The Theory of Interest. Revision of the Austrian Approach. Annexe 2: The Problem of Robinson

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When looking for the essence, or the origin of interest, I presented interest as an intersubjective concept in my work The Theory of Interest. Revision of the Austrian Approach and Annexe 1: Remarks, Relations and Arguing over the Work of Pavel Potužák. It means that its essence can be described only in a view of at least two human subjects mutually economically interacting in time continuum. So, the concept of interest is not subjective. In this context it was pointed out e.g. in Annexe 1 of my theory the following:

„If we interpret the problem of interest by Robinson’s example, we must state that there is no way for him how to derive interest. Sure, he considers TP2 (time preference in the second sense) and regards his future also by means of TPr (time projections, or TP1 — time preference in the first sense) in the context of various personal strategies of reaching a more or less preferred sum of goods, i.e. internal strategy of survival (to get income, to save his life). However, the difference between given internal “production” strategies and their selection does not generate a type of internal interest rate. There is no way how to do it. Comparison/assessment with an indirect way of satisfying needs is missing. For Robinson there is only Hülsmann-Braun’s assessment of ends and means in time continuum.“

Two interesting issues result from the above mentioned. First, if interest is an intersubjective concept, does something like internal interest rate, which must be by its nature subjective, exist? If it does not exist, on the basis of what do we assess whether intersubjective interest rate is or is not suitable for us? The second issue results from the first one, i.e. if internal interest rate exists, why e.g. Robinson does not perceive it and does not decide his production strategies in time on its basis?

I claim that internal interest “rate” exists; actually it is not the rate in the proper sense of the term; it is a more or less preferred planning of state of affairs. However, what I say is that we can grasp it as a real concept in the context of existence of the other one, or more precisely, in the context of what the other one offers to exchange in time. This work should more precisely and more specifically answer two fundamental questions that were not solved in the previous works about interest:

a) Why internal interest rate does not exist in Robinson case if he is alone on the island?

b) What is internal interest rate derived from the intersubjective concept (at least Robinson and Friday must have been on the island) and how do we perceive it then?

These two issues will be explained in the following way: I will show why Robinson himself cannot perceive concept interest as a real concept. You will see that it is impossible irrespective of the fact that Robinson will use all three reasons for existence of interest in Böhm Bawerk terminology[1]. And vice versa, you will see why he starts to perceive interest once Friday appears. On the basis of that we can describe what internal interest concept is and how a man grasps it subjectively. At the same time, thanks to this thought experiment, I will be able to show why interest is an intersubjective concept and why intersubjectivity of its nature is its very essence.

Robinson Thought Experiment

Robinson is alone on the island until Friday appears. I claim that Robinson cannot use concept of interest until Friday appears. Interest as a concept develops only when Friday appears and when Robinson and Friday start to interact economically. Only then there is potential for the concept of interest to develop and at the same time Robinson (as well as Friday) can become aware of internal interest derived from their mutual economic interaction[2].

Robinson makes decisions even though he is alone. He tries to satisfy the needs he perceives by chosen means (goods). When making decision about his own “production structure” he gives priority to what will satisfy his needs faster and better over something else, he thinks, would satisfy his needs slower and not sufficiently. Let’s say that he considers four production processes:

A. putting up a ladder in order to gather coconuts while supposing that thanks to this he will be able to gather 10 coconuts per hour

B. getting a pole for knocking down coconuts while supposing that thanks to this he will be able to gather 17 coconuts per hour

C. tree-coconut-shaker, i.e. an instrument for shaking a coconut palm supposing that thanks to this he will be able to gather 23 coconuts per hour

X. hunt for 3 squirrels.

Let’s start simply and let’s say that he estimates that every process is identical in terms of time, e.g. he estimates that he needs one day of work for performing A, B, C and X. Which process will he choose? If there were no real time differences among the processes, he would prefer the one which, he supposes, satisfies his subjective needs the most. Let’s say that for this reason he rejects the process X — hunt, or let´s say that for any reason he needs nuts. Subsequently, we should remind that he does not have to prefer a process ensuring a nominally higher rate of economic goods (coconuts) in the future. He can still prefer the process A ensuring the least number of nuts, because it is total satisfaction of needs which is in question. If Robinson is sufficiently “weird” and a convinced coconut-zealot believing that he must take care of the gathered nuts and that he must inevitably and sustainably maintain coconut flora on the island, then he can prefer the production process A supposing that it can ensure him clearly 7, or 13 nuts less per hour compare to A. He considers the process A as the one satisfying his total needs, including minimum intervention to the island climate, the most. So, he assesses his total objectives and the impact of gaining nuts on his total sum of objectives in the context of what Robinson already has, i.e. his portfolio of existing economic goods. If we suppose that all the processes are identically time consuming, then Robinson would decide in the context of what I call time projection in my interest theory, or what Böhm Bawerk calls time preference in the sense of the first reason (TP1), for the existence of interest.

At the beginning we simply supposed that all four processes would take the same time. But if the given assumption does not apply and e.g. the process A would take three days, the process B one day, the process C eighty days and the process X one day, Robinson could change the resulting decision, which would prevail over his perception of sustainability of the island environment because he would be forced by the urgency of the perceived need to get nuts. It means that he would prefer B because he inevitably needs nuts and he does not have e.g. sufficient stock of anything else, thus his need of sustainability of the island environment would be suppressed. Robinson would consider what he can do faster and what slower. Robinson would apply what Böhm Bawerk calls time preference, which is Böhm Bawerk’s second reason for existence of interest (TP2)[3].

As we can see Robinson considers four types of roundabout methods of production of some goods associated with satisfaction of his needs. He can find out that some considered processes cannot be implemented (e.g. the process C with the tree-coconut-shaker, which would need some instruments Robinson does not simply have, or knowledge he lacks, or anything else he does not have available). Therefore, he could realistic decide only between process A and B. As we have shown, the choice between them could be considered in the context of time-consuming, labor or feasibility or a complex of his ends. In connection with the existence of roundabout production methods, Böhm Bawerk states that this is the third reason for the existence of interest. Roundabout methods of production are time consuming due to which current production methods are more preferred than the future ones[4].

So, here we have all three reasons/conditions which Böhm Bawerk considers as the basis of interest[5]. When assessing his decision between two (and more) production processes, does Robinson use interest rate or not? I claim that not. When Robinson is all alone on the island, he does not use interest because he cannot assess real competitive and economic projects[6]. Let’s compare the situation when he is alone on the island and, subsequently, when Friday appears.

When Robinson is alone on the island, everything what he does is that he considers four processes of production in time “t”. He does it at the individual mental level. The motifs for choosing the process A are not essential. If Friday was alone on the island, he might consider the given alternations in a completely different way and make decision on the basis of different mental-individual deliberation.

The choice always and under all circumstances puts other processes to the mode of thought, or option. Robinson knows how to potentially implement other ideas (if ever) but in different time, due to which they consequently become incomparable vis-à-vis time t, when Robinson considers his possibilities, i.e. his objectives and subjectively best perceived means for reaching them. In time t Robinson considers ideas and projection of the future, on the basis of which he makes decisions. He surely prefers earlier to later satisfaction of needs and higher to lower satisfaction of needs (but it does not inevitably mean more goods!) and in this context he assesses intended production processes. He creates projection of the future and then he decides which of the processes is subjectively the most advantageous for him. However, he cannot assess real spread of the four conceived projects. If we can speculate about what he assesses, then it may deal of conceived spreads of the conceived projects. But how can we derive the real phenomenon of interest from it if we do not want to claim that internal interest is a conceived phenomenon of conceived and never implemented projects? There is no way how Robinson can do that. He never knows how to compare potentially factual states of production processes by definition. He cannot perform two things simultaneously in time. Robinson needs Friday in order to be able to perceive interest and to compare something real. Friday’s arrival is important.

However, Robinson and Friday do not start to play a mutual psychological game about various thought spreads of their thought projects after Friday’s arrival. When Friday arrives, the situation changes. First of all two real processes can be compared. Robinson can see how successful/unsuccessful Friday is and vice versa. Their production processes do not have to be focused on satisfaction of identical needs. But processes must produce associated means with Robinson’s aims. The contrary applies to Friday. So, Friday can without worries perform the process D: let’s say that he has a solar-powered drone which can very effectively and very economically gather coconuts. Friday performs the process D in order to e.g. satisfy the need of the island’s Gods and he builds small pyramids from nuts. However, Robinson is satisfied with Friday’s activity. It gives him new and real economic information about coconut gathering, irrespective of the fact that Robinson has different plans with the nuts than Friday. And irrespective of the fact that Robinson only pondered what he can achieve with the process A, B or C. Parallelism of Robinson’s (let´s say that Robinson realize process A) and Friday’s processes allows to assess suitability of the processes in a qualitatively different way than in the case that Robinson is alone on the island. Nevertheless, none of them has started using interest yet. The only thing that has changed is the fact that they can compare two real production processes.

They will start using interest, both as market and internal phenomena, only when they start to discuss exchange in time. It means that e.g. Robinson can supply Friday with nuts from his own stock today and Friday can much faster build pyramids and satisfy Gods’ needs. Later on, Friday will regularly supply Robinson with nuts and their careful gathering. It is clear that in time t assessment of the exchange is only an intention from the view of Robinson and Friday, i.e. a plan, subjective projection about the future. However, it deals of real phenomena. A real phenomenon makes it the assessments a concept of commitment. If Robinson or Friday do not meet their conditions, the concept of commitment triggers subsequent processes of legal character, e.g. Robinson takes Friday’s collateral, so besides nuts gathering in time t he takes also Friday’s drone, or Friday commits to work off his debt. The concept in time t has, therefore, a real character, i.e. a realistically assessed production process. It is enforced as a real phenomenon. If Robinson is alone on the island, nothing such as this cannot be derived. While comparing four, or even more projects, Robinson himself can promise anything, but it leads to nothing. Irrespective of whether he prefers earlier to later satisfaction of needs or whether he projects and plans his economic activities or the amount of goods in the future, or whether he uses roundabout methods of economic goods production, i.e. he combines resources available in time in order to reach higher satisfaction of needs in the future (not necessarily a higher number of goods). He does not use real interest, even though Böhm Bawerk defines the given conditions as reasons for interest. The given conditions are not the essence of interest.

The essence of interest can be demonstrated on the example of Robinson and Friday using market interest rate (intersubjective concept[7]) and from it derived internal interest “rate”. Robinson (and Friday) subjectively use time preferences in Böhm Bawer’s terminology, specifically reason 1 and 2, and on their basis they decide about production processes (reason 3) and, in the context of their objectives and possible means. However, in a real mode of assessment of possibilities of mutual indirect satisfaction of needs in time. Well, how do they start to perceive interest? For the simplification let’s describe only Robinson’s situation. Exchange implies that mutatis mutandis argumentation applies to Friday. Only the reasons and considered alternations are different from his own perspective.

Robinson has his own portfolio of economic goods which satisfies his sum of ends. When considering what he adds to the portfolio he also considers how the activity producing some goods will change the given portfolio. He asks “Will I be able with planned portfolio (enriched by goods in consideration) react to the caleidic future better or worse?” So, he considers how marginal change in portfolio[8] will satisfy his sum of ends in time. Let’s say that Friday will play the role of a debtor. So, he makes a commitment to supply Robinson with 110 nuts in t+1 and Robinson will give him 100 nuts from his stock to complete building of pyramid quickly.

Robinson considers whether to give up nuts in time t in favour of Friday for his promise to supply nuts in time t+1 (and potentially to engage in the project X) versus (not to give up the nuts and) to dedicate resources (time and work) to the projects A (B, C) versus the project X in the context of how the decision influences his total perception of portfolio of goods which satisfies his ends in time[9]. Such real and factual considering of economic activities (of Robinson and Friday) allows Robinson to use what I call interest, both internal and (intersubjective) market interest. This way Robinson is able to consider real results and alternatives. And he can identify a marginal point of his preference. He can assess that while Friday does not provide Robinson with the desired amount of nuts in the future, Robinson will not supply Friday with the existing nuts today. It means that if Friday offers only 109 (and less nuts) in t+1, the offer does not correspond to Robinson’s idea of marginal change in time. So, Robinson will prefer such a portfolio that consists from already gathered nuts and e.g. intended result of the activity A (if he rejects the project X). Assumption of such a portfolio is more acceptable for Robinson than any other alternative, while he made decision in the context of what Friday was offering, i.e. in the context of interest rate. If Friday is willing to provide up to 110 nuts in time t+1, Robinson’s interest rate is lower than the intersubjective, and Robinson prefers to give up nuts in time t and to engage in the project X — hunting and to get nuts from Friday in time t+1.

Why 109 nuts in time t+1 are not acceptable for Friday and why 110 are — that is a question relating to subjective assessment of internal interest rate looking like this: “change (in total portfolio) in Robinson’s total amount of goods in time t+1 caused by the project X and simultaneously its complementation by less than 10 nuts from Friday.”

Thus, Robinson perceives the following spreads:

A/ spread associated with satisfaction of his ends by portfolio of means/goods in time t (PAt) and expected change in portfolio in t+1 (PAt+1) caused by own economic activity aimed at satisfaction of his ends in t+1

B/ spread associated with giving up part of his portfolio in favour of Friday in t (PBt), so that the portfolio ensures satisfaction of his ends in t for having a portfolio of means/goods (PBt+1) enriched in results of the project X and coconuts from Friday satisfying his total ends.

Friday perceives these spreads:

C/ spread associated with immediate enrichment of his portfolio in nuts (PCt) in time t, which immediately satisfies his total ends since he achieves his portfolio of means/goods (PCt+1), which both satisfies his ends and provides Robinson with nuts, in t+1 by his economic activity.

D/ spread associated with satisfaction of his ends by portfolio of means/goods in time t (PDt) with expected change in portfolio in t+1 (PDt) caused by his economic activity aimed at satisfaction of his needs in t+1.

Robinson considers spread K (change in PAt → PAt+1 vs. PBt → PBt+1), while Friday considers spread H (change in PCt → PCt+1 vs. PDt → PDt+1). Intersubjective interest rate develops between spread K and spread H.

Internal interest rate is derived from it as well. Robinson perceives that it deals of marginal rate of what he is willing to accept if he should get rid of 100 nuts in time t in favour of Friday. His reasons may relate to perception of high risk associated with Friday’s activity in time, or lack of confidence in his technology, or high alternative costs linked with giving up 100 nuts in time t. For Robinson to enter into a given exchange Friday must make intersubjective interest rate higher than internal. Then “change in Robinson’s portfolio in time t+1 caused by the project X and completion of at least 10 nuts from Robinson will cause that intersubjective spread is more preferred than Robinson’s marginal spread.”

It follows that the possibility to assess a real outcome of two potential future states of Robinson’s portfolio resulting from commitment arises only with Friday’s arrival. Robinson prefers still the earliest satisfaction of his needs (TP2) but in the context of indirect satisfaction provided by Friday. He keeps still considering time projection (TP1) in the context of whether dedicating his saved resources to Friday is worthwhile, meaning Friday allows Robinson to reach e.g. more variable portfolio of savings in the future, which Robinson would not get without Friday’s offer of exchange in time. It is on the basis of the assessment of these options which will trigger or not the implementation of roundabout methods of production. If Robinson and Friday do not come to an agreement, interest rate will cause that Robinson considers the project A the best and Friday the project D. And vice versa, if they reach an agreement, interest rate will cause that Robinson will perform the project X and give up part of his goods in time t in favour of Friday, while Friday will perform the project D later in time however his ends to satisfy the need of the island’s Gods will be satisfied earlier.

The Concept of Internal Interest Rate

The concept of internal interest rate is derived from the assessment of what the second human subject offers in exchange in time continuum. Internal interest rate does not manifest itself as a specific number, but it shows in a subjective, ordinary, way. If a creditor (Robinson) refuses to enter into exchange, his subjective interest rate will be lower than what a debtor (Friday) offers by its project. Vice versa, if a debtor refuses to enter into exchange, he demonstrates that his internal interest rate is higher than what a creditor requires for provision of economic resources in time t. In this case at the subjective level we cannot unambiguously determine exact number of internal interest rate, but we can ordinarily determine whether the mutually estimated interest rate is lower from the debtor’s view or higher from the creditor’s view than what human subjects are willing to accept mutually. If the agreement fails, the only thing we can say about internal interest rate is that it was lower than required by the creditor and higher than required by the debtor. And vice versa. It will never manifest itself in a specific objective form; it is on the ordinary scale. It can be identified only in the context of the ongoing agreement in time t, when dedication of the existing resources and formation of economic commitment is negotiated.

The Essence of Interest Rate

If Robinson is alone on the island, he assesses potential change in portfolio of goods in time. He also assesses change in portfolio in case that Friday is on the island, if they do not collaborate economically. Qualitative change develops on the basis of their collaboration in time. They both start to perceive change in portfolio of goods in time in a different qualitative manner. Qualitative change in perception of portfolio change in time which should satisfy ends in time is what we call interest. It is a result of assessing spread of direct and indirect satisfaction of ends in time from the view of at least two people mutually[10].

Thus, interest is part of every exchange. Every exchange takes place in time — barter “direct” exchange performed immediately too. However, perception of interest is negligible in short time intervals. The reason for negligibility is a relatively high rate of certainty forecast of change in portfolio of goods in the context of use of occurred portfolio of subjects entering into exchange in order to satisfy needs in time. Simply put, if I am exchanging a pear for an apple (and vice versa from the view of the other one) now and here, I know what I am doing and why. Even though we perceive caleidicity of the future.

However, if we “invest” more time to the exchange, we come across the caleidic future in much higher rate. Higher rate of caleidicity of potential value changes results in the use of the intersubjective tool — interpersonal instrument — interest.

Perception of interest depends on rate and significance of marginal change in portfolio of at least two human subjects entering into exchange in the context of assumed use of future portfolio for satisfaction of ends of human subjects in time caleidic continuum. Monetary (precise) expression of interest rate and full awareness of interest as a concept depends subsequently on use of money.[11]

If Böhm Bawerk asks “Whence and why does the capitalist receive this endless and effortless flow of wealth?”[12], then it is necessary to quit three Böhm Bawerk’s reasons from the perspective of interest essentiality, or to admit that the first two are only satisfactory conditions[13] of development of interest rate, i.e. they influence interest rate, and to answer his question as follows. This source of incomes results from never ending assessment of rate and significance of marginal change in portfolios of at least two human subjects entering into (debt) exchange in time in the context of use of future portfolios of these human subjects for satisfaction of their ends in time caleidic continuum. This way human subjects assess direct and indirect options of satisfaction of their ends in time caleidic continuum.

Matúš Pošvanc, 15. 05. 2019

[1] Böhm Bawerk describes three reasons for existence of interest. As Robert Murphy states „To explain the existence of such a premium Böhm-Bawerk offered three main reasons. First, in general people expect to grow wealthier over time, and thus on that account they value the marginal present good more highly than the marginal future good. Second, for various psychological reasons, in general people tend to systematically discount future satisfactions. And third, Böhm-Bawerk claimed that as a technological fact, more “roundabout” production processes were more physically productive, and so present goods (because they can be employed in processes that are more roundabout) possess a higher value (since it is always better to have more output than less. ).“ (in italic originally). For more detail see Murphy, R.: Unanticipated Intertemporal Change in Theories of Interest. p.60–61. WWW DOCUMENT <http://consultingbyrpm.com/uploads/Dissertation.pdf>

[2] Be aware of the very fact that we are dealing here only with the thought experiment. People have always and under all circumstances live in any social tie. The thought experiment about Robinson only enables better interpretation of the concept of interest.

[3] When explaining interest Mises uses primarily this type of time preference. Murphy calls it pure time preference.

[4] Besides traditional explanations why Böhm Bawerk´s third reason for the existence of interest cannot be considered as relevant is the fact that in the case it is valid, it would mean that nature “left us” in its deterministic arrangement just the concept of interest. It means that by combination of time and deterministic combination of production processes we would be discovering interest in the meaning “Look, there is as a beautiful 3% of interest possible in this particular process and in another one is 7%”. So, the third reason for existence of interest rate would be objectivistic nature, i.e. given by nature.

It is men who creates the concept interest, not nature. It is necessary to reject Böhm Bawerk´s third reason completely. It is not the cause of existence of interest. The choice of roundabout methods of production is the consequence of using this tool — interest rate. As the reader will see however, the choice of a roundabout method does not depend on interest at a strictly individual level of an individual, but in the context of mutual economic acting of individuals, i.e. in the context of economic action of the other one.

Explanation (not defend) of Böhm Bawerk´s third reason for the existence of interest see in Murphy, R.: Unanticipated Intertemporal Change in Theories of Interest. WWW DOCUMENT <http://consultingbyrpm.com/uploads/Dissertation.pdf>

[5] Murphy inclines only to the first reason for the existence of interest and he states that this is the basis of interest rate. See p. 85 where he writes: Now that we have exhaustively demonstrated the manner in which TP <time preference; add by MPo> in sense (i) may be considered necessary and sufficient for interest, we can easily show why TP in sense (ii) is neither necessary nor sufficient. Just because someone discounts future utility

or satisfactions per se does not ensure that he will value future goods at a discount, because other things may not be equal“.

This statement can be undermined in two ways. First, nothing like higher amount of goods does not exist in the future. Second, people do not prefer more to less goods of the same type and quality in time. They prefer higher satisfaction of needs to lower. So, goods themselves are not that essential, but higher rate of satisfaction of needs in time is.

[6] Robinson can claim that he uses interest for decision-making. Does he lie? It is an ontological question. In any case he would not use for decision-making concerning production processes what as he would if Friday comes to the island. From the ontological point of view Robinson would use something else about what he claims (lies) that it is an interest. It can be expressed in the opposite way: he would use something completely different from what he would use if Friday was on the island. However, both concepts cannot be simultaneously considered the same, i.e. interest.

[7] At this point it is necessary to note that in our example a specific objective price of market interest does not have to develop with respect to the fact that Robinson ad Friday do not have to agree on the conditions of debt exchange. However, it does not have to interfere with the intersubjective character of interest. If more inhabitants lived on the island, the intersubjectivity of interest would generate some specific and objective interest rate as objective price (its illustration in the market) only if the given human subjects perform exchange in time of course.

[8] I mean total change in portfolio, i.e. he considers not only adding new economic good but also consumption of the existing ones.

[9] This concept (ΣEnds→ΣMeans, i.e. satisfaction of a sum of ends by portfolio/sum of means) is easily applicable in time since it is a mathematic time-invariant construct, so a particular economic good (absolute quantity) is not considered in time, but change of portfolio (relative quantity) is. We therefore compare the same concept in time t, i.e. relative quantity — a portfolio, as in time t+1.

[10] The easiest test of checking why interest rate should be an intersubjective concept is that the creditor prefers its higher form and the debtor its lower form.

[11] I describe conjunctural history of perception of interest rate and development of money in more detail in Pošvanc, M.: Theory of Intersubjective Perception of Value of Money. WWW DOCUMENT < https://www.hayek.sk/theory-of-intersubjective-perception-of-value-of-money/>

[12] Murphy, R.: Unanticipated Intertemporal Change in Theories of Interest. p.58. WWW DOCUMENT <http://consultingbyrpm.com/uploads/Dissertation.pdf>

[13] I do not agree with Murphy at this point, since he claims that the second reason for interest is not even satisfactory condition for development of interest. The disagreement results from two reasons. The first is different assumption where I claim that people do not prefer more goods of the same type and quality in time but they prefer higher over lower satisfaction of needs. The second reason is modification of Mises-Rothbard´s preferential theory where we do not compare specific goods in time but always only change in portfolio of goods (sums of means) in the context of total sum of perceived ends. I deal with the first reason in more detail in Theory of Interest and Annexe I and the second reason of this disagreement is described in Pošvanc, M.: Evolučné možnosti vzniku ekonomickej kalkulácie a peňazí. Problém nemožnosti socializmu. WWW DOCUMENT <http://www.hayek.sk/evolucne-moznosti-vzniku-ekonomickej-kalkulacie-a-penazi-problem-nemoznosti-socializmu/> in part 3.1.