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• Editor’s Preface
• Ludwig M. Lachmann, an Austrian Stocktaking: Unsettled Questions and Tentative Answers
• John B. Egger, the Austrian Method
• Mario J. Rizzo, Praxeology and Econometrics: a Critique of Positivist Economics
• Israel M. Kirzner, Economics and Error
• S. C. Littlechild, the Problem of Social Cost
• D. T. Armentano, a Critique of Neoclassical and Austrian Monopoly Theory
• Gerald P. O’driscoll, Jr., Spontaneous Order and the Coordination of Economic Activities∗
• Murray N. Rothbard, Austrian Definitions of the Supply of Money
• Laurence S. Moss, the Emergence of Interest In a Pure Exchange Economy: Notes On a Theorem Attributed to Ludwig Von Mises
• Roger W. Garrison, Austrian Macroeconomics: a Diagrammatical Exposition
• Louis M. Spadaro, Toward a Program of Research and Development For Austrian Economics

The Emergence of Interest in a Pure Exchange Economy: Notes on a Theorem Attributed to Ludwig von Mises

Laurence S. Moss

• Babson College

1. Individuals faced with alternatives equally attractive in all respects except their position in time prefer proximate enjoyments to those more remote. According to Ludwig von Mises, this preference for earlier rather than later enjoyments is inherent in all acts of individual choice and is termed “time preference.”1 It has been claimed that Misesian time preference guarantees the emergence of a positive rate of interest in a pure exchange economy, that is, where there is no production and the economic future is known with certainty.2 Furthermore, the interest rate that “invariably” emerges results entirely from the interaction of valuing minds and is therefore a subjective phenomenon, not being dependent on the technology of production or the productivity of capital. Interest is not a payment for a monopolized agent of production, nor does it reflect a particular distribution of the means of production that can be done away with by reorganizing the social order in a manner prescribed by Socialist visionaries.3

The claim that a positive rate of interest will emerge in a pure exchange economy seems fundamental to, and consistent with, Mises’ entire theoretical system. While in his early economic writings Mises embraced Eugen von Böhm-Bawerk’s theory that the height of the interest rate is determined by the technological superiority of roundabout methods of production, his later writings repudiated the productivity theory of interest rate determination in favor of the pure time-preference theory advanced in the United States by Frank A. Fetter at the turn of this century.4 As has been claimed by recent Austrian economists, Mises’ adoption of the so-called pure time-preference concept indicates an abandonment of Böhm-Bawerkian theory and a return to the more thoroughgoing subjectivism characteristic of Carl Menger’s thought.5 In fact, a fundamental theoretical difference between Mises and Friedrich A. Hayek may well turn on the issue of the influence the material structure of the world exerts on the individual’s personal valuation of goods now as opposed to goods later.6 To the extent that the payment of interest is necessitated by the material conditions surrounding the production and distribution of commodities rather than by man’s subjective estimate of future enjoyments, then to that extent the capitalist system (i.e., the market economy) seems less permanent and more dependent on a historical stage in the evolution of these material conditions. Thus, modern Austrian economists who view capitalism as the only social system compatible with the nature of man attach great importance to their interest theory and to the theorem I shall discuss in this paper.7

What I offer here is a model of a pure exchange economy with an analysis of the circumstances under which a positive market rate of interest will emerge. I shall show that much of the misunderstanding regarding Mises’ interest theory has to do with the special meaning Mises attached to the term time preference. Still, when Mises’ theorem is correctly stated and understood, it will be seen that the emergence of interest is not inevitable but depends in part on the existence of certain objective conditions that prevent the individual from “internally financing” an increase in present consumption even when he can afford to do so. And these objective conditions that make possible the emergence of interest are hardly the sort that can be eliminated by a reorganization of the social order along the lines advocated by antimarket reformers.

2. Consider an economy consisting of a number of individuals each facing a time horizon made up of n consumption periods. Also, assume that each individual is guaranteed an endowment of a single consumption good (apples) and knows how many units of this single consumption good will be made available to him at the beginning of each of the n consumption periods. We assume the individual is able to rank this particular time allocation among all other conceivable time allocations, and we write the individual’s utility function as follows:

where U represents, for individual I, the utility level associated with the time pattern of consumption offered by his original endowment, and C represents the number of units of a consumption good available to the individual at the beginning of the i^th period of consumption (where i ranges over the n periods).

It may be useful to think of a prisoner of war camp where each of the prisoners is told in advance how many apples he will be given at each of n successive dates in the future. Each individual is absolutely certain that he will obtain that number of apples on schedule as promised.8 Now suppose that after this information, is disclosed, each prisoner is given the option of transferring some of the apples promised in remoter consumption periods to periods more proximate. For example, an individual may request that an apple promised in period number 10 be supplied in period number 3. Also, if we assume that storage costs are zero, individuals can always move apples from earlier periods to later periods simply by holding them in the form of inventory.9 In such a world each individual will redistribute his consumption stream over time so that he can achieve a preferred level of satisfaction over the whole planning period. Let us represent this preferred allocation as follows:

where U^d₁ represents the desired level of satisfaction of individual I and C represents the desired number of apples to be consumed in the i^th period. As should be clear from the description of the problem, the arithmetic sum of apples consumed over the entire planning horizon must be equal to the sum of apples promised in the original situation, that is,

Stated another way, if we define net borrowing between any two periods as

then the sum of net borrowing over the entire planning horizon must be zero, or

3. It is clear that, if the individual chooses to increase his apple consumption in some periods, he must decrease it in other periods by an exact amount.10 The utility maximizing allocation has the property that the marginal utility of apple consumption is roughly equal in each period, or the marginal rate of substitution between apples in any two periods is equal to unity and is the same for all individuals.11 It may at first seem that the marginal utility of an apple scheduled to be received x periods in the future must be perceived as being of smaller intensity than it will actually turn out to be when that period of consumption is reached.12 It may be realistic to assume this in actual life situations where individuals often fail to provide adequately for their old age, but in our model the assumption of perfect knowledge assures us that no such shortsighted valuation takes place. The individual is equipped with the power to project his feelings (or value orderings) forward in time and anticipate quite accurately what his future requirements will be.

It is apparent that individuals starting out with identical apple endowments will not necessarily arrive at identical consumption plans. Economists such as Irving Fisher and more recently Gary Becker tried to say something more definite about the relationship between individual tastes and final consumption patterns. For this purpose they distinguished among positive, negative, and zero (or neutral) time preference.13 An individual who possesses positive time preference will, when given an equal endowment of apples in two adjacent periods, trade more than one future apple for one present apple. On the other hand the individual who is willing to give up more than one present apple for a future apple when his endowment of apples is the same in the two adjacent periods is said to possess negative time preference (though we would not observe such a trade, as I shall argue below). Finally, an individual satisfied with an equal number of apples in each time period is said to display neutral or zero time preference. Since any one of these three situations is evidence for what Mises called “time preference,” he must have meant by the term something different from what has become standard terminology among neoclassical economists.

In Mises’ view an individual demonstrates time preference in any period simply by consuming some apples in that period rather than none at all. If (in terms of our n-period model) an individual reallocated his apple endowment so that he consumed nothing in the first n-1 periods and everything in the last period, we would have a situation close to what Mises described as the absence of time preference.14 According to Mises, the very act of consuming during the planning period demonstrates (positive) time preference. In Mises’ writings this concept might better be termed time allocation than time preference.

I do not wish to enter into a discussion of which definition of time preference is best for modern economics. I do wish to point out, however, that (1) the Misesian notion of time preference (that is, time allocation) does not make use of the notion of “choice at the margin,” or at least it is obscure as to what and where the notion of the margin might enter into such a definition;15 and (2) when semantic considerations are put aside, there is no fundamental issue separating Mises from the remainder of the economics profession. A great deal of confusion has resulted from Mises’ frequent use of the expression time preference to mean time allocation without indicating that his special use of the term was different from that of those whom he credited with originating the concept.16

4. We may now ask whether Mises was correct when he insisted that time allocation gives rise to a market for claims to future consumption (that is, a bond market) with a positive rate of interest. Obviously, we would not observe a negative interest rate in our model of a pure exchange economy where storage costs are assumed to be zero. No one would trade a present apple for a claim to less than one future apple when he could obtain a whole future apple simply by storing the present apple until that later date. If consumption goods could be transferred not only from the present to the future but also from the future to the present, no one would find it economical to trade a claim for more than one unit of future consumption goods for a unit of present goods when that same present good could be obtained more cheaply by transferring goods back through time. In a world with this type of symmetrical time transfer, an individual time allocator would trade only with himself, and there would be no economic incentive to create a market in which claims on future goods are exchanged.

It is only when we drop the assumption that apples can be transferred from the future to the present (though present apples can still be held for future consumption) that a (bond) market will merge in which claims to future apples are exchanged. Here individuals who want more than one future apple for a present apple and are unable to acquire that apple from their future endowment induce others by means of an interest payment to give up some of their current stock of apples. The actual market rate of interest will move to equate the supply of, and demand for, goods. Furthermore, the equilibrium interest rate can never fall below zero, because individuals can always hold present goods until a later period at zero cost.

The existence of an organized market in which claims to future consumption are traded now makes it possible for a single individual’s total n-period consumption to be greater or less than his total aggregate apple endowment. Whether it will be greater or less depends, of course, on whether over the n periods he was a net interest payer or receiver. It remains true, however, that total apple consumption for the entire society must equal total apple endowment when both totals are summed over all individuals and all periods. That is,

where all symbols are defined as before and j ranges over all k members of society. It is interesting to point out the major difference between a pure exchange economy and an economy with production and exchange: Production removes the constraint on societal consumption represented by equation (6). With production it is possible for all members of society simultaneously to reduce present consumption and have future consumption rise by an even greater amount. It was this phenomenon Böhm-Bawerk had in mind when he wrote of the productivity of roundabout methods of production.17 It is not my purpose here to explore any further the interesting dynamics of the production economy.

5. In conclusion, we say that in a pure exchange economy a market will emerge in which claims to future consumer goods are sold at positive prices. If it were technologically possible to order up future goods ahead of time (and storage costs were zero), then no economizing individual would pay more than one unit of a present good for a claim to a future good. In such a world, there would be no economic incentive to create a bond market, and a zero rate of interest would prevail. It is only because of the asymmetry in the time market, namely, that present goods can be costlessly transferred to the future but future goods cannot be conjured to the present, that we have every reason to expect the emergence of a market for claims to future goods along with a positive interest rate.

Thus, interest will emerge in a Socialist economy as it does in a market economy because time allocation proceeds in a world where the present gradually unfolds into the future rather than the other way around. Mises’ attempt to present a purely subjective time preference (read “time allocation”) theory of interest must at the very least admit the empirical or broadly technological assumption that the transfer of goods through time is indeed a one-way street.

NOTES

[1]Ludwig von Mises, Human Action: A Treatise on Economics(Chicago: Henry Regnery Co., 1966), pp. 479–90; idem, “A Critique of Böhm-Bawerk’s Reasoning in Support of His Time Preference Theory,” in Percy L. Greaves, Jr., Mises Made Easier: A Glossary for Ludwig von Mises’ Human Action (New York: Free Market Books, 1974), pp. 150–57.

[2]See Israel M. Kirzner, “Ludwig von Mises and the Theory of Capital and Interest,” in The Economics of Ludwig von Mises: Toward a Critical Reappraisal, ed. Laurence S. Moss (Kansas City: Sheed & Ward, 1976), pp. 61–65. Kirzner wrote, “Mises’ views on capital and on interest may be conveniently summarized as follows ... interest expresses the universal—phenomenon of time preference and will therefore inevitably emerge also in a pure exchange economy without production” (p. 53).

We are trying to explain what Mises called “originary interest,” which is the market rate of interest less a premium for uncertainty (or risk) and less the anticipated rate of price inflation.

[3]Mises, Human Action, pp. 458, 528, 532.

[4]On Fetter’s contribution, see the introduction to Frank A. Fetter, Capital, Interest, and Rent: Essays in the Theory of Distribution, ed. Murray N. Rothbard (Kansas City: Sheed Andrews and McMeel, 1977), pp. 1–24. On Mises’ adoption and subsequent dissatisfaction with Böhm-Bawerk’s theory, see Ludwig von Mises, The Theory of Money and Credit (New Haven: Yale University Press, 1959), p. 24; Kirzner, “Mises and the Theory of Capital,” p. 52; and Mises, “A Critique of Böhm-Bawerk’s Reasoning in Support of His Time Preference Theory,” in Percy L. Greaves, Jr., Mises Made Easier (New York: Free Market Book, 1974), pp. 150–57.

[5]See Ludwig M. Lachmann, “On Austrian Capital Theory,” in The Foundations of Modern Austrian Economics, ed. Edwin G. Dolan (Kansas City: Sheed & Ward, 1976), pp. 145–51.

[6]Cf. Friedrich A. Hayek, “Time Preference and Productivity: A Reconsideration,” Economica 12 (February 1945): 22–25.

[7]Murray N. Rothbard, Man, Economy, and State,2 vols. (New York: D. Van Nostrand, 1962), 1:350–56.

[8]Cf. R. A. Radford, “The Economic Organization of a P.O.W. Camp,” Economica 12 (November 1945): 189–201.

[9]I am also assuming that the apples do not spoil and that there is no possibility of theft or accidental destruction.

[10]There are no fraudulent traders in our model economy; accordingly, without production one cannot promise to pay more than one’s assets will allow.

[11]If the marginal utility of an apple in period m is significantly greater than the marginal utility in period n, then the individual would do better to reallocate his apples out of period-n consumption and into period-m consumption. By the familiar law of diminishing returns the marginal utility of apples in period m falls and rises in period n. This will continue so long as the marginal utilities in any two periods are larger than some value say ⊘, i.e.,

When (MUm−MUn) > ⊘ then apples are transferred from period n to period m.The size of ⊘ depends on the perceived opportunity costs of making such a transfer. This last value will differ among individuals. When ⊘ is small and the same for all consumers, then reallocation will continue until

MUm = MUn. Multiplying both sides of this equality by ΔA and dividing by MUn yields,

MUm/MUn = ΔA/ΔA Now the left-hand side is the marginal rate of substitution for any individual and the right-hand side the “terms of trade” between period m and n which is 1 by the assumptions of this model.

[12]This is an important point. Böhm-Bawerk and other writers tried to explain interest by postulating a psychological tendency for individuals to systematically undervalue their future needs. Besides being bad psychology, in that it disregards at the very least the paranoid miser who does quite the opposite, such misvaluation is ruled out by my assumption of certainty about future conditions and needs. Cf. Mises, “A Critique of Böhm-Bawerk’s Reasoning,” pp. 150–55.

[13]Irving Fisher, The Theory of Interest as Determined by Impatience to Spend Income and Opportunity to Invest It (New York: Macmillan Co., 1930), pp. 61–68; see also, for example, Gilbert R. Ghez and Gary S. Becker, The Allocation of Time and Goods over the Life Cycle (New York: National Bureau of Economic Research, 1975), pp. 8–14.

[14]This is how I interpret the following passage by Mises in the context of an n-period model: “Whoever eats and consumes anything is making a choice between a satisfaction in the immediate future and one in the more distant future. If he were to decide differently, that is, if he were not to prefer the earlier to the later satisfaction, he would never be able to consume at all. He could not even eat and consume tomorrow, because when tomorrow became today, and the day after tomorrow became tomorrow, the decision to consume would still call for valuing an earlier satisfaction more than a later satisfaction. Otherwise, consumption would have to be delayed still further” (Mises, “A Critique of Böhm-Bawerk’s Reasoning,” p. 157).

[15]See Roger W. Garrison, “Reflections on Misesian Time Preference” (paper presented at Seminar in Austrian Economics, University of Virginia, April 1975), pp. 4–5.

[16]Mises, Human Action, p. 489; see also Garrison, “Reflections,” pp. 9–13.

[17]Eugen von Böhm-Bawerk, “Positive Theory of Capital,” in Capital and Interest, trans. George D. Hunche and Hans F. Sennholz (South Holland, Ill.: Libertarian Press; 1959), pp. 10–12.