a current scale as ΣEnds → ΣMeans relationships in the context of some perceived actual ΣEnds → ΣMeans relations and counterfactual ΣEnds, which do not necessarily have to have a defined corresponding ΣMeans (as we described in the illustration), on the basis of which one determines his current preferences in some subjectively perceived time continuum.

While the claim that the mind evaluates just a particular End-Mean relation and at the same time “competitive” End-Mean relations would imply, that mind would have to handle extreme number of different alternatives and connections between End-Mean given that an End can be theoretically satisfied in a N-number of ways through countless number of specific means. Suggested mathematical perception of ΣEnds → ΣMeans greatly simplifies the whole process. We can imagine it in the way that the total sum of what we mean by “being full” (or being satiated), can be currently satisfied by different combinations of sums of goods from very specific combinations (like this meat prepared in such a way satisfies my end of hunger this way or another), through different combinations (for example, kosher food is related to a combination of religious ends and ends of satisfying one’s hunger, meaning a sum of the value properties of the good of kosher food must correspond with a given sum of ends) up to very general ones (since I had eaten such a berry yesterday and I was no longer hungry after that, so I shall eat today this one, though looking different). The access to the problem through sums of Ends and Means allow us to change and perceive the ends-means causality very flexibly.

The ΣEnds → ΣMeans relation allows us at the same time to explain the evaluation and preferences of the economic goods in the time continuum. We need not to decide between these two statements:

  1. we prefer some specific good M at time t and we prefer from the praxeological point of view a completely different kind of good M at time t+1;


  • we prefer the good M at time t and then our preferences do not change against the time t+1, so we prefer the very same M; such identical valuation of M demands a validity of a Law of the diminishing marginal utility.

The explanation of how we realize the valuation in the time continuum is allowed specifically by a mathematical view of the causal ΣEnds → ΣMeans relationship. We do not need to claim that M is later in time different in value given that with the change of the economic context there is necessarily a change of the placement on our preferential scale of the End, which was satisfied by M. ΣMeans relativizes the placement of M, and thus allows to explain the preference of goods in the time continuum, because the specific M is a part of the ΣMeans. It means it is in a relative position towards other goods. In other words, since the particular End and particular Mean are a part of some perceived sums, their particular evaluation changes of course. But the change of the particular valuation of End and the preference of some particular good is, however, irrelevant since one looks at the given problem in terms of total factual and counterfactual value perception of ΣEnds → ΣMeans, which he applies over time. In principle, there is no change in the valuation and preference of the particular end and mean (good) per se. What changes is the preference perception of the given good within the overall preference of the entire portfolio of goods. This way the Law of the diminishing marginal utility remains valid, since we do not apply it on the one particular good, but rather on the marginal change of the sum of goods. Thereby claims by Mises and Rothbard that in the time continuum the valuation and attribution of value must necessarily change, are valid and at the same time the Law of the diminishing marginal utility is valid as well. The valuation and preferences are indeed changing, but the comparison cam be made given that it is a marginal change of valuation of two sums of ends and marginal change of preference of sum of goods over time[37].

This approach also enables to combine the identified “equation problem” between the valuation of ends and means by Mises and Rothbard through the derivation approach, i.e. the derivation of value. Since it is a mathematical relation, Mises’s approach is consistent in the context of the equation and so is applicable the Rothbard’s approach of the derivation of value. In our interpretation it is a connected relationship implying the feasibility of equation as well as the derivation of value. We can, therefore, explain how valuation is transformed into the preference of goods, i.e. the concept of sum of valuation is transformed into the concept of sum of preferences of goods; the same concept is applied on “different worlds” – normative (human one) and objective reality. 

However, the relationship implies the necessity of some alteration of the perception of valuation of goods (value imputation). Valuation of goods is not realized in the context of the transferring of the valuation of the end per se on the good per se. It is realized in the context of the sum of satisfaction of the perceived factual and counterfactual ends through the sum of goods, i.e. the portfolio human has. It follows from this, that one does not prefer moor goods over fewer goods of the same kind and quality. One prefers a higher rate of the satisfaction of ends to a lower rate of the satisfaction of ends. In this context one builds his portfolio of goods. The more a portfolio of goods is suitable to the satisfaction of factual and counterfactual ends, the more it will be preferred to another portfolio of goods. Adding or removing of a good to/from portfolio through one’s direct action[38] or exchange, or debt exchange over time (meaning building a new portfolio), is evaluated in the context of whether the old portfolio (build on one´s action, exchange, savings, heritage in the past) can satisfy the perceived needs more or less over time. This way it is possible to explain the action of an ordinary person, but also of people such as martyrs, hermits, or suicidal persons. Value imputation is thus mathematically transferred (through perceived sums or identical concepts) from a thought assessment of the given relations, i.e. from the assessment of ΣEnds to the reality, i.e. to the ΣMeans[39].

After these modifications the core of Biľo’s theory remains valid and we have eliminated our reservations to his theory. The suggested solution enables further to explain the economic calculation principle, first without money at the individual level, then at the level of exchange without money and finally at the level of exchange using money, with one principle following from another.

3.2 Economic calculation as an accounting standard of the other one

The necessity to explain the principle of calculation at the individual level and subsequently at the level of exchange – first non-monetary and only then monetary – stems from the fact that our predecessors somehow had to decide, what to produce and what to prefer to something else, while it is clear that they had not used money immediately and at the same time it had to be some kind of successful strategy. Otherwise none of us would be here today.

As Mises shows, the valuation can be realized only on the ordinal scale or ordinal basis. It is impossible to use cardinalist calculation of value. Cardinalist calculation is possible only once we can use objective inputs. For Mises the inputs were prices; and on top of that expressed in a single denominator – money.

Our solution introduces the solution of the problem a certain scope of the use of mathematics; it relativizes the mutual status of goods in the context of the perceived ΣEnds. This allows to explain preference of ΣMeans1 to a different ΣMeans2. A marginal addition or removal of a certain good to / from a portfolio of goods changes ΣMeans1 to ΣMeans2. The solution also enables one to prefer different portfolios over time; the person does not compare a specific good over time, which is subject to value change due to the changes in man’s preferences over time. The person compares the sums of goods – portfolios, which are mathematical concepts and which can be compared over time. This equally maintains the possibility of a comparison of potential changes of ΣEnds, which results from the changes in the economic context.

As we have shown the value stems from the assessment of ΣEnds, which are already in a causal and indivisible relationship to the ΣMeans. Human subject does not apriori prefer more goods of the same kind and quality to less. Human subject apriori prefers a higher degree of satisfaction of his ends over time. Only in case that a higher degree of satisfaction of ends is associated with a higher number of goods, he will also prefer more goods. However, if a higher degree of satisfaction of ends is associated with other combination of goods rather than the one with the highest number of them, he will prefer such alternative.

Already at this level it is possible to undertake the individual calculation, which has an ordinal principle and is expressed in the sum of diverse and changing goods in the context of the satisfaction of one’s ends over time. The subject finds himself in a state of higher satisfaction, if ΣMeans (portfolio) satisfies his ΣEnds in the time continuum in the context of subjective perceived anticipation of the ΣEnds à ΣMeans relationship and vice versa. He can, however, evaluate a marginal change of ΣMeans. That means that he can compare different strategies aimed at getting more or less preferred ΣMeans (different portfolios). His calculation “unit” can only be the entire ΣMeans (portfolio). It is obviously a very subjective calculation unit and a very complicated one. At this level, however, there should be clear difference between Mises’s approach and approach used here. The value relationship ΣEnds à ΣMeans enables us to realize a very basic calculation also on a completely individual level. This makes it possible to assess the success or failure of the activities of the individual. Of course, very “ordinarily” and in the context of expressing that I am / I am not successful at the satisfaction of my ΣEnds, however, through the changes of ΣMeans (portfolio of goods), i.e. I can assess that the addition of e.g. 13 apples to the portfolio is more satisfying for me than the addition of 1 apple (or vice versa) while the given calculation is realized in the context of other goods such as a bow, house, or some fur, which can protect me from cold and so on[40]. The fact that the calculation unit is the entire portfolio of goods is best realized when we imagine, for example, that another subject could prefer the addition of 2 apples to 13 in the context of other goods in the portfolio. It all depends on what ΣEnds the portfolio satisfies.

Calculation can only be realized in the context of factually perceived ΣEnds in the units of portfolio, i.e. ΣMeans. Obviously, the problem is the calculation in the context of counterfactually perceived ΣEnds because we do not know whether the planned change in ΣMeans will be useful later in time to satisfy today only the counterfactually perceived ΣEnds. This means that human subject can only estimate whether the goods acquired among the ΣMeans will have a different kind of use as the one, which is factually perceived in the context of factually perceived ΣEnds. This problem is not at all a trivial one. We will come back to it again and again, since it is one of the motivational factors of the creation of money and the monetary calculation. It is a monetary unit at the end of the day which allows full solution to this problem. Human subjects could have solve this problem at this level only by diversification of ΣMeans[41].

At the same time, a man has never lived alone. He always developed within a community. Even at this level, even if we presumed that there was not exchange between people, human subject would have at least the opportunity to compare ΣMeans (portfolio) of the other person to his own portfolio and imply, whether his neighbor is more successful than him and vice versa. Individual calculation is enriched in community by a comparison of different ΣMeans, i.e. other portfolios, however, still just in the context of very diverse personal accounting standards. The ΣMeans (portfolio) thus represents a fully subjective calculation unit of not interacting human subjects. This, however, already allows some comparison between at least two of them[42].

But let us move on and let go off the unrealistic presumption that people have not realized any exchanges. On the contrary, life in a community implies the exchange, i.e. the opportunity to satisfy ΣEnds by another one. Of course, prices of goods are created during the exchange. However, as we know, past prices are irrelevant. So, how do two human subjects calculate during the exchange, when the price becomes the past? Again, let us repeat that the human subjects do not prefer more goods in the exchange, they prefer a higher degree of satisfaction of their ends. The higher satisfaction could be done also indirectly by exchange. Thus, they exchange the goods in the context of satisfying the factually perceived ΣEnds and they perceive them in the context of the used and already owned ΣMeans (portfolio). We need to realize that the exchange is based on the indirect satisfaction of ends. That means I have to give up something to get something else, but in the context of what I have. And here comes the price-related information. The price of the exchanged good X for Y (from the other subject’s point of view it is the other way round) is not assessed against a past price (it may have never even been created because X never had to have been exchanged for Y before). The price informs the subject, how much one will have to give up to the other, compare how much he acquires, i.e. how acquired thing contributes to his ΣMeans (portfolio). Here, the human subject compares his ΣMeans minus the good X against the ΣMeans plus the good Y in the context of the factual ΣEnds. Thus, he always assesses, whether the new ΣMeans satisfies ΣEnds, however, while in the previous example he could have only compared ΣMeans of the other person to his own portfolio, during the exchange he uses a part of the portfolio of the other human subject expressed in Y to achieve a new and better satisfactory structure of his ΣMeans in the context of his ΣEnds, while he assumes for any reasons that he will be better off, i.e. he will be able to satisfy his factually perceived ΣEnds better this way. The price X/Y informs him at the given place and given time, whether it is worth getting rid of X and acquire Y in the context of the comparison of the portfolio before the exchange and after the exchange. Again let us repeat that the anticipation of the counterfactually perceived ΣEnds and its potential satisfaction is still very complicated, even if a bit simpler given that the exchange implies that a man could start to realize that the counterfactually perceived ΣEnds, in case it becomes factually perceived, can be satisfied through the exchange without having to anticipate through his portfolio ΣMeans all the possible eventualities associated with the counterfactually perceived ΣEnds. Already the exchange itself and the calculation in the exchange reduces the problem of the uncertainty in the time continuum.

As we can see, the human subjects start to uncover much more including their own preferences and their personal costs and revenues in the exchange. While in the first example the subject could “envy” the other one in terms of what ΣMeans he has and how can he satisfy the presumed ΣEnds, he did not know in principle, how the other human subject values the parts of his portfolio, what his subjectively perceived costs are and how he perceives his revenues. Note that the interpretation is still focused on the future. The other human subject reveals his costs in the exchange, however only in the context of what it means for him to give up Y for the acquired X. It is not, therefore, a particular calculation of the costs of the production of Y. It is a ratio of what in the context of his ΣMeans Y actually means, in order to satisfy his ΣEnds. He equally evaluates, what his revenue means for him, i.e. the acquiring of X in the context of his remaining ΣMeans, which he keeps after giving up Y. Thus, the human subjects no longer compare just their own portfolios as we have mentioned in the first example, they begin to interact economically. It is possible to refer here at the correct statement of Mises, that the subjects beginning during the exchange to objectivise their subjectively perceived state of things (see his quote in the beginning of this work), which as we have shown, however, leads Mises directly to money and he does not explain this in the environment without money[43].

The currently perceived price of the exchange allows the subjects to know the subjectively perceived scarcity of goods derived from the action of other one. And as the attentive reader surely notices, this is directed to the future. The potentially existing past prices of this X/Y exchange are not completely dis-interesting for the human subjects. Although it is true, that they are not crucial. The crucial thing is the current status. The past potential prices just inform us about the past state of things and about the fact that in case of some change in the context of the new ration, say 2X/3Y something has happened in the sense of the changed perception of the state of things by other members of the community.

As we have indicated above, it is only the debt exchange, or the existence of the obligation over time, or the existence of securing[44] of ΣEnds à ΣMeans by the community per se, which is in some prehistoric community much more likely than barter. As we have already shown, the obligation in time, which is expressed in some good M, allows a direct economic calculation. Its elimination by a debtor later in time, expressed in M, which the creditor demands, makes it possible to do several things. First, the debtor can identify, whether his economic activity focused on the clearing of the debt in M (the debtor must obtain M), causes a higher or lower satisfaction of ΣEnds after he received from the creditor some good at time t. He can identify this way, whether or not he is in a loss. Frist, he must clear the obligation in M. In case that he succeeds in time t+1, then what he has left as ΣMeans he can consider to be his profit/loss, which he evaluates in the context of ΣEnds. Second, in order for the debtor to be able to clear the obligation, he must either gradually create or exchange with others during the period t à t + 1 the good M, which the creditor demands at t+1. This way the prices arise in the given community expressed in M, and the debtor expresses his activity, which should ensure the clearing of the obligation to the creditor, in M. The agreed standard of the clearing of the obligation with the other person in M then does not cause anything else but the fact that the debtor can express in M a part of his activity leading to the clearing of his debt and equally he can express in M what he got from the creditor at time t, while at the time t+1 he can evaluate the correctness of his decision at time t. In other words, he can evaluate in M, whether what he got from the creditor at time t helped him satisfy his ΣEnds more or less. And at the same time the creditor can express, whether the clearing of the debt at time t+1 in the agreed M increases or decreases the satisfaction of his perceived ΣEnds. The common denominator of the calculation at least between two subjects has been established[45].

Let us get back again to our problem of the planning of the satisfaction of also counterfactually perceived ΣEnds. The debt exchange, which takes place over time acquires qualitatively completely new characteristics. The abstraction of the plan related to the securing of some ΣMeans later in time implies two states. Either that humans subjects do not presume the change of the factually perceived ΣEnds later in time, i.e. the debt exchange is realized in the context of the factually perceived ΣEnds, or they presume a change in the factually perceived ΣEnds in the context of counterfactually perceived ΣEnds, meaning the debt exchange is realized also in the context of the counterfactually perceived ΣEnds. Both of these states imply the idea of the human subject in the time continuum. And both states imply the solution to the same problem – the future securing of ΣEnds and a planned lowering of insecurity related to the future. While in the direct exchange at time t we can imply just potential thinking about the solution to the problem of the future securing of ΣEnds, in the case of debt exchange it is a planned state. The good M, which is used in the debt exchange gains liquidity in the context of this planned state.

The crucial question is, however, how M becomes the general denominator, and at the same time, how is it possible that we can compare prices of our economic activities (profit/loss) expressed in M at time “t” and “t+n” without claiming that M has a purchasing power on its own. We have to realize that we can compare the effectiveness of our activity over time expressed in M. However what is more crucial, we can explicitly compare the activities of multiple subjects with each other over time and expressed in M. And it is valid regardless of the fact that the costs and revenues have subjective character. And what is the most crucial we can compare with someone else, whether our subjective costs/expenses are higher/lower than someone else’s even over time. In other words, we are facing with the problem of explaining why we can value-invariantly calculate in one constant good M in time continuum. Please think about this once again. These are crucial problems connected with monetary calculation unit which seems to us as it has some kind of objective exchange value per se. 

And it is not at all responsible just to declare that the rest is left to competition of which good is the most suitable as M. This is not the case! In explaining the purchasing power of the good M, this method (let´s competition decide) is chosen by Menger, and subsequently by Mises-Rothbard, when they claim that M has become the most salable good in the economic community. This is, however, a very problematic claim.

In my other works, “Theory of intersubjectively perceived value of money” and “Why We Needn’t (Inevitable) Gold Standard But Free Banking System”, I have explained that the theory of the most salable good in the community necessarily leads to the petito principi error. The purchasing power of the most salable good, i.e. money cannot be explained based on the fact that it is most traded. Either the good is the most traded and is money already or it is not the most traded, and thus it is not money. And on the other side, I have explained that the problem of this logical circle needs to be solved by stepping out of it and “pulling out” the economic good money (i.e. M) to as if a separate layer of thinking, which is formed as human (intersubjective and not individual) abstraction of mind. At the same time, I have explained, that it is the fact that human mind has realized the existence of new end per se in the form of “how to satisfy one’s perceived ends indirectly over time” and solves this problem through an obligation, i.e. exchange over time, which becomes a mean on its own. The modus operandi of economic reality and human actions. The obligation is also expressed in M. The obligation in time becomes as it is an economic good per se. As an empirical fact the obligation needs to be created – produced like any other good and it is per se tradeable as well. I have equally shown, that the amount of M must be therefore entrepreneurially explored; based on the very fact that we express obligations in M. This is associated with the fact that the marginal unit of M mediates an additional debt exchange, thus correctly reflecting the interest rate as a separate value phenomenon. What the previous works allow to explain is the question, why we can even value-invariantly calculate in one constant good M. As an aid to the interpretation of this very context, I can use again an important note of Mises, where he faces this problem[46]:

Money is no yardstick of value, nor yet of price. Value is not indeed measured in money, nor is price. They merely consist in money. Money as an economic good is not of stable value as has been naively, but wrongly, assumed in using it as a “standard of deferred payments.” The exchange-relationship which obtains between money and goods is subjected to constant, if (as a rule) not too violent, fluctuations originating not only from the side of other economic goods, but also from the side of money.“ (emphasis added)

Although Mises is referring to the changes of so-called objective exchange value of money in the form of the changes of the number of monetary units, which stems from the context of his other works, he realizes that the purchasing power of money changes as well, and subsequently causes changes in the price levels, in the exchange of money for other goods. This means that money needs to be viewed from a twofold perspective. On the one hand, it is true that the price level expressed in M changes according to how human subjects change their value approach to the goods exchanged for money. On the other hand, it is equally true that it is very the change of the purchasing power of the good M, which causes changes of the price levels. That can only imply one thing. The choice of the good M from other goods and subsequent changes of the purchasing power of the money “good” must be described separately. Given that I have shown in the previous works, that through money we express the tradeable obligation in time, which is a good per se (the obligation as such is the good per se), through which we satisfy a separately perceived end of satisfying of other specific goods in time, we can realize:

  1. a separate description of economic processes, which affect the acquisition of the purchasing power of money separately;
  2. the choice of the good separately; and,
  3. separately we can describe even the economic processes related to the changes of its purchasing power.

It is a three-dimensional character of the problem. The calculation outside of the monetary economy was described as being the ratio of what I have to give up from my ΣMeans (without the good X) against how the new ΣMeans (with the added good Y) will satisfy my ΣEnds. In the monetary economy the good M must solve the identical problem, although at a different qualitative level – multidimensionally and in the time continuum. It is this that opens a problem we set and a question of why can we calculate in different times in M so that the given calculation makes sense to people. The division of the problem to three separate dimensions allows us to follow the level – the existence of the purchasing power on the horizontal axis, the second level – the mutual competition of the goods M and any other M´, on the second axis in space and the third dimension – the oscillation of the purchasing power on the vertical axis. Illustratively and simplistically we can outline the problem through Figure no. 2 (see below).

The figure shows a three-dimensional character of money. We have there the upper layer of the economic relations (cubes / rectangles) we express them through money. Under this layer there is a layer of economic goods (gray rectangle area), which is as if it is “controlled” by money; economic goods are moved and enter into the economic relations based on what happens in upper (money) layer. In the bottom (gray area) layer there is an exchange of goods (labor, consumer and capital goods) for money. Capital production structures are created based on this process. The bottom layer are all those goods that in the monetary economy have their value expressed in money, i.e. in the good M (under the commodity money-B one can imagine a different layer of goods, which is not drawn there for the sake of the clarity of the picture). The upper layer is thus also a price level of goods in the bottom layer. In the figure there is an illustration of the time continuum, in which all of the economic processes take place (cubes and rectangles are put together). The upper layer is a separate monetary layer, which is created over time and is created based on the debt exchange[47].

The X-axis shows the undertaken debt exchanges. Each area (of cube or rectangle) represent one debt exchange followed by consequent one. In their case the creditor demands in this context elimination of this exchange at time t+1 the good M. The debt exchange is thus expressed in the good M (our calculating standard).  It is also illustrated on the spatial axis – Z, the good B (there could be other competitive commodities illustrated as well), as a competitive monetary commodity, which has a different range of spread than M has. In the figure we see the good M has a narrower and more stable spread of the exchange (width of cubes is more similar). The exchanges expressed in the good B are illustrated with wider spread in the last debt exchange; as you can see the spread has changed – it has widened, e.g. due to the lack of the given good B, or due to the inappropriate physical-chemical qualities of B (durability, divisibility). It is possible to show this way that in the economic community people would prefer a more stable and narrower spread, which M has in comparison to B. So this will motivate agents to use M instead of B when they want to conclude another debt exchange agreement later in time. They have negative experience with using B from this point of view of suitability of B compare to M.

On the vertical axis subsequently success / failure of the debt exchange is illustrated. The success comes with the correct estimate of the success of given economic project, for which the money should be used, i.e. the money M were used on the purchase of goods in the bottom layer at time t, the combination of which produces new and productive goods at time t+1, which are successfully sold for money M. The debt exchange is successful and the purchasing power (per se) of the commodity M thus rises (we see it when we move from first cube to the second). All of this works also the other way. The changes are, thus, illustrated by the oscillation on the vertical axis, when it can be seen that the through the good M some exchanges did not work out and the M loses the purchasing power per se (from second to third cube), while on the other hand in the case of the good B the exchanges were more successful (cubes in money-B are drawn as more stable). The figure, therefore, shows that, from this point of view (!), the good B could seem to be more suitable than good M. The economic community must, hence, decide between some form of “trade-off” between the two goods, where one may have a wider spread or more stable purchasing power and the second has a more fluctuating purchasing power, but has a more stable spread of the given exchange (for example due to the fact that it is more flexible to use this commodity).

The above-described motivations of the sale of the debtor-produced goods within time period t à t+1 for M, or the obtaining of M by the creditor in time t+1, while at time t he got rid of the good X (which he gave to the debtor), are just motivations or consequences so that the M has a relatively higher liquidity than other goods. The reason (horizontal axis), why the M can be used over time, is elsewhere. It lays in the abstraction of the calculation of the obligation and obligation value invariability over time. It means that it is the obligation which will simply remain an obligation, i.e. the same abstraction at time t but also t+1, and so on. That is exactly why the subjects could start to perceive the problem of the debt exchange per se and they could, thus, create a new abstractive layer of the economic insight into the reality in some good, in which the obligation is expressed. And they are doing this together and in the very same way; and that is the reason why we perceive the value of money in the same way in time no matter that from time to time horizontal and vertical spreads could change. And this way is the competition among possible money-goods also by humans considered.

Figure. 2: Illustrative 3D displaying of purchasing power of money:

The reason (the spatial axis), why the subjects choose from the competition of goods M or any other M’ (or B) is again dependent on how well and appropriately the people can express the mutual obligations in M (or B), i.e. how they will perceive the width of the spread of the obligation expressed in M, while they value physical and chemical qualities of M. And the reason for the oscillation of the purchasing power (the vertical axis) is the success or the failure of the debt exchange in the time continuum, which is expressed in M. All three reasons affect the calculation in M and its use in the time continuum. Let us shed a bit more light on these reasons.

The fact that two subjects decide to eliminate the obligation at time t+1 in good M has the form of the expression of the given abstraction in M. The extent of the purchasing power (vertical axis), which is attributed to M, stems from the success / failure to fulfil or not fulfil the obligation. The fulfilment of the obligation means for the creditor that his ΣMeans will be enriched by the good M. For the debtor it means that he must within the period of time t à t+1 obtain the good M from someone else or he must directly produce / find it. It is, thus, the decision of the creditor (the horizontal axis) to add the good M to his portfolio (spatial axis), and the success of the debtor to fulfil the obligation (vertical axis) in exchange for the fact that at time t the creditor provided the good X, which enables over the time t à t+1 express the economic activity of the debtor in M, which is thus derived from the part of the subjective accounting standard of the creditor who demands M and when M becomes the accounting standard of the two human subjects.

In the context of the horizontal and spatial axis it does not matter, whether the activity of the debtor is successful. If it is not successful, the purchasing power of the good M as such “just” oscillates, because the creditor at time t provided the debtor with the good X, where the debtor did not provide M at time t+1, i.e. the creditor at time t+1 has neither X nor M, which could have served to satisfy his ΣEnds. However it is still possible to calculate. Even in such a case the creditor can quantify his loss in M and the debtor his relative economic “profit” and the relative legal “loss”. The creditor knows this based on the calculation of his loss of X expressed in M because M was not delivered in the context of his ΣMeans and the debtor based on the calculation of his economic “profit” in the form of X within his context of ΣMeans because he have not provided M. However, calculation of debtor has to include also the legal loss (following from the rules of the community enforcing the obligation) against the M which was not provided. In case of the fulfilment of the obligation the same happens from the calculation point of view, only with the difference that M increases its purchasing power as the debtor fulfilled his obligation, while he had to satisfy the ends of others within the period of t à t+1 (otherwise he would not obtain M for his economic activity) or he would have to find M (he would have to conduct some form of economic activity to obtain M).

Therefore, the answer to our question, how the economic calculation is possible in the unit of measure of some good (money) over time, is the following. The possibility of the economic calculation results from the fact that the human subjects infinitely (ad infinitum) solve the satisfaction of their ends in time indirectly, i.e. they use the obligation, a form of modus operandi, a recurring process, while they express it in M; we imply here the mutual agreement of at least two human subjects, that they express the given obligation in M. This is modus operandi of value time invariance of money. The value invariance of M is, therefore, dependent on the decision to enter into a debt exchange by two human subjects, while they jointly agree on the accounting standard (the horizontal and spatial axis). In this respect the economic calculation is possible over time. However, as we have said the purchasing power is also impacted by the fact that M is also linked with the economic process of “movement” of other economic goods (as if by the lower economic layer) and whose purchasing power is, thus, also completely dependent on the fact, whether the given debt exchanges and economic processes which they represent are economically successful or not. The influence of the spatial and vertical axis, therefore, impacts on the accuracy of the economic calculation in the good M over time.

The possibility and, consequently, the accuracy of the economic calculation is then dependent from how well the economic community can estimate the success of the indirect satisfaction of the ends in the time continuum. It is not at all a straightforward process, it is an entrepreneurial discovery; discovering of the market level of the interest rate in the economic community, the discovery of the time preferences of the members of the community, the discovery of the institutional system (financial and banking sector), the discovery of the just rules regulating business, which directly impact the economic processes surrounding money. This is naturally associated with errors and the attempts for their elimination and/or political interference into this specialized market process. This is not at all about, whether one community uses coconuts to express the given relationship and the other one uses gold. It is about the given modus operandi and the surrounding system. If it exists, then so does the comparativeness of the economic calculations of different groups of population, while the exchange rate emerges between the goods used as money. The comparison of the economic calculation over time is equally dependent on, whether the given modus operandi from time t is maintained at the following t+1, the following t+2 and the following t+n. Once it is, we are dealing with the very same concept in time and then it is only about the arithmetic of the whole process which enables one to calculate over time. Even when there are improvements or, vice versa, deteriorations of the tools of the financial system. The comparability is available because of the same modus operandi behind.

The convergence of the subjects to a single M is then associated with a single factor (this concerns the spatial axis of the problem). The spread. Dealing with this factor is all about the specialization and the division of labor. Just as it is in the case of any other goods. In the case of M, which can be anything in the beginning (from apple, to a house), it is just the width of the spread of the given exchange which motivate human subjects (entrepreneurs in the area in question) to narrow it. While the width of spread associated with, say, apples can face the problem of storage of apples between time t à t+1 and in case the problem is the indivisibility of the good, or non-mobility, the given spread is narrowed and people naturally converge to some good, which is from their viewpoint best one to use it (narrows the spread). Subsequent awareness of the exchange over time in the form of its components – time preference, interest, principal, legal circumstances of the debt – also have an impact on the effort to discover the narrowest spread of the given exchange and the most suitable good, through which the given problem can be solved.

The more the process of the discovering of realization of a marginal debt exchange, i.e. an indirect form of the satisfaction of ends over time, is successful, the M has a more stable purchasing power and allows a more accurate calculation. With the accuracy of calculation we need to remember, that human subjects can inter-subjectively compare their different perception of costs and revenues (perceived completely subjectively). At that point they begin to use an identical accounting standard – money. The interesting thing is that the given area is not a separate area from the economic community. Quite on the contrary, it is intrinsically bound to it. It is actually as if the top economic layer, which “moves” – in terms of value and physically – the lower one composed of other goods.

As we can see, even in the monetary economy, it still holds that we consider ΣEnds, which we solve through ΣMeans, while we prefer that ΣMeans, which better satisfy ΣEnds. We have not dispensed our ordinal value insight through money. That is, why it is still valid that the costs and revenues have subjective character. However, the changes brought through the discovery of money have twofold character. First, through money we can better react to subjective factually and counterfactually perceived ΣEnds of each individual, given that through money as good we can satisfy in principle any factually as well as counterfactually perceived real ΣEnds, thanks to the reason that money becomes a very important liquid asset, within the individual portfolio, i.e. ΣMeans. Second, it is also possible to compare subjective costs and subjective revenues. In this respect the monetary-price perception of the world is a tool of humanity, how to communicate mutually our subjective economic ideas about the world in the context of others. This is reason for illustration this as a separate layer of the perception of the economic reality (in the Figure no. 2,). This is exactly what brings the qualitative change in the process of satisfying the perceived, whether factual or counterfactual, ΣEnds, given the possibility of much more specialization of various activities of different people, the growth of production structures, and thus expanding the portfolios of ΣMeans of different people, so that the satisfaction of the ΣEnds, whether at the individual level or the level of the entire community, increased.

Thus, it is a tool formed by the two sides of the same coin – money and prices of goods expressed in money (in the Figure no. 2 this relationship is indicated by arrows connecting the level of goods, to which people attribute so-called use value, and the monetary level expressed in form of the goods M or B, to which people attribute only a so-called exchange value). The humanity further continues to refine this tool (and will continue to refine it). On one hand, there are specific activities – banking activities, through which we discover the purchasing power of our money (vertical axis in the Figure no. 2, which can be realized at the individual level, but also by the specialized entrepreneurs in the banking sectors[48]). And on the other hand, there are tools for the discovery of the correct reflection of value preferences of people in the form of the institutions focused on the discovery of the market prices of goods, for example stock exchanges, markets (these are institutions, which specialize on the discovery of prices of goods in money-good; in the Figure no. 2, this is the area of arrows connecting the upper level of money with the level of goods). It is already at this point that the reader might feel that our interpretation is fully in line with what Hayek wrote in 1945, albeit from a different perspective and that in the case of economic calculation the so-called knowledge problem is neither vicarious, nor secondary problem.

The difference between Mises’s line of reasoning and the argumentation presented here should be obvious also from the point of view of his claims about the distinction of the calculation in simple and complicated production structures. The Mises’s interpretation of the problem of the economic calculation “pushes” him to claims that the economic calculation is not so problematic at the level of the consumer goods, as is at the level of the more complicated production structures. It is in these cases that we inevitably need money in his opinion. It is quite a complicated assumption, because it implies three questions. Does this mean that money is a precondition for the complicated production structures? Which production structures are still simple, for which we do not need money, and which are already complicated, and thus can come from money and monetary calculations? Then how did money come about as the most saleable good, when according to Mises we first need money and then we can expand the production structures, which are, however, a precondition for having something to trade and find out, which good is the most sealable one?

The line of reasoning presented here is of different nature. The expansion of the production structures is a process preceding the creation of money. First there is a change of time preferences of human subjects related to the existence of the obligation. Human subjects entering to the debt exchange in time calculate even without money. As we have shown they are able assess their costs against their earnings already on this level. What is, however, more important, they spontaneously discover the possibility of the debt exchange over time. The exchange of X for Y in different times (interest implicitly included) creates an environment for wider production structures. Connected problems motivates human subjects to seek the solution of the problem of this exchange; money. The tool, which of course enables further to develop the more effective planning in the production of goods, given that people know better, through the calculation in money, to reveal their preferences (they have an evaluation tool which show them if they are successful in satisfying the other one) and at the same time they are able better to compare the mutually realized production processes.

Let us stop, finally, at the claim that through money people reveal their mutual preferences. It is again a simplifying element of the human understanding of the economic system, and thus the given element is spreading among people. In the barter exchange human subjects reveal, what they demand from the other in exchange for what they offer and vice versa. The use of money sort of “packages” this process into a new form and simplify it significantly. While previously the members of some community know that the person X wants apples for pears, a spade for pears, or wood for pears, then after the discovery of money, the person X wants money for pears. In principle on one hand he covers all his preferences in the time continuum into one good, through which he communicates his preferences. As we can see, this does not mean that he was not calculating previously or that he did not produce anything. It means that he transfers the problem to a different level of understanding. And according to Hayek, that is exactly, how our brain works[49].

3.3 Historical context of the evolution of money and economic calculation

We are, thus, left with the last problem awaiting us, to show the connection of the theory on other, rather empirical research projects conducted in the area of the creation of money. Empirical research projects of the today’s primitive communities indicate various problems in the context of the economic calculation. For example, they show that the members of the primitive communities can count only to 2 or 5 and everything else is just “more”. These research projects also imply that it could have been very similar in the past as well. Can / could such people even calculate? What lies behind the pre-historical discoveries of so-called tally sticks, which in turn imply some form of (economic?) records of our predecessors? And even when we look into the economic system of recent or still existing, so-called primitive communities, we see that even these communities use a variety of kinds of goods in the context of what the modern society calls money. How do these empirical facts fall into our theory?

Of course, the objective of this paper is not to assess and answer all the questions related to the evolution of money. The ambition of this paper is rather to link (and even that only to a certain extent) the empirical research in this area with the presented calculation theory. We pose here a question, how our predecessors likely calculated? And how they discovered the concept of calculation and the concept of money?

In the answers to these questions, let us have the following structure. First let us introduce, what theories of the creation of money are being considered, let us look at, what ideas the Austrian school of economics has about the creation of money, given that in its context I present this work, then we try to link the presented theory to some existing theory of the money creation and, finally, let us try to evolutionarily reconstruct the problem of the economic calculation and the common denominator – money.

In his book Primitive Money: In its Ethnological, Historical and Economic Aspects[50], Paul Einzig identifies the following 10 theories of the creation of money[51]: 1. Theory of the origin of money as a medium of exchange, 2. Theory of the origin of money through external trade, 3. Theory of the origin of money though the internal trade, 4. Theory of the origin of money as the standard of value, 5. Theory of the origin of money as the store of value, 6. Theory of the origin of money as the standard of the deferred payments, 7. Theory of the origin of money based on the ornamental and ceremonial functions, 8. Theory of the origin of money based on the religion, 9. Theory of the origin of money based on the political decision and 10. Theory of the origin of money based on the settlement of the marital relations.

Einzig explains that money was not invented out of the blue and did not start to be used all over the world after their discovery. Multiple times such institution of money was copied from other communities, multiple times the communities solved this question through their very specific and particular way and simplistically without knowing that other community solves the given problem in a similar or completely different manner. This really suggests a spontaneous and uncoordinated creation of the institution of money. Which of the above-mentioned theories is the correct one cannot be determined according to Einzig.

From the point of view of the Austrian theory, which is greatly influenced in this question by the works of Mises, which follows Menger, only one theory is considered to be the right one. In the context of Einzig’s classification it is the theory no. 1, i.e. the theory of money as the medium of exchange. The theory is founded on the premise of so-called marketability, i.e. the biggest salability of some chosen good. Menger’s theory is based on the description of barter, in which the market generates goods, which given their characteristics are more salable than any other goods, which directs the market gradually to the situation, that it chooses the most traded commodity to become money. Mises chooses it for the following reasons:

„If the objective exchange value of money must always be linked with a pre-existing market exchange ratio between money and other economic goods (since otherwise individuals would not be in a position to estimate the value of the money), it follows that an object cannot be used as money unless, at the moment when its use as money begins, it already possesses an objective exchange value based on some other use. This provides both a refutation of those theories which derive the origin of money from a general agreement to impute fictitious value to things intrinsically valueless and a confirmation of Menger’s hypothesis concerning the origin of the use of money. This link with a pre-existing exchange value is necessary not only for commodity money, but equally for credit money and fiat money. No fiat money could ever come into existence if it did not satisfy this condition.[52]

The problem with this theory is not the theory on its own, but rather its interpretation by Mises. I have shown this already in multiple works[53]. And in principle it concern the fact that Mises claims that people have attributed to the money-good at time, when the money-good should have been created, both so-called use value and also exchange value at the same time, which is illogical. The subjects use money only in the context of the exchange value. Mises, thus, has to come to the claim that some most salable good has exchange value per se, which means that he uses objectivism to explain the exchange value of the good in question, which is not in line with the subjective value theory. It is, thus, not surprising that Mises is able to claim in the citation above „that an object cannot be used as money unless, at the moment when its use as money begins, it already possesses an objective exchange value based on some other use.“ It is in this statement that we can see that he attributes value to the good per se and he does not derive it from human action or valuation.

The theory of economic calculation presented here, which also relates to my theories of the creation of money, has very reason to fall into the category of what Mises calls the so-called catallactic theories[54],[55]. In the sense of the work by Einzig it is probably most similar to the Theory no. 6. The theory of the origin of money as the standard of deferred payments. Einzig describes that the probability of the existence of debt in the primitive societies is certainly strong and likely to be higher than the existence of barter and concept of debt should precede any medium of exchange. However, the empirical studies suggest that the chronological character may not have been in some communities the same as is suggested by this theory, i.e. debt à barter à means of exchange, but rather just the opposite, meaning that the given means of exchange started to be used for the clearing of the debt, which undermines the general validity of the theory. Theories of the creation of money on the basis of debt are nothing new. In his book The Money and Credit Mises subjects these theories to criticism. Rightfully so. Theory of the money creation based on the deferred payments is focused on the explanation of the purchasing power of currency (we use currencies today as money) and not commodity money and describes rather the functioning of the banking system, which is in my opinion only a superstructure above money (commodity). The theory of the deferred payments claims that money has the form of the debt, or that they are the debt by themselves. These theories considered money as general claims for or records of debt which the society has against the current owner of money. This theory, however, does not explain the creation of commodity money, i.e. the final eliminator of the debt. Our presented theory, however, can be linked to the Theory of the origin of money as the standard of deferred payments (Einzig’s theory), or on the so-called Banking school (Mises’s terminology). For this, however, we need to slightly change the context and to show the possibility of the emergence of the commodity money even within the theory of the purchasing power based on debt.

Construction of the theory of the evolution of money and economic calculation

In the context of the theory of the standard of the deferred payments, or the so-called Banking school, the money is considered to be debt. The commodity money are not debt! Its purchasing power, however, stems from the mediation of the exchange over time, meaning in the expression of the debt (abstraction) in the commodity. The debt and the commodity money are separate phenomena. Acceptance of obligation and its elimination (elimination of debt) can be realized even without the commodity money. This modification or the realization of this fact allows the explanation of how some commodity acquired a purchasing power and becomes money. The exchange over time, the obligation, is perceived mean (good) per se. Two or more human subjects react through obligation to the newly created abstract End to satisfy needs of human subjects indirectly in the time continuum in general. It is, therefore, a new thought layer or construct related to the abstraction of mind in the form of planning of the future, which becomes an End per se[56], which is satisfied through the obligation expressed in money (some commodity). This way it is possible to explain, on one hand, the creation of the commodity money and at the same time also a further evolution of this abstraction in the form of the banking sector (as another relationship layer)[57], which is subsequently a subject matter of the theories of the so-called Banking school.

In addition, from the perspective of the problem of the economic calculation and money we must focus on the numerosity of the problem itself. The number and calculation are equally complicated abstractions. Money is not the same abstraction as the number. It is a real good, which we own and which we prefer just as other goods. It is, however, a good, which obtains purchasing power based on what the person tries to do, and as a separate problem, whether he ensures his own ƩEnds in the time continuum, directly or indirectly. That means that its purchasing power is related with the abstraction of the emergence of numbers and mathematics. We have in front of us two abstractions, which had to gradually develop in the minds of our predecessors[58].

Within the presented theory it needs to be noted, that the main role to explain the phenomenon in question is “played” by time, or the perception of the obligation over time, which causes that the mind approaches the given problem through the abstraction of the mind. Of course, the abstraction of mind implies the conscious behavior of human subjects. However, assuming the existence of identically conscious mind of the pre-historic and today’s person is a not very realistic assumption. The mind of our pre-historic predecessors could from the today’s perspective more resemble a mind of today’s children. There are some “signs” of awareness, however, much of the activity goes on somewhere in the background. The creation of money needs to be sought, therefore, somewhere in the lower form of awareness and spontaneously emerging rules of the community. But can this be combined? Can it be explained, how from the vaguely aware activity of the prehistoric man emerges some thought abstraction, which is present in every human being?

For the sake of clarity, we must link the presented theory explaining the gradual and evolutionary creation of these abstractions, by which we overcome not fully aware and just very specific perception of reality by our predecessors. This is where we can use Hayek-Pavlík’s theory of mind, within which simplifying mental models of the interpretation of the surrounding reality (a concrete state of affairs) are created. In the case these meet their limits, they generate new mental ties, which cause again more abstract and again slightly simplified perception of the surrounding reality (the concrete state of affairs becomes the new abstraction, which becomes consequently a new concrete state of affairs; and the process continues onward). And using the Hayek-Pavík’s perception of the spontaneous creation of catallactic rules when the theory of the spontaneous order and cultural evolution needs to be applied first on the so-called norms of the distributive justice, which while “blindly” (supported by, say, religion) lead human subjects to live within the prehistoric community, while in the background of these undertaken activities the sediments of the catallactic rules are being formed. The theory states that catallactic rules are grasped by human subjects only after human subjects reach a higher level of self-awareness[59].

What we can say with some certainty about the first mathematical calculations it follows that they existed already by 5000 B.C. and they were used in the context of the records about the payments in the standardized rate of wheat – commodity money of Sumerians. Everything before is just our guesswork, based on either excavations or our explorations of the linguistic-mathematical structures of the populations of different tribes who previously had not had an explicit contact with our civilization. The oldest potential sings of counting or records of something, date somewhere to 32 thousand B.C. and it is most probably the oldest record of the so-called tally stick[60]. Tally sticks were used for the record of the trading activity (record of debt) in principle until recently (19th – 20th century). Were tally sticks, then, the first records about some form of trade, debt, obligations in some prehistoric communities long before money was created? We do not know. We can just assume that this is a relevant record, which we can imply from the fact that tally sticks were used for this purpose later and from the fact that the precision of the record suggests that some effort had to be undertaken for the given records, so it is not just a case of some random creation of lines into some stick.

A realistic assumption is that if our predecessor realized the given records, then the level of abstraction was low, i.e. this was rather a specific description of the state of things. Only then could the given specific description of the state of things become higher level of abstraction[61]. As a subsequent argument we can support this idea from the fact that even the mathematical grasping of the reality developed gradually[62] from the specific records à through the grouping of the records into larger units (collection principle) à subsequent addition of the summation (the adding composition principle) à the creation of the base principle of numbers (base-2, base-4, base-5, base-10, base-60 system) [63] à recursion principle (application of the identical rules of the result of the mathematical operation) à or finally the principle of the numerical place and value (this way the concept of zero was created) [64]. These stages of the mathematical perceptions of the reality are nothing else just a principle of changing particular state of affairs into the higher abstraction, when the mind of the person changes a specific perception of reality to a higher form of abstraction.

The same assumption can be realized in relation to our problem of calculation as the accounting calculation principle of the other one in the exchange over time. As we have shown, the economic obligation over time allows the human subject (debtor) to express in some good, through which he can clear his obligation towards the other one (creditor), calculate his activity and evaluate the suitability / unsuitability of the satisfaction of his ends over time directly or indirectly. While from the beginning of the use of this institute this probably involved different kinds of very specific goods, with the more frequent use of the institute of obligation human subjects tried to solve potential problems associated with the fact that the given obligation even passed in time. In fact they tried to lower the uncertainty that if they chose an unsuitable economic good for the clearing of the debt, which unnecessarily expanded the spread of the obligation over time, they were unsuccessful. Therefore, they moved from these diverse goods to those they evaluated from the perspective of their (objective) physical qualities that made it possible to better respond to the problems that emerged – whether in terms of their storage, durability, divisibility or salability, or even from the perspective the religious rituals, communal coexistence, traditions, or political or societal rules and norms, which the given community (blindly) followed and through which it enforced the given obligation (as a separate concept). It is the very activities of human subjects and their life in the community, which imply that it is not necessary to presume the identical conscious humans as we see today. On the contrary, multiple human activities could have been intuitive, or guided by the rules of the cultural evolution. However, in the background of given activities, sediments of thinking about these concepts arose, having gradually emerged through the spontaneous discovery by emerging language. Thus, the mutual and spontaneous economic interaction taking place over time, having various combinations of specific forms, led us to the perception of money- more abstract phenomenon.

While the Menger / Mises’s version of the description of money chooses one theory, the theory presented here is in my opinion in principle applicable to all the theories presented by Einzig at once. The theories in question describe only the empirical variants of above mention problems and solutions of communities leading them to the emergence of money. And to leave out one of them would mean to ignore some of the motivations. The reason, why here presented theory can be applied across the other theories is the fact that it explains the creation of money as a reaction of Ego on the emerging abstraction, a new problem, i.e. the solution to the problem of indirect satisfaction of ends of the people mutually and over time, which people gradually recognized as a separate problem per se at the background of their spontaneous activities within communities ruled by spontaneously developed rules. The main roles play here: a) the problem of time, b) the problem of changing preferences over time and c) the life within a community. These problems had to be gradually processed by an emerging mind of humans, as they emerged step by step on the background of the (spontaneous) activities of human subjects within that communities. And particularly this has created a new layer of thought and new way of grasping of economic reality, which is solved by money and later through the institute of banking system.

What does this mean in other words? It means that the emerging abstraction of the mind is applicable to each of the presented theories as they describe more the empirical context of how the given abstraction manifested in the economic reality. This means that even the political theory is valid[65], it is a subset of events, when the moneyness in the community was ensured through the decision of the local rulers. What about the theory of the most salable good? Mises and Menger cannot explain through this theory the universality of the objective exchange value of money or even, how the calculation monetary standard was created, which, however, does not mean, that human subjects would not use the most salable commodity for the clearing of the obligations, or that over time they would not attribute to the surpluses of the commodity even the exchange value. Nor it is any surprise, when Einzig claims, that in some documented cases, abstract and ideal units of measure have been used in the context of the origin of money as a standard of value, which had no concrete representation in reality, and thus could not be used as the medium of exchange[66]. Why would the ornamental, ceremonial, religious, or the marriage-related circumstances in the prehistoric communities be separated from the development of the given abstraction and equally with the change and the development in the internal and external trade among communities? The fact that people have responded to the abstract nature of thought, which appears in their mind first vaguely and subsequently as an explicit problem, through money, explains why each of the presented theories bears its part of rationality and allows us to state that in the context of our theory all of them are in principle valid. They focus on the empirical diversity of the reaction of Ego on the common nature of thinking of humanity. While Einzig claims that none of the aforementioned theories can be unambiguously determined as the valid one, our line of argument shows that, on the contrary, each of the mentioned theories presents certain empirical realities that have led the mankind to money and it is possible to claim that all of them are valid.

4. The problem of the impossibility of socialism and the problem of economic efficiency

The problem of the absolute impossibility of socialism based on the argument of the impossibility of the economic calculation must be, based on our line of reasoning, rejected. This does not mean that socialism is the correct social system. It means that it is not possible decide about the correctness / incorrectness of the given system through the economic calculation argument. In order to do this, we need to use a different apparatus of arguments. As we shall see, socialism has an inherent component of economic coercion from the very definition of its nature. And that is the argument, based on which it can be rejected.

As we have shown, the non-monetary economic calculation is the adopted accounting standard of the other one (creditor). It is not dependent upon the knowledge of past prices and their expression in money. It is dependent on the degree of mutual “adoption”, or as if a natural penetration of the individual and subjective accounting standards of members of the economic community. In the context of the subjective value the costs and revenues are completely subjective. However, this does not mean that they are not comparable through the economic calculation, as the accounting standard of the other one. As we have shown, the economic calculation enables numerous possibilities of a mutual comparison of subjectively perceived costs and revenues in the context of the perceived ƩEnds and the used ƩMeans. Even without the exchange subjects can at least imply, whether some ƩMeans could satisfy their ƩEnds better or worse. In the case of barter exchange they can evaluate the marginal acquisition of some good X and at the same time a marginal loss of their own good Y in the context of their overall perception of ƩMeans, which should satisfy their ƩEnds. Even at this level they can compare the extent of what they have to give up against what they gain and they can equally estimate what is preferred by the other one and what the human has to give up. They reveal the mutual subjective perception of their costs and revenues to others. The discovery and the use of the common denominator of exchange through the indirect satisfaction of the mutual ends over time has led into the situation, when they collectively calculate within a certain unit of some good, which subsequently spreads within the community given the lowering of spread of the debt exchange. Human subjects can mutually compare their costs and revenues this way to the extent that they commonly use the common denominator of the economic calculation. This does not mean that the costs and revenues are objective. They remain subjective in the context of ƩEnds, which the ƩMeans should satisfy. What is objectified (or more precisely, inter-subjectivised) is the possibility of comparing the effectiveness of their economic activities. Nor does this mean that at some specific case of some economic activity, which is completely different from others we can say that the subject X does something wrong. We can only say that he conducts his economic activity differently to someone else. The economic efficiency is inevitably a relative term. There is no possibility of its objectification. Its inter-subjectification is dependent always on what other people set as their economic benchmark. In the specific case it means for example that if the subject X spends a lot of time on the social networks, we cannot say about him that he is not efficient per se. He has a subjective perception of costs and revenues. The only thing we can tell about his activity is that there is also a subject Y who, for example, works more and has a different kind of preferences and different kind of perception of his economic costs and revenues. And this is what we can compare. Money (and the prices of economic activities) allow us relatively well[67] to compare the costs and revenues of X and Y in some common unit of measure. We can for example say that the X must give up his hourly wage in favor of spending more time on the social networks, while Y obtains some hourly wage. It equally does not mean that the opportunity costs of X are worse than of Y or vice versa. The only thing this means is that we can compare something. And comparison is important.

The view radically changes in case that the X contractually commits himself to work for Y. He voluntarily adopts the standard of Y. Based on this we can evaluate the economic activities of X, for example in the context of his comparison with the other employees of Y, or for example in comparison with the employees of another company belonging to the subject Z, whose goal is to achieve profit just as the Y who has the same goal of achieving profit. If then somebody spend his time on social networks instead of working, we are able consequently state that he/she is inefficient despite he/she has subjective cost/revenue perception. It is the benchmark which change the point of view. The economic evaluation of the activities is, therefore, always relative; it is always in the context of some goal. And goal may or may not be widespread in the economic community.

This implies a rather simple conclusion in the context of socialism. Socialism is possible. As we see it is all about relative assessment of economic possibilities and successes and what it brings to members of the economic community. Any form of socialism implies that the accounting calculation standard is determined differently than by market discovery. That means that some economic activity that affects the determination of the given accounting standards is determined either by some individuals or on the basis of a different kind of decision (for example by Politburo). It is therefore based on different method compare to the discovery of the common accounting standard on the market. From a socio-economic perspective, this is actually a question of the rate of voluntary acceptance and discovery of calculation / accounting standard vs. the rate of politically given standard.

At the level of family, company, private club, but also a small primitive community, or kibbutz, it is a common and “voluntarily” accepted accounting standard given by someone in “power”[68]. However, even within these institutions it is determined in different ways. While at the level of the family and in some communities the key role can be played by the father for example, however in others it can be the key role of mother (ΣEnds is determined by them). The standard can be equally influenced by very different cultural-societal backgrounds. It is similar from the perspective of the company. While some companies are in the hands of the individual “despotic” owners, which decide everything, then for example in the case of the joint stock companies, the company (as entity) has created separate – democratic – voting rights about what standard will be enforced; whether the company shall try to achieve for example a complete profit maximization, or it will be in this context also environmentally friendly context of standard, because consumers demand it (maybe even for some strange reasons), etc..

However, the degree of voluntariness is quite different in the political organizational units. Political organizational units different to capitalism are not infeasible in principle from the economic point of view. It is about to what extent the common, politically determined, accounting standard is accepted in the given community and what other mechanisms the given community perform to make the common standard (at least partly) accepted. If we use Hoppe’s division of the socialist societies[69] and add various despotic tyrannies or idealistic versions of socialism, then these differ in principle only in what kind of mechanisms the societies create in the context of how the political “elites” [70] decide, meaning what political accounting standard is enforced in the community. By the politically determined accounting standard I mean what part of the economic activity is left to the decision of the political elites. The extent of the given political decision can obviously change from some form of the mini-city states, through minimal state all the way to the despotic tyrannies. Neither of these options means that the economic calculation is impossible within them. It means just that it is determined by something specific and for a specific purpose rather than being discovered in the market. These communities approach the determination of the economic standard in different ways – beginning with a direct despotic determination, i.e. someone literally makes up and plucks out of thin air the prices of goods, because he can and has the power to do it, through the effort to simulate the market mechanisms (e.g. Taylor – Lange), the copying of the market prices, decide about the “most clever ones“ decision makers or only suitable representatives through the democratic processes all the way to some forms of social engineering[71]. None of this means that the socialism is impossible. The tyrant does not care, actually. He enforces his vision, which he imposes on others and if others do not identify with his vision, he uses his political power or some other methods. This power is sometimes despotic and sometimes more moderate, sometimes it is even acceptable for the community, as we can see today in the examples of the social-democratic and partially market based political regimes[72].

The problem we face from the perspective of the economic calculation is that the economic efficiency is a relative term. From the view of the theory of subjective value it is not primarily about preferring more goods to fewer goods of the same kind and quality. It is about the preference of a higher degree of satisfaction of Ends. At the same time humanity has created mechanisms, which allow the comparison of the mutual effectiveness of its members. However, there are, by definition, no objective goals, or an objective evaluation tools of what is economically more effective or not. The costs and revenues are by definition subjective. Thus, from the perspective of the economic efficiency we live in the economic relativism. There is no other option, our preferences are subjective. However, humans cannot live based on relativism. It is therefore the very reason they develop tools (money, calculation as common standard, catallactic rules, language, etc.) which help them to eliminate relativism and to find out what the most suitable state of affairs for them (as individuals living within the society) is[73].

To reject socialism is possible only from other perspective. From the perspective of the universal validity of societal norms. Those, on the other hand, allow us to define generally valid rules for the functioning of the society. These rules are and will be evolutionarily discovered in very continuity. Some of them we have already as humanity discovered, others still only await as the challenges of the era that still awaits us. Already discovered include, for example, the protection of the private property and personal freedoms of the individual. These are moral and intersubjectively valid ethical maxims, whose importance, definition of their boundaries and their content are continuously refined and which should be firmly enshrined in the legal framework. They create a universally valid benchmark, which unlike the economic efficiency, is intersubjectively fully valid. Only within this framework it is possible to apply subjective preferences of people, meaning to apply mutually and at the same time subjective preferences with respect to each other.

This implies that it depends on the extent of the imposition vs. voluntary acceptance of the societal accounting standard (economic calculation of the other one) on the remaining human subjects, from which follows the assessment of the economic ineffectiveness. While in the family, a private club, or a small community, or within the so called ideal of free market the acceptance of the given standard can be fully voluntary, and thus included among the intersubjective preferences of all members of the given community, and thus subjectively effective, in the political organization, within which the given voluntary acceptance cannot be assumed[74], the imposition of the standard of the other one is inevitably enforced through power or there are used other more or less suitable instruments (democracy, social engineering, etc.), compare to completely free market system. It follows that we can then state that socialist economic behavior is economically less effective. The member of the socialist community must accept it. In the given socialist community there must be suboptimal economic processes; i.e. there are no optimal prices, profits, costs or even the economic calculation. In this case any attempts to determine and solve a problem of economic calculation must, by definition, face the inaccuracy of its determination. But not impossibility. We can state that such prices and calculation is ineffective from the perspective of all of the agents. None of this, however, implies that a central planner cannot impose his idea of an accounting standard on the whole society. He can do it through the coercion and power. And in principle he does not care that he is wrong and uses the resources ineffectively[75].

Thus, the denial of socialism is only possible in the context of the intersubjectivised societal maxims, i.e. in the form of the societal rules, which in turn enable people to fully express their subjective preferences with respect to each other at the same time. The economic calculation on its own is, however, a knowledge problem. It is the question of the effectiveness of the economic calculation and usability of scarce resources that is a so-called private property problem.

It follows that capitalism must be always more effective system, because it ensures that an economic accounting standard is voluntarily accepted by all the members of the community. And conversely socialism is always a less effective system, because the accounting standard of the other one is always involuntarily imposed and enforced on the others. Therefore, socialism must be, by definition, the less effective economic system; but not impossible one. 

Matúš Pošvanc

Original final Slovak version of the article was published on March 26th 2019. English version was published on June 27th 2019.

[1] Mises, L. 1920. Economic Calculation in the Socialist Commonwealth. WWW DOCUMENT <https://mises.org/library/economic-calculation-socialist-commonwealth/html>

[2] Hayek, F.A. 1945. The Use of Knowledge in Society. WWW DOCUMENT <https://www.econlib.org/library/Essays/hykKnw.html?chapter_num=1#book-reader>

[3] Kinsela, S. The Great Mises-Hayek Dehomogenization/Economic Calculation Debate. WWW DOCUMENT <http://www.stephankinsella.com/2016/02/the-great-mises-hayek-dehomogenizationeconomic-calculation-debate/>

[4] Caplan, B. Is socialism really “impossible”? WWW DOCUMENT  <https://www.tandfonline.com/doi/abs/10.1080/08913810408443598>

[5] These works are published e.g on the webpage https://www.hayek.sk/category/austrian-school-research-center-en/

[6] This problem is usually avoided by the authors of the Austrian School. See for example de Soto, J. H. (2012) Socialism, Economic Calculation and Entrepreneurship, p. 131, Bratislava: Conservative Institute of M. R. Stefanik, where de Soto dedicates to the problem the following statement: „A koncom 19. storočia Walter Bagehot jasne odpozoroval, že primitívni divosi neboli schopní urobiť ani jednoduché odhady výnosov a nákladov.“ 

[7] Hülsmann used contradictory regressus ad infinitum e.g. against Selgin. See in Hülsmann, Jörg Guido. “A Realist Approach to Equilibrium Analysis.”  The Quarterly Journal of Austrian Economics 3, No.4 (Winter 2000), p. 45

[8] See e.g. in Hülsmann, J.G., Knowledge, Judgment, and the Use of Property. p. 47. WWW DOCUMENT <https://mises.org/library/knowledge-judgment-and-use-property> 

[9] I have realized Mises’ criticism of the regression theorem and the problem of acquiring the purchasing power of money in Pošvanc, M. The theory of intersubjectively perceived value of money. WWW DOCUMENT <https://www.hayek.sk/theory-of-intersubjective-perception-of-value-of-money/ >, and in “Why We needn’t (inevitable) Gold Standard but Free Banking System. (not published in English).

[10] I consider the term “accounting standard” as proper due to the fact that it is agreement between two or among more human subjects about the conditions of the debt and its elimination later in time. It is agreement about what is Y, how many units of Y is used later in time, timescale, and also about what is collateral and what happens if this or that happens and debt is not eliminated. It has many implications as: e.g. it is a banking sector which creates very same unit of account standard however on institutional level, or the problem of economic error is inherent intersubjective phenomenon of this agreed standard or the problem of large scale error of entrepreneurs (crisis) is very connected with the issue and also it has implication on theory of capital. I will develop more implications in more detail in later texts.

[11] Biľo, Š. 2004. The Theory of Imputation: A context of value spreads between means and ends. WWW DOCUMENT <http://www2.gcc.edu/dept/econ/ASSC/Papers2004/Imputation_Bilo.pdf>

[12] Hülsmann writes: „Mises brings up the following case:

 <Let us suppose that the scale of values of the possessor of an apple, a pear, and a glass of lemonade, is as follows:

1. An apple

2. A piece of cake

3. A glass of lemonade

4. A pear

If now this man is given the opportunity of exchanging his pear for a piece of cake, this opportunity will increase the significance that he attaches to the pear. He will now value the pear more highly than the lemonade.>

It is true that this passage is no clear-cut evidence that Mises championed value imputation theory. Mises does not actually say that the value of the goal of the exchange (the piece of cake) is fully imputed on the means (the pear); he just says that the exchange opportunity will increase the significance of the pear, to the point that the value of the pear will now be higher than the value of the glass of lemonade—but not necessarily equal to the value of the cake“. See in more detail in Hülsmann, J.G. Theory of Interest. WWW DOCUMENT <https://mises-media.s3.amazonaws.com/qjae5_4_7.pdf> p.89

[13] Ibid. p. 20

[14] It is a pity that he does not proceed further and does not introduce his view on the issue of transition from valuation to appraisement, or the relation between value and appraisement. It is equally a pity that he avoided the application of his theory within the time.

[15] Ibid. p. 11 (footnote no. 5)

[16] Ibid. p. 16. „The static auxiliary tool of “praxeological point” will help us to understand the relation and interdependence of concrete decision-making aspects in the dynamics of human action. It also enables us to deal with the problem of value by itself and not distort our analysis by the phenomenon of time that is not under the present scope of investigation. This holds true especially for the actions the end of which is fulfilled in the same “physical time” as they are performed, for example exchange. In the “praxeological point”-analysis, we are easily able to see “pre action” and “action result” categories and not to confuse ourselves with considerations of unchanged physical world“

[17] A more detailed description of this problem can be seen in Potužák, P. 2016. CAPITAL AND THE MONETARY BUSINESS CYCLE THEORY.  pp. 100-110.WWW DOCUMENT <https://vskp.vse.cz/49157_capital_and_the_monetary_business_cycle_theory_essays_on_the_austrian_theory_of_capital_interest_and_business_cycle> My proposed solution of the given problem can be found in v Pošvanc, M. he Theory of Interest. Revision of the Austrian Approach. Annex 1: Remarks, Relations and Arguing over the Work of Pavel Potužák. WWW DOCUMENT <https://www.hayek.sk/the-theory-of-interest-revision-of-the-austrian-approach-annex-1-remarks-relations-and-arguing-over-the-work-of-pavel-potuzak/>

[18] Mises does not hesitate to claim that the scarcity of the reality is the presumption of the action and at the same time claim that it is the action, which economizes the reality, meaning that reality is perceived as economically scarce as a result of action.

[19] Menger, K. Principles of Economics. p.120. WWW DOCUMENT < https://mises-media.s3.amazonaws.com/Principles%20of%20Economics_5.pdf?file=1&type=document

[20] See for example Biľo, Š. 2004. Imputation and Value in the works of Menger, Bohm-Bawek and Wieser. Str. 9. „Böhm-Bawerk’s muddle is the question of what he is really counting – utility, prices, or both is easily seen in the end of this exposition, where he simply skips from the “utility economy” to examples with monetary prices (ibid., p. 167).“ WWW DOCUMENT <https://nb.vse.cz/kfil/elogos/miscellany/bilo105.pdf>

[21] It should be noted that this is not something new. The relationship in question occurs in all the works of the authors. At the same time, it is not a pragmatic solution like “when it is not possible either in one direction or the other one, let’s try it through the middle”. The solution in question is, in my opinion, very well connected, for example with the Hayek’s Sensory order or works of other authors, which are focused on the fact that our thinking has categorization, i.e. relational character. Thus, we can connect the thesis on the ends-means relationship with the causal world, i.e. how our mind works.

[22] Hülsmann, J.G. A Theory of Interest. pp.86-87. WWW DOCUMENT <https://mises-media.s3.amazonaws.com/qjae5_4_7.pdf?file=1&type=document>

[23] Biľo, Š. 2004. The Theory of Imputation: A context of value spreads between means and ends. str.8. WWW DOCUMENT <http://www2.gcc.edu/dept/econ/ASSC/Papers2004/Imputation_Bilo.pdf>

[24] Mises, L. Human Action. p. 93 WWW DOCUMENT <https://mises.org/library/human-action-0/html/pp/663>

[25] Biľo shows its inaccuracy from a different point of view.

[26]Means are always scarce compared with desired services, otherwise there would be no need for action in connection with them and they would be only “general conditions of human welfare”. See in Biľo, Š. 2004. The Theory of Imputation: A context of value spreads between means and ends. p.10. WWW DOCUMENT <http://www2.gcc.edu/dept/econ/ASSC/Papers2004/Imputation_Bilo.pdf>

[27] We can also use thought experiment to show the point. If we assume a Garden of Eden a permanently living body (we do not die there) and also let us suppose that there is a community of, say 100 people, and let us also assume, that each of the person realizes the maximum potential of the possible consciousness of others, in other word he would be aware of the 99 other ones and vice versa, even in this situation there can be a scarcity in the form of role-play of these eternal and all-conscious beings. From this, it follows that the scarcity is the result of the thinking, not the result of the surrounding reality. The reality just is. What makes it scarce is our thinking in the context of our ends – for example for the needs of the play of these beings. The same applies also for the Hülsmann’s abstraction of the situation of having the opportunity to satisfy our ends without the need to choose the means. This given causality can still exist in our thought experiment in the context of the game of the all-conscious and eternal beings. That means that these beings would for example willfully abandon the general state of satisfaction of ends and they acted as if they did not have it and would have to choose means.

[28] It is a thing of reality, with which we realize that it satisfy some of our ends and at the same time we do not have to economize the given thing.

[29] The Law applies generally. It has to apply then also for example for the case of air. In the normal state we demand air e.g. roughly 12 breaths per minute and not more regardless of the fact that there is unlimited amount of it (the body regulates the satisfaction of the given end of course automatically) and only with the changes in our goals, for example I want to run, changes its use, we actually economize it, if we alter the goal to, say, “survive under water”. In case of air we see, that it is not a practical problem of scarcity, but the change of the goals (ends), which cause the change in term of the perception of need for air. While the causality “need to breathe – air” exists before the good air is economized.

[30] For a greater degree of precision, it must be noted, that the mind categorizes the given relations on multiple levels of knowledge. Multi-level character of ends-means relationship could be illustrate by example of division of knowledge provided by Karl Engliš. Engliš divides the knowledge to empirical (causal level), teleological (economic level) and normative level, over which exists a formal-logical knowledge framework, so we can look at the given relation on one hand from the physically-chemical causal viewpoint, i.e. water eliminates the thirst, however, at the same time the mind categorizes the given relation from the teleological view point, when it evaluates the rate, intensity and the time character of the given relationship in the context of our needs, i.e. I prefer thirst-water to say warm-fire, or I prefer the thirst-water immediately, not tomorrow. Subsequently after thirst-water I want to satisfy the end of rest so I prefer rest-sleep relationship, etc.. Normative level grasp the relationship from the point of view of property rights or possibilities to acquire water. The causal relation End-Mean is assessed here from different viewpoints, while the scarcity as such is evaluated in the sense of Engliš’s terminology within the teleological knowledge. Of course, the Hayekian evolutionary monism will explain this principle in a different manner, through the mental maps. However, it is just a different illustration of how we view the world.

[31] We are not describe something unusual from the empirical point of view. Humans built always some kind of portfolio of goods to satisfy different kinds of ends. And we are going here only slightly adjust present theory of value when we are focused on ΣEnds in their totality which is satisfied by ΣMeans (portfolio of goods). The law of diminishing marginal utility is here applied to the marginal change of portfolio instead of marginal change of particular good.

[32] Chroustal, F. Personal interview. Vienna. 20th March 2019.

[33] „Human action is realised in the actual movement of the body and in the actual activity of the mind. But it also contains two types of unrealised parts: the ends sought after and the foregone alternatives. This fact is almost universally acknowledged, but while the analysis of the subjective and objective role of ends has attracted at least some attention among economists (under headings such as “intentionality” and “meaning”), the analysis of foregone alternatives, the hidden side of choice, has been neglected.“ Hülsmann, J.G. FACTS AND COUNTERFACTUALS IN ECONOMIC LAW. p 70. WWW DOCUMENT <https://bastiat.mises.org/sites/default/files/17_1_3.pdf> see also Tyler, N. Counterfactual Shortcomings in Economic Law. WWW DOCUMENT <http://www2.gcc.edu/dept/econ/ASSC/Papers2005/ASSC05_Tyler.pdf>

[34] The difference from for example Rothbard’s interpretation of the scale should be obvious. Rothbard claims that the scale is formed in the following manner:

„The actor may be interpreted as ranking his alternative ends in accordance with their value to him. This scaling of ends may be described as assigning ranks of value to the ends by the actor, or as a process of valuation. Thus, suppose that Jones ranked his alternative ends for the use of an hour of time as follows:

(First) 1. Continuing to watch the baseball game

(Second) 2. Going for a drive

(Third) 3. Playing bridge

This was his scale of values or scale of preferences. The supply of means (time) available was sufficient for the attainment of only one of these ends, and the fact that he chose the baseball game shows that he ranked that highest (or first)….“ Rothbard, M. Man, Economy and State. p. 6. WWW DOCUMENT <https://mises-media.s3.amazonaws.com/Man%2C%20Economy%2C%20and%20State%2C%20with%20Power%20and%20Market_2.pdf>

[35] This is one of the reasons why we demand money. The diversification of portfolio of ΣMeans is replaced by money as the most liquid good. However, as reader will see below, the path to this discovery of mankind was not so straightforward.

[36] Menger is instructive in this point: „When men recognise that their wellbeing is bound up with the command over certain goods within certain periods of time, and that such goods are likely to be insufficient for their demand, their impulse is (1) to get such goods into their possession or disposal; (2) to preserve the useful properties of the same ; (3) to decide which are their more important and which their less important wants, and to satisfy the former only ; and (4) to so dispose of the goods as to get the greatest possible result or satisfaction on the whole, and to obtain every individual result with the smallest possible expenditure. ” The activity men direct to those ends, in its totality, we call their ‘ economy,’ and the goods which stand in these quantitative relations, as the exclusive objects of that economy, we call ‘ economic goods.’ ” See in Menger, K. Grundsatze, chap. ii. § 3. cit Smart, W. An Introduction to the Theory of Value. p. 17. WWW DOCUMENT < https://mises-media.s3.amazonaws.com/An%20Introduction%20to%20the%20Theory%20of%20Value_2.pdf>

[37] This solution is used also to explain the interest problem. For more details see e.g. Pošvanc, M. The Theory of Interest. Revision of the Austrian Approach. Annex 1: Remarks, Relations and Arguing over the Work of Pavel Potužák WWW DOCUMENT <https://www.hayek.sk/the-theory-of-interest-revision-of-the-austrian-approach-annex-1-remarks-relations-and-arguing-over-the-work-of-pavel-potuzak>

[38] I mean here action focused on direct satisfaction of ends. Indirect action is exchange.

[39] The approach in my opinion allows a certain mathematization of the problem in its nature. This would equally suggest that the mainstream economics and its tools are to a certain extent a suitable tool for a description of a human action in the context of the abstract description. However, this interpretation explicitly implies the impossibility of knowing the individual preferences in their total sum.

[40] Note at the same time that the description is constantly focused towards the future. Even at this individual level we value ΣMeans, i.e. our individual calculation unit in the context of whether we satisfy the anticipated ΣEnds successfully or unsuccessfully. The calculation unit is not expressed by a single good, it is expressed by all goods in the portfolio. So we are able to compare it in time.

[41] To realize the depth of this problem, which outside of the monetary economy we solve precisely through the diversification of the portfolio of goods, is suitable to use this very apt note from Hoppe with Hülsmann and Block, which they actually make in a different context, however, it exactly explains what the man faces and what he solves through money:

„… this feature of money as the most easily and widely saleable commodity, far from rendering it a future good, qualifies money at the same time as the good best suited to alleviate presently felt uncertainty and, as such, the most universally present good of all. Although only indirectly useful — in this regard like producer goods, and unlike any consumer good — money is precisely on account of its supreme saleability a uniquely present good — in this regard like consumer goods, and unlike any producer good. Because money can be employed for the instant removal of the widest range of possible needs (or the satisfaction of the widest range of possible desires), it provides its owner with the best humanly possible protection (insurance) against uncertainty, that is, against his uneasiness of not being able to predict — of not being certain about — all of his future needs and desires. In holding money, its owner gains in the satisfaction of being able instantly to meet, as they arise unpredictably, the widest possible range of future contingencies.“ (emphasis added). See in Hoppe, H. with Hülsmann, J.G. Block, W.: Against Fiduciary Media. WWW DOCUMENT <https://mises-media.s3.amazonaws.com/qjae1_1_2.pdf> p.45.

The invention of money must have been a crucial invention for mankind in this respect. With money we are able to react to our changing needs very flexibly. And it is a quite huge problem to flexibly react at the counterfactually perceived ΣEnds by one´s portfolio of ΣMeans at the individual level unless money was invented. Using of as much diversified portfolio as possible is significantly limited in the context of estimation what purposes ΣMeans could or should serve later in time. 

[42] I do not know, whether the reader notices, but we have just made a step towards a standardization of the expression of calculation. We are starting to compare different calculation standards. This means that if a calculation standard (portfolio consist of meat, bow, house, apples) appears to be from the point of view of another one as more successful as a different standard (portfolio bow, sleigh, house, pears) and it is say house and apple that others in the community miss in their personal calculation standard for the satisfaction of their ends, the community can start to perceive these goods, which others want to include in their calculation standard as more valuable, thereby creating space for inter-subjective comparison of calculation standards expressed in some commodity, which has a higher chance to become the good M (how it happens potentially see below) 

[43] During the exchange we do not compare the specific good to a specific good. We compare a mathematical concept of one person against a mathematical concept of another one, or from the point of the view of human subjects we mutually compare relative, not absolute, variables, i.e. marginal addition of some good X against ΣMeans (in the context of ΣEnds) and giving up of Y in this context. We do not compare apples to oranges. We compare mathematical functions. On the other hand, compare what Mises writes on the given subject: „Calculation in kind is to be substituted for calculation in terms of money. This method is worthless. One cannot add or subtract numbers of different kinds (heterogeneous quantities)“. Herbener adds to this: „ The impossibility of comparing the number of apples to the number of oranges is an arithmetic problem; and a fundamental, not trivial, problem of arithmetic. Without its solution, no arithmetic operations can be conducted at all..“ See in Herbener, J. M. Calculation and the Question of Arithmetic. pp. 153-154. WWW DOCUMENT <https://mises.org/library/ludwig-von-mises-and-austrian-school-economics> 

[44] Communal securing of ΣEnds → ΣMeans is not unlikely. We can see it today for example in the family. In the given example, the group of the individuals shares a common accounting standard and tries for a common securing of ΣEnds. The communal level also implies the existence of the obligation of the others against the member of the group and vice versa. It is at the same time the most probable route, experienced by our predecessors and only subsequently the communities became more individualized. Barter exchange has equally developed as a later concept.

Preceding examples of individual comparison of standards and barter exchange only demonstrate the possibility to use here presented concept also on these options of calculation. The author believes that the emergence of calculation was based on debt exchange which is much more likely concept among our predecessors. See e.g. Graeber, D.: Debt. The First 5000 Years. Melville House. 2012.

[45] This implies an explicit answer to the Caplan’s question, which he poses against the Mises’s interpretation of the economic calculation. He writes: „Crusoe runs his one-man economy under the guidance of what Mises calls “calculation in kind.”  He mentally weighs his preferences and opportunities.  Why would a socialist planner be unable to do the same? Mises’s only response is to declare this method unworkable for a larger economy: <To suppose that a socialist community could substitute calculations in kind for calculations in terms of money is an illusion. In an economy that does not practice exchange, calculations in kind can never cover more than consumption goods. They break down completely where goods of higher order are concerned. (Mises 1981, 102.)> This passage suggests a question: Does Crusoe’s one-man socialism “completely break down” when Friday shows up?“

The answer, whether anything changes, once Friday shows up, is certainly Yes. Once Friday shows up, everything changes completely. By having Friday show up, there is a possibility of comparison and mutual economic interaction and mutual satisfaction of the ends, from which mutatis mutandis follows the possibility of economic calculation. See in Caplan, B. Is socialism really “impossible”? p. 10. WWW DOCUMENT  <https://www.tandfonline.com/doi/abs/10.1080/08913810408443598>

[46] Mises, L: Economic Calculation in the Socialist Commonwealth. WWW DOCUMENT <https://mises.org/library/economic-calculation-socialist-commonwealth/html/c/10>

[47] Let´s reaped it once again. It is a new – abstract – layer of the perception of the economic reality. Human subjects pulled out the problem of exchange over time (per se) into a separately perceived environment, which is expressed for example in the good M. It means that humans by doing debt exchange in time create a separate problem per se, which is solved and expressed by good M.

[48] The “attack” of the human mind on the narrow spread does not end with the discovery of money (the good M). Above the good M that became money there can be a new layer of relations – based on the clearing of debts between people in space and between people over time. This is nothing else than the fractional reserve banking. The following rule applies to it. The more successful the mutual clearing of debts in the banking IOUs in space and mainly in time, the more narrow the spread of the given exchange becomes, which will at the same time incline to use more IOUs than to money. And vice versa. It implies of course an advanced banking system, but also an efficient system of debt recovery. This is, however, a different topic, which we do not address in this paper.

[49]  See Hayek, F.A. (1952, 2010). Sensory Order. Kessinger Publishing, LLC.

[50] For more detail see Einzig, P. (1966, 2014). Primitive Money: In its Ethnological, Historical and Economic Aspects. Pergamon Publisher.

Even though many economists ignore the anthropological research in the area of the economic history, it is still interesting to look at its findings and try to offer a theory that will answer also the questions raised by anthropology. This is also the purpose of this chapter of my paper, to try to link the presented economic theories, so that the observed anthropological phenomena can be explained.

[51] Einzig is a fairly honest empiricist and in his book he does not dare to decide, which of the theories is the correct one or valid one. This is justified by the in-depth approach to money he have chosen and within which he have shown not only a wide variety of goods we can and cannot consider money from the historical, anthropological or theoretical perspective across world and across the literature, which describes the given phenomena, but also the summary of different theoretical approaches described the creation of money.

[52] Mises, L. The Theory of Money and Credit. p.110. WWW DOCUMENT <https://mises.org/library/theory-money-and-credit/html/ppp/1230>

[53] See for example in Pošvanc, M. The theory of intersubjectively perceived value of money. WWW DOCUMENT <https://www.hayek.sk/theory-of-intersubjective-perception-of-value-of-money/ >, and in “Why We needn’t (inevitable) Gold Standard but Free Banking System. (not published yet).

[54]The catallactic theories of money, … do fit into a theory of exchange ratios. They look for what is essential in money in the negotiation of exchanges; they explain its value by the laws of exchange. It should be possible for every general theory of value to provide a theory of the value of money also, and for every theory of the value of money to be included in a general theory of value. The fact that a general theory of value or a theory of the value of money fulfils these conditions is by no means a proof of its correctness.“ Mises, L. The Theory of Money and Credit. p. 462. WWW DOCUMENT <https://mises.org/library/theory-money-and-credit/html/ppp/1230>

[55] Paradoxically, it is the Mises’s doctrine and theory, which does not meet its own definition of the catallactic theory, since Mises uses objectivism to explain the objective exchange value of money.

[56] In terms of the theory of value presented in this work the obligation (the plan to borrow the goods and the plan to return the goods with interest) is composed into the preferential scale among ƩEnds → ƩMeans relationship of the two human subjects at the same time and in the very same manner – of course in different context (one subject is the creditor and other is a debtor). From the creditor’s point of view, the factually perceived surrender of some good at time t is compensated by the counterfactually perceived relation ƩEnds → ƩMeans at time t+1. That means that the creditor imagines at time t+1 the acquisition of some goods from the debtor, which are to be at time t+1 a part of the portfolio ƩMeans, which he believes that it will at time t+1 better ensure the planned perceived ƩEnds. From the point of view of the debtor, the given exchange is perceived time-inversely. This means that at time t, he satisfies factually perceived ƩEnds → ƩMeans relationship through the good from the creditor who enriches his portfolio, and thus satisfies factually perceived ends, while he counterfactually perceives at time t+1 that he has to give up some good from his newly formed ƩMeans.

[57] This is possible only due to the fact that we are connecting money with different thinking layer of economic relations (in our interpretation money are inter-subjetive concept) and Mises is looking for the cause of money within human subject per se.

[58] The fact that the development of the concept of numbers and subsequently mathematics was quite complicated should follow just from the fact that the humanity has discovered the mathematical abstraction in the form of “0” (zero) from the perspective of its history in principle only recently (in the Euro-Indian culture it is used since circa 700 AD, while its development can be traced somewhere to year 300 AD. It seems that for example Mayan culture very likely independent from the Euro-Indian culture uses this concept from 450 AD, if not earlier). See in Butterworth, B. (1999). What Counts. The Free Press. pp 78-84.  

[59] See Hayek, F.A. (1952, 2010). Sensory Order. Kessinger Publishing, LLC., and also in PAVLÍK, Ján. Austrian Economics and the Problems of Apriorism. E-Logos – Electronic Journal for Philosophy


, 2006, Vol. 13, pp. 1–73. ISSN 1211-0442. URL: http://nb.vse.cz/kfil/elogos/science/pavl106.pdf. and in PAVLÍK, Ján. About the Spontaneous Emergence of the Norms of Distributive Justice and Catallactic Rules. E-Logos – Electronic Journal for Philosophy, 1999. ISSN 1211-0442

[60] Butterworth, B. (1999). What Counts. The Free Press. pp. 32-48

[61] Attentive reader sees that we used here Hayek-Pavlik´s theory of mind

[62] See in Butterworth, B. (1999). What Counts. The Free Press. pp. 68-75

[63] The base principle means that our predecessors counted for example in the base-4 (quaternary numerals system), by having explicit name for the numbers 1-4 and then they made a record of the group and started counting as 4+1, 4+2, 4+3 and 4+4, and so on. The given counting principle has equally developed. Today we use for example base-20 numeral system, but China uses for example base-10 system. Even if the base-2 system it is possible to conduct different mathematical operations and so to calculate. However, it is much more difficult than in other bases. As a potentially possible system before the base system is the system of the body parts. Our predecessors have developed different technological aids in the form of mathematical tablets and others for the given base systems. See for example in lbid. pp 49-68

[64] Ibid. pp 68-75

[65] The political theory is often used within the Austrian school as an example of incorrect approach to the emergence of moneyness of some good. As we can see in our theory it certainly has its place. The political circumstances were just as historical circumstances as any other circumstances. Paradoxically it is also the history of gold as money, which became dominant in the economic ties also thanks to its popularity related to the political powers.

[66] „In a large number of instances, the units serving as a standard of value could not possibly have been used as media of exchange, for the simple reason that they were merely ideal units without any concrete existence. Admittedly it is possible that in the remote past those abstract units were represented by concrete objects serving as media of exchange. It is, to say the least, conceivable that some units of account at any rate were purely imaginary from the outset. Einzig, P. (1966, 2014). Primitive Money: In its Ethnological, Historical and Economic Aspects. Pergamon Publisher. p.367

[67] It would be relatively tougher to compare the costs and revenues in some form of barter, where we would have to set some common benchmark of the exchange in the context of what they have to give up in order to gain something and the most difficult it would be to compare the revenues and costs if they did not enter into the exchange. What I am trying to suggest is that we can see the options of the mutual comparisons, or difficulties associated with it based in barter and how the humanity could create an interesting tool of the comparison of the mutual activity in the form of money and economic calculation.

[68] It does not mean that particular member of the given community cannot abandon a given standard or to change it somehow. However, in terms of his ƩEnds he voluntarily incorporate some common ƩEnds which are typical for the given organizational unit of the community.

[69] Hoppe recognizes the socialism of the Russian type, the socialism of the social-democratic type, conservative socialism and the social engineering. See in Hoppe, H.H. A Theory of Socialism and Capitalism. WWW DOCUMENT <https://mises-media.s3.amazonaws.com/Theory%20of%20Socialism%20and%20Capitalism%2C%20A_4.pdf>     

[70] In numerous cases these are not some elites in the true sense of the word. The empirical experience shows often an exact opposite of what the word elite actually means.

[71] Caplan for example describes absence of proper incentives within socialism and some efforts to introduce these incentives, which always crash with the political power. He sees the problem of socialism rather in the absence of the opportunities to do business, rather than in the calculation. See for example in Caplan, B. IS SOCIALISM REALLY “IMPOSSIBLE”? WWW DOCUMENT https://www.tandfonline.com/doi/abs/10.1080/08913810408443598>

[72] From this point of view, there is an interesting question of what is and what is not acceptable for individuals within such different socialist communities and what is taken voluntarily and what is given by real force.

[73] This particular change of premise changes the whole perspective. The premise “I prefer more goods which are the same kind and quality over less” has objectivist character and paradoxically is not possible to use it over time because of the problem of change of valuation of goods in time. The premise “I prefer higher satisfaction of ends over smaller” is fully subjective and as I have shown it is possible to use it over time. The very true is that it introduces some kind of economic relativism. I will deal with the issue in more detail in later works focused on the problem of economic error, dealing with uncertainty and the problem of equilibrium concept.

[74] I think that the Hayek’s problem of the centralized nature of the information about the preferences of people in the big society versus a smaller community needs to be taken exactly in this context. The problem exists in the small community as well as in the large one. In the small community, however, the agents voluntarily adapt the “centrally” determined standard of calculation – by an owner of the club, the head of the family, the chief of the clan, to the spontaneously created rules of the pre-historic community and so on. It is a voluntary acceptance of a standard and not a solution to the problem of the subjective preferences. And the given community calculates in the context of the given standard what it considers to be a profit and loss. The fact that other community can consider the economic activity senseless, is not the sign of a lower efficiency. The ƩEnds voluntarily accepted by them, which they try to satisfy by some ƩMeans, may have for them some sense, which we may not know. That is why these voluntarily organized units of society cannot face the identical problem as socialism does. The voluntary organizational unit must have by definition an identical weight at the mutual acceptance of the accounting standard of another one in the communication of the mutual economic preferences as a subject by itself. In this respect the voluntary organizational units are equally the tool, through which the subjects perceive the surrounding economic reality. Confront this with Hoppe, H. H.: A Property or Knowledge problem? str.144. WWW DOCUMENT <https://mises.org/library/socialism-property-or-knowledge-problem>

[75] Within the original discussion about the economic calculation authors like Taylor or Lange suggests nothing else than some kind of way of forcefully determining an accounting economic standard (it does not matter that was inspired by market process) that cannot be realized without people being forced to accept it. We must inevitably say about these attempts that these are ineffective and bad attempts. However, the fact remains that they are feasible. For more details about the original discussion see e.g. de Soto, J.H. (2012) Socializmus, Ekonomická kalkulácia a podnikanie. pp. 167-274. Bratislava. Konzervatívny inštitút M. R. Štefánika.

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