Dictionary of Arguments

Philosophical and Scientific Issues in Dispute

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Disputed term/author/ism	Author	Entry	Reference
Capital	Solow	Harcourt I 7 Capital/Measurements/return on investment/Fisher/SolowVsFisher/Solow/Harcourt: Solow [1963a⁽¹⁾, 1966⁽²⁾, 1967⁽³⁾, 1970⁽⁴⁾]: Solow's purpose was, in part, to get away from the obstacles of the measurement of capital and its related problems by developing instead the concept of the rate of return on investment. His own contributions were to graft technical progress on to Fisher's analysis and to apply the resulting concepts empirically, in order to obtain estimates of the orders of magnitude of the rates of return on investment in post-war U.S.A. and West Germany. >Irving Fisher. Joan RobinsonVsSolow: It is argued that neither in theory nor in empirical work has Solow been able completely to escape from the need to define and measure aggregate capital and to work within the confines of a one-commodity model. >Aggregate Capital. Harcourt I 46 Capital/SolowVsRobinson/Solow/Harcourt: Solow's comment in Solow [1956a]⁽⁵⁾ on Joan Robinson's [1953-4]⁽⁶⁾ article: Solow investigated the conditions under which it would be legitimate to aggregate heterogeneous capital items into a single figure, no doubt having in mind his subsequent econometric studies. >Econometrics. He found that the conditions were very stringent - the rate at which one capital good could be substituted for another had to be independent of the amounts of labour which subsequently would be used with each. (He discusses in this context a neoclassical model in which continuous substitution is possible, not the discrete case of Joan Robinson's article, but he also looks at the latter towards the end of his article.) >Neoclassical economics. His conclusion is quoted in full below because it is an extremely clear statement of the stand that he takes in the debates that followed: „I conclude that discreteness is unlikely to help matters. Only in very special cases will it be possible to define a consistent measure of capital-in-general. Some comfort may be gleaned from the reflection that when capital-labour ratios differ widely we hardly need a subtle index to tell us so, and when differences are slight we are unlikely to believe what any particular index says.“ (p. 108.)⁽⁵⁾ Harcourt: For Solow, 'Capital as a number is not an issue of principle. All rigorously valid results come from n-capital-good models. In particular there is no justification ever for supposing that output can be made a function of labour and the VALUE of capital whose partial derivatives do the right thing.' Capital as a number is purely an aid to empirical work 'and you want to get away with the smallest dimensionality possible' (Solow [1969]⁽⁷⁾). >Capital, >Economic models. Harcourt: Had the contestants been content to leave the discussion here, the literature of the following years might have served to generate far more light - and certainly a lot less heat.* >Cambridge Capital Controversy. Harcourt I 92 Capital/Solow/Swan/Harcourt: Solow's basic puzzle concerning a simple, unique measure of capital which in fact has many dimensions and characteristics has been put splendidly by Swan [1956]⁽¹⁰⁾ as follows: „That there should be great difficulties in handling the concept of Capital in a process of change is not surprising. A piece of durable equipment or a pipe-line of work-in-progress has dimensions in time that bind together sequences of inputs and outputs jointly demanded or jointly-supplied at different dates. The aggregation of capital into a single stock at a point of time is thus the correlative of an aggregation of the whole economic process, not only in crosssection (which gives rise to the ordinary index-number problems), but also in time itself: in other words, the reduction of a very highorder system of lagged equations - in which each event, its past origins and its future consequences, could be properly dated and traced backward and forward in time-to a more manageable system with fewer lags. This second kind of aggregation introduces a further set of ambiguities, similar in principle to those of indexnumbers, but as yet hardly investigated . . . From the idea of capital as a single stock there is in principle no sudden transition to 'the enormous who's who of all the goods in existence'. Between the two extremes lies an ascending scale of nth-order dynamic systems, in which capital like everything else is more and more finely subdivided and dated, with ascending degrees of (potential) realism and (actual) complexity. In fact, most of us are left at ground-level, on ground that moves under our feet.“ (p. 345.) Solow/Harcourt: As a self-confessed middlebrow, Solow sees the rate of return on investment as the link between highbrow capital theory - Harcourt I 93 the microeconomic theory of resource allocation and prices which allows for the fact that commodities can be transformed into others over time and which is only complete when it also explains the distribution between factors - and lowbrow theory, which is concerned with aggregation and approximation and relates to the empirical implications of saving and investment decisions. By analysing these problems in terms of a rate of return, i.e. a price, we take cognizance of the fact that 'the theory of capital has as its "dual" a theory of intertemporal pricing . . .' (Solow [1963a]⁽¹¹⁾, p. 14.) >Return on investment/Solow. * Solow's latest statement of these views is in Solow [1970](8), pp. 424 and 427-8 (but see, also, Pasinetti [1970](9), pp. 428-9). 1. Solow, R. M [1963] 'Heterogeneous Capital and Smooth Production Functions: An Experimental Study', Econometrica, xxxi, pp. 623-45. 2. Solow, R. M., Tobin, J., von Weizsacker, C. C. and Yaari, M. [1966] 'Neoclassical Growth with Fixed Factor Proportions', Review of Economic Studies, xxxm, pp. 79-115. 3. Solow, R. M. [1967] 'The Interest Rate and Transition between Techniques', Socialism, Capitalism and Economic Growth, Essays presented to Maurice Dobb, ed. by C. H. Feinstein (Cambridge: Cambridge University Press), pp. 30-9. 4. Solow, R. M [1970] 'On the Rate of Return: Reply to Pasinetti.Economic Journal, LXXX, pp.423-8. 5. Solow, R. M. [1956a] 'The Production Function and the Theory of Capital', Review of Economic Studies, xxin, pp. 101-8. 6. Robinson, Joan (1953-4). 'The Production Function and the Theory of Capital', Review of Economic Studies, xxi. 7. Solow, R. M. [1969] Letter to author. 8. Solow, R. M. [1970] 'On the Rate of Return: Reply to Pasinetti Economic Journal, LXXX, pp.423-8. 9.Pasinetti, L.L. [1970] 'Again on Capital Theory and Solow's "Rate of Return" ', Economic Journal, LXXX, pp. 428-31. 10.. Swan, T. W. [1956] 'Economic Growth and Capital Accumulation', Economic Record, xxxn, pp. 334-61. 11. Solow, Robert M. [1963a] (Professor Dr. F. De Vries Lectures, 1963) Capital Theory and the Rate of Return (Amsterdam: North-Holland).	Solow I Robert M. Solow A Contribution to the Theory of Economic Growth Cambridge 1956 Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972
CES Production Function	Fisher	Harcourt I 174 Cobb-Douglas production function/CES production function/F. M. Fisher/Harcourt: [In] F. M. Fisher [1970]⁽¹⁾, (…) he reports the results of a simulation experiment. His main conclusion is that if the real world behaves in such a way as to throw up, say, a constant share of wages, or a linear relationship in the logarithms between productivity and wages, it is these findings which explain the 'apparent success' of the Cobb-Douglas and CES production functions respectively rather than the other way around. „. . . the view that the constancy of labour's share is due to the presence of an aggregate Cobb-Douglas production function is mistaken. Causation runs the other way and the apparent success of aggregate Cobb-Douglas functions is due to the relative constancy of labour's share.“ (p. 4.) The present results suggest... that the explanation of that wageoutput per man relationship may not be in the existence of an aggregate CES but rather that the apparent existence of an aggregate CES may be explained by that relationship.“ (p. 32.) Econometrics/HarcourtVsFisher, F. M.: Fisher appears to have been too literal in his understanding of the nature of the econometric hypotheses involving the Cobb-Douglas and the CES functions. Their proponents have never believed that they actually existed, only that it may be useful to interpret trends in real world observations 'as if they were observations thrown up by a jelly world of either the Cobb-Douglas or CES variety. Harcourt I 175 Distribution/factor prices/Harcourt: If, then, a small (but, I like to think, significant) section of the trade is convinced that the distribution of income and factor prices cannot be explained either within the system of production alone or, relevantly, as the outcome of a general equilibrium system even when (because) we use marginal productivity notions and modern programming methods, factors and forces elsewhere in the economic system - and other than these - must be introduced. >Measurements/Sraffa. 1. Fisher, F. M. [1970] 'Aggregate Production Functions and the Explanation of Wages: A Simulation Experiment', Working Paper 61, Department of Economics, M.I.T.	F.M. Fisher I Franklin M. Fisher Disequilibrium Foundations of Equilibrium Economics (Econometric Society Monographs) Cambridge 1989 Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972
Currency in Circulation	Rothbard	Rothbard III 760 Currency in Circulation/Rothbard: At any one time there is a given total stock of the money commodity. This stock will, at any time, be owned by someone. RothbardVsFisher, Irving: It is therefore dangerously misleading to adopt the custom of American economists since Irving Fisher's day of treating money as somehow "circulating," or worse still, as divided into "circulating money" and "idle money."⁽¹⁾This concept conjures up the image of the former as moving somewhere at all times, while the latter sits idly in "hoards." This is a grave error. There is, actually, no such thing as "circulation," and there is no mysterious arena where money "moves." At any one time all the money is owned by someone, i.e., rests in someone's cash balance. >Cash balance/Rothbard, >Money/Rothbard, >Demand for money/Rothbard. Whatever the stock of money, therefore, people's actions must bring it into accord with the total demand for money to hold (…). For even pre-income money acquired in exchange must be held at least momentarily in one's cash balance before being transferred to someone else's balance. Total demand for money/market: All total demand is therefore to hold (…) Total stock must therefore be brought into agreement, on the market, with the total quantity of money demanded. >Purchasing power/Rothbard. 1. Cf. Irving Fisher, The Purchasing Power of Money (2nd ed.; New York: Macmillan & Co., 1913).	Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Equation of Exchange	Fisher	Rothbard III 830 Equation of Exchange/Fisher/Rothbard: The classic exposition of the equation of exchange was in Irving Fisher's Purchasing Power of Money.⁽¹⁾ Fisher describes the chief purpose of his work as that of investigating "the causes determining the purchasing power of money." Money is a generally acceptable medium of exchange, and purchasing power is rightly defined as the "quantities of other goods which a given quantity of goods will buy.“⁽²⁾ He explains that the Iower the prices of goods, the larger will be the quantities that can be bought by a given amount of money, and therefore the greater the purchasing power of money. Vice versa if the prices of goods rise. Rothbard III 831 RothbardVsFisher, Irving: This is correct; but then comes this flagrant non sequitur: "In Short, the purchasing power of money is the reciprocal of the level of prices; so that the Study of the purchasing power of money is identical with the Study of price levels.“⁽³⁾ Rothbard: From then on, Fisher proceeds to investigate the causes of the "price level"; thus, by a simple "in short," Fisher has leaped from the real world of an array of individual prices for an innumerable list of concrete goods into the misleading fiction of a "price level," without discussing the grave diffculties which any such concept must face. >Price level/Fisher. Rothbard III 832 Def price level/Fisher/Rothbard: The "price level" is allegedly determined by three aggregative factors: the quantity of money in circulation, its "velocity of circulation" - the average number of times during a period that a unit of money is exchanged for goods - and the total volume of goods bought for money. These are related by the famous equation of exchange: MV = PT. M - Money supply V - Velocity of circulation P – Price level T - Expenditures This equation of exchange is built up by Fisher in the following way: Def price level/Fisher: First, consider an individual exchange transaction - Smith buys 10 pounds of sugar for 7 cents a pound.⁽⁴⁾ An exchange has been made, Smith giving up 70 cents to Jones, and Jones transferring 10 pounds of sugar to Smith. From this fact Fisher somehow deduces that "10 pounds of sugar have been regarded as equal to 70 cents, and this fact may be expressed thus: 70 cents = 10 pounds multiplied by 7 cents a pound.⁽⁵⁾ RothbardVsFisher: This off-hand assumption of equality is not self-evident, as Fisher apparently assumes, but a tangle of fallacy and irrelevance. Value/equality/valuation: Who has "regarded" the 10 pounds of sugar as equal to the 70 cents? Certainly not Smith, the buyer of the sugar. He bought the sugar precisely because he considered the two quantities as unequal in value; to him the value of the sugar was greater than the value of the 70 cents, and that is why he made the exchange. On the other hand, Jones, the seller of the sugar, made the exchange precisely because the values of the two goods were unequal in the opposite direction, i.e., he valued the 70 cents more than he did the sugar. Exchange/RothbardVsAristotle: There is thus never any equality of values on the part of the two participants. The assumption that an exchange presumes some sort of equality has been a delusion of economic theory since Aristotle, and it is surprising that Fisher, an exponent of the subjective theory of value in many respects, fell into the ancient trap. Equality: There is certainly no equality of values between two goods exchanged or, as in this case, between the money and the good. Is there an equality in anything else, and can Fisher's doctrine be salvaged by finding such an equality? Obviously not; there is no equality in weight, length, or any other magnitude. But to Fisher, the equation represents an equality in value between the "money Side" and the "goods side"; (…). Rothbard III 833 Fisher: „[T]he total money paid is equal in value to the total value of the goods bought. The equation thus has a money side and a goods Side. The money side is the total money paid.... The goods side is made up of the products of quantities of goods exchanged multiplied by respective prices.“⁽⁶⁾ Rothbard III 834 Equation of exchange: Fisher considers that this equation yields the significant information that the price is determined by the total money spent divided by the total supply of goods sold. RothbardVsFisher: Actually, of course, the equation, as an equation, tells us nothing about the determinants of price; thus, we could set up an equally truistic equation (…) This equation is just as mathematically true as the other, and, on Fisher's own mathematical grounds, we could argue cogently that Fisher has "left the important wheat price out of the equation." We could easily add innumerable equations with an infinite number of complex factors that "determine" price. Solution/Rothbard: The only knowledge we can have of the determinants of price is the knowledge deduced logically from the axioms of praxeology. ((s) I.e. from subjective valuations in the course of human action.) >Praxeology/Rothbard. Rothbard III 835 Determinants of price/Fisher: If we consider the equation of exchange as revealing the determinants ofprice, we find that Fisher must be implying that the determinants are [e.g.,] the "70 cents" and the "10 pounds of sugar." RothbardVsFisher: But it should be clear that things cannot determine prices. Things, whether pieces of money or pieces of sugar or pieces of anything else, can never act; they cannot set prices or supply and demand schedules. All this can be done only by human action: only individual actors can decide whether or not to buy; only their value scales determine prices. >Value/Rothbard, >Price level/Fisher. Rothbard III 839 Weighted average/Solution/Fisher: Fisher's more complicated concept of a weighted average, with the prices weighted by the quantities of each good sold, solves the problem of units in the numerator but not in the denominator: P = pQ + p’Q‘ + p‘‘Q‘‘ / Q + Q‘ + Q‘‘. RothbardVsFisher: The pQs are all money, but the Q's are still different units. Thus, any concept of average price level involves adding or multiplying quantities of completely different units of goods, such as butter, hats, sugar, etc., and is therefore meaningless and illegitimate. Even pounds of sugar and pounds of butter cannot be added together, because they are two different goods and their valuation is completely different. And if one is tempted to use poundage as the common unit of quantity, what is the pound weight of a concert or a medical or legal service?⁽⁷⁾ Equation of Exchange/RothbardVsFisher: It is evident that PT, in the total equation of exchange, is a completely fallacious concept. While the equation E = pQf or an individual transaction is at least a trivial truism, although not very enlightening, the equation E = PT for the whole society is a false one. Neither P nor T can be defined meaningfully, and this would be necessary for this equation to have any validity. We are left only with E = pQ + p'Q', etc., which gives us only the useless truism, E =E.⁽⁸⁾ >Velocity of circulation/Fisher. Rothbard III 840 Rothbard: In fact, since V is not an independently defined variable, M must be eliminated from the equation as well as V, and the Fisherine (and the Cambridge) equation cannot be used to demonstrate the "quantity theory of money." And since M and V must disappear, there are an infinite number of other "equations of exchange" that we could, with equal invalidity, uphold as "determinants of the price level." Thus, the aggregate stock of sugar in the economy may be termed s, and the ratio of E to the total stock of sugar may be called "average sugar turnover," or U. This new "equation of exchange" would be: SU = PT, and the stock of sugar would suddenly become a major determinant of the price level. Or we could substitute A = number of salesmen in the country, and x = total expenditures per salesman, or "salesmen turnover," to arrive at a new set of "determinants" in a new equation. And so on. >Quantity theory. 1. Fisher, Irving, Purchasing Power of Money, 2nd ed. New York: Macmillan, [1913] 1926. Reprinted as volume 4 of The Works of Irving Fisher, William J. Barber and James Tobin, eds. Pickering, 1997. especially pp. 13 ff. 2. Ibid., p. 13. 3. Ibid., p. 14. 4. We are using "dollars" and "cents" here instead of weights of gold for the sake of simplicity and because Fisher himself uses these expressions. 5. Fisher, Purchasing Power of Money, p. 16. 6. Ibid., p. 17. 7. For a brilliant critique of the disturbing effects of averaging even when a commensurable unit does exist, see Louis M. Spadaro, "Averages and Aggregates in Economics" in on Freedom and Free Enterprise, pp. 140-60. 8. See Clark Warburton, "Elementary Algebra and the Equation of Exchange," American Economic Review, June, 1953, pp. 3 58-61. Also see Mises, Human Action, p. 396; B.M. Anderson, Jr., The Value of Money (New York: Macmillan & Co., 1926), pp. 154-64; and Greidanus, Value of Money, pp. 59-62.	F.M. Fisher I Franklin M. Fisher Disequilibrium Foundations of Equilibrium Economics (Econometric Society Monographs) Cambridge 1989 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Income Tax	Economic Theories	Rothbard III 916 Income tax/Economic theories/Rothbard: (…) an income tax will shift the social proportion toward more consumption and less saving and investment. >Income tax/Rothbard, >Time preference/Rothbard. VsTime preference: It might be objected that the time-preference reason is invalid, since the government offcials and the people they subsidize will receive the tax revenues and find that their money stock has increased just as that of the taxpayers has declined. Saving/Investments/RothbardVsVs: (…) no truly productive savings and investments can be made by government, its employees, or the recipients of its subsidies. Saving/Investments/economic theories/VsIncome tax: Some economists maintain that income taxation reduces savings and investment in society in yet a third way. They assert that income taxation, by its very nature, imposes a "double" tax on savings-investment as against consumption.⁽¹⁾ The reasoning runs as follows: Saving and consumption are really not symmetrical. Saving: All saving is directed toward enjoying more consumption in the future; otherwise, there would be no point at all to saving. Saving is abstaining from possible present consumption in return for the expectation of increased consumption at some time in the future. No one wants capital goods for their own sake. They are only the embodiment of increased consumption in the future. ⁽²⁾ Rothbard: This line of reasoning correctly explains the investment-consumption process. RothbardVsFisher, Irving: [Fisher’s theory] suffers, however, from a grave defect: it is irrelevant to problems of taxation. It is true that saving is a fructifying agent. But the point is that everyone knows this; that is precisely why people save. Rothbard III 917 Time preference/saving/Rothbard: Yet, even though they know that saving is a fructifying agent, they do not save all their income. Why? Because of their time preferences for present consumption. >Time preference/Rothbard. Every individual, given his current income and value scales, allocates that income in the most desirable proportions between consumption, investment, and additions to his cash balance. >Cash balance/Rothbard. Any other allocation would satisfy his desires less well and Iower his position on his value scale. The fructifying power of saving is already taken into account when he makes his allocation. Double penalizing: There is therefore no reason to say that an income tax doubly penalizes saving-investment; it penalizes the individual's entire standard of living, encompassing present consumption, future consumption, and his cash balance. It does not per se penalize saving any more than the other avenues of income allocation. >Neutral taxation/Rothbard, >Neutral taxation/Economic theories, >Cost principle/Rothbard, >Benefit principle/Rothbard. 1. Thus, cf. Irving and Herbert W. Fisher, Constructive Income Taxation (New York: Harper & Bros., 1942). "Double" is used in the sense of two instances, not arithmetically twice. 2. These economists generally conclude that not income, but only consumption, should be taxed as the only "real" income.	Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Marginal Utility	Mises	Rothbard IV 13 Money/Marginal Utility/Mises/Rothbard: Ludwig von Mises set out to repair [the] split [between money, “price levels,” “national product,” and spending], and to ground the economics of money and its purchasing power (miscalled the “price level”) on the Austrian analysis of the individual and the market economy: to arrive at a great integrated economics that would explain all parts of the economic system.⁽¹⁾ >Austrian School. Rothbard IV 14 Individuals/MisesVsFisher, Irving: At last, economics was whole, an integrated body of analysis grounded on individual action; there would have to be no split between money and relative prices, between micro and macro. The mechanistic Fisherine view of automatic relations between the quantity of money and the price level, of “velocities of circulation” and “equations of exchange” was explicitly demolished by Mises on behalf of an integrated application of the marginal utility theory to the supply and demand for money itself. >Irving Fisher. Specifically, Mises showed that, just as the price of any other good was determined by its quantity available and the intensity of consumer demands for that good (based on its marginal utility to the consumers), so the “price” or purchasing power of the money-unit is determined on the market in the very same way. In the case of money, its demand is a demand for holding in one’s cash balance (in one’s wallet or in the bank so as to spend it sooner or later on useful goods and services). The marginal utility of the money unit (the dollar, franc, or gold-ounce) determines the intensity of the demand for cash balances; and the interaction between the quantity of money available and the demand for it determines the “price” of the dollar (i.e., how much of other goods the dollar can buy in exchange). Quantity theory: Mises agreed with the classical “quantity theory” that an increase in the supply of dollars or gold ounces will lead to a fall in its value or “price” (i.e., a rise in the prices of other goods and services); but he enormously refined this crude approach and integrated it with general economic analysis. >Quantity theory. Rothbard IV 15 Marginal utility/Mises: (…) [von Mises] showed that this movement is scarcely proportional; an increase in the supply of money will tend to lower its value, but how much it does, or even if it does at all, depends on what happens to the marginal utility of money and hence the demand of the public to keep its money in cash balances. Furthermore, Mises showed that the “quantity of money” does not increase in a lump sum: the increase is injected at one point in the economic system and prices will only rise as the new money spreads in ripples throughout the economy. If the government prints new money and spends it, say, on paper clips, what happens is not a simple increase in the “price level,” as non-Austrian economists would say; what happens is that first the incomes and the prices of paper clips increase, and then the prices of the suppliers of the paper clip industry, and so on. So that an increase in the supply of money changes relative prices at least temporarily, and may result in a permanent change in relative incomes as well. >Money supply/Mises. Rothbard IV 16 Marginal utility/Money/Mises/Rothbard: In applying marginal utility to money, Mises had to overcome the problem which most economists saw as insuperable: the so-called “Austrian circle.” Economists could see how the prices of eggs or horses or bread could be determined by the respective marginal utilities of these items; but, unlike these goods, which are demanded in order to be consumed, money is demanded and kept in cash balances in order to be spent on goods. No one, therefore, can demand money (and have a marginal utility for it) unless it already was in existence, commanding a price and purchasing power on the market. But how then can we fully explain the price of money in terms of its marginal utility if money has to have a pre-existing price (value) in order to be demanded in the first place? Regression theorem: In his “Regression theorem,” Mises overcame the “Austrian circle” in one of his most important theoretical achievements; for he showed that logically one can push back this time component in the demand for money until the ancient day when the money commodity was not money but a useful barter commodity in its own right; in short, until the day when the money-commodity (e.g., gold or silver) was demanded solely for its qualities as a consumable and directly usable commodity. >Regression theorem. Not only did Mises thus complete the logical explanation of the price or purchasing power of money, but his findings had other important implications. For it meant that money could only originate in one way: on the free market, and out of the direct demand in that market, for a useful commodity. And this meant that money could not have originated either by the government proclaiming something as money or by some sort of one-shot social contract; it could only have developed out of a generally useful and valuable commodity. Menger had previously shown that money was likely to emerge in this way; but it was Mises who established the absolute necessity of this market origin of money. Value of money/Rothbard: But this had still further implications. For it meant, in contrast to the views of most economists then and now, that “money” is not simply arbitrary units or pieces of paper as defined by the government: “dollars,” “pounds,” “francs,” etc. Money must have originated as a useful commodity: as gold, silver, or whatever. The original money unit, the unit of account and exchange, was not the “franc” or the “mark” but the gold gram or the silver ounce. Rothbard IV 17 Gold standard/Central Banks/Mises/Rothbard: This analysis, combined with Mises’s demonstration of the unmitigated social evils of the government’s increase of the supply of arbitrarily produced “dollars” and “francs,” points the way for a total separation of government from the monetary system. For it means that the essence of money is a weight of gold or silver, and it means that it is quite possible to return to a world when such weights will once again be the unit of account and the medium of monetary exchanges. A gold standard, far from being a barbarous fetish or another arbitrary device of government, is seen able to provide a money produced solely on the market and not subject to the inherent inflationary and redistributive tendencies of coercive government. A sound, non-governmental money would mean a world where prices and costs would once more be falling in response to increases in productivity. >Gold standard/Mises, >Marginal Utility/Austrian School. Rothbard IV 19/20 Marginal utility/Mises/Rothbard: Building on the insight of his fellow student at the Böhm-Bawerk seminar, the Czech, Franz Cuhel, Mises devastatingly refuted the idea of marginal utility being in any sense measurable, and showed that marginal utility is a strictly ordinal ranking, in which the individual lists his values by preference ranks (“I prefer A to B, and B to C”), without assuming any mythological unit or quantity of utility. Rothbard IV 20 If it makes no sense to say that an individual can “measure his own utility,” then it makes even less sense to try to compare utilities between people in society. Yet statists and egalitarians have been trying to use utility theory in this way throughout this century. If you can say that each man’s marginal utility of a dollar falls as he accumulates more money, then cannot you say also that the government can increase “social utility,” by taking a dollar away from a rich man who values it little and giving it to a poor man who will value it highly? Mises/Rothbard: Mises’s demonstration that utilities cannot be measured completely eliminates the marginal utility case for egalitarian policies by the State. And yet, while economists generally pay lip service to the idea that utility cannot be compared between individuals, they presume to go ahead and try to compare and sum up “social benefits” and “social costs.” Rothbard IV 58 Thus, if we take the utility to the consumer of a carton of a dozen eggs, it is impermissible to make this utility some sort Rothbard IV 59 of a "total utility," in some mathematical relation to the "marginal utility of one egg." Instead, we are merely dealing with marginal utilities of different-sized units. In one case a dozen-egg package, in the other case of one egg. The only thing we can say about the two marginal utilities is that the marginal utility of a dozen eggs is worth more than one egg. Period. Mises's correction of his mentors was consistent with the fundamental Austrian methodology of focusing always on the real actions of individuals, and allowing no drift into relying on mechanistic aggregates.⁽²⁾ >Individuals/Austrian School. 1. Ludwig von Mises. 1912. The Theory of Money and Credit (Theorie des Geldes und der Umlaufsmittel, Translated by H.E. Batson in 1934; reprinted with “Monetary Reconstruction» (New Haven, Conn.: Yale University Press, 1953). Reprinted by the Foundation for Economic Education, 1971; reprinted with an Introduction by Murray N. Rothbard, Liberty Press Liberty Classics, 1989. 2. For a discussion of this point, see Murray N. Rothbard, Toward a Reconstruction of Utility and Welfare Economics (New York: Center for Libertarian Studies, [1956] 19 77), pp. 9-15. Franz Cuhel's contribution is in his Zur Lehre von den Bedürfnissen (Innsbruck, 1906), pp. 186ff. Böhm-Bawerk's attempt to refute Cuhel can be found in Eugen von Böhm-Bawerk, Capital and Interest (South Holland, 111.: Libertarian Press, 1959), 111, pp. 124-36.	EconMises I Ludwig von Mises Die Gemeinwirtschaft Jena 1922 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Market Interest Rate	Fisher	Rothbard III 792 Market Interest Rate/Fisher, Irving/Rothbard: Many economists, beginning with Irving Fisher, have asserted that the market rate of interest, in addition to containing specific entrepreneurial components superimposed on the pure rate of interest, also contains a "price" or a "purchasing-power component." Purchasing power: When the purchasing power of money is generally expected to rise, the theory asserts that the market rate of interest falls correspondingly; when the PPM (purchasing power of monetary unit) is expected to fall, the theory declares that the market rate of interest rises correspondingly. RothbardVsFisher, Irving: These economists erred by concentrating on the Ioan rate rather than on the natural rate (the rate of return). The reasoning behind this theory was as follows: If the purchasing power of money is expected to change, then the pure rate of interest (determined by time preference) will no longer be the same in "real terms." Suppose that 100 gold ounces exchange for 105 gold ounces a year from now - i.e., that the rate of interest is 5 percent. Now, suddenly, let there be a general expectation that the purchasing power of money will increase. In that case, a Iower amount to be returned, say 102 ounces, may yield 5 percent real interest in terms of purchasing power. A general expectation of a rise in purchasing power, therefore, will Iower the market rate of interest at present, while a general expectation of a fall in purchasing power will raise the rate.⁽¹⁾ Rothbard III 793 RothbardVsFisher, Irving. There is a fatal defect in this generally accepted line of reasoning. Suppose, for example, that prices are generally expected to fall by 50 percent in the next Year. Would someone lend 100 gold ounces to exchange for 53 ounces one year from now? Why not? This would certainly preserve the real interest rate at 5 percent. But then why should the would-be lenders not simply hold on to their money and double their real assets as a result of the price fall? And that is precisely what they would do; they certainly would not give money away, even though their real assets would be greater than before. FisherVsVs: Fisher simply shrugged off this point by saying that the purchasing-power premium could never make the interest rate negative. But this flaw vitiates the entire theory. Rothbard III 794 Natural rate of interest: The root of the diffculty consists in ignoring the natural rate of interest. Let us consider the interest rate in those terms. Then, suppose 100 ounces are paid for factors that will be transformed in one year into a product that sells for 105 gold ounces, for an interest gain of five and an interest return of 5 percent. Now a general expectation arises of a general halving of prices one year from now. The selling price of the product will be 53 ounces in a year's time. What happens now? Will entrepreneurs buy factors for 100 and sell at 53 merely because their real interest rate is preserved? Certainly not. They will do so only if they do not at all anticipate the change in purchasing power. But to the extent that it is anticipated, they will hold money rather than buy factors. This will immediately Iower factor prices to their expected future levels, say from 100 to 50. Loan rate: What happens to the Ioan rate is analytically quite trivial. It is simply a reflection of the natural rate and depends on how the expectations and judgment of the people on the Ioan market compare with those on the stock and other markets. Free market/Rothbard: For the free economy, there is no point in separately analyzing the Ioan market. Analysis of the Fisher problem - the relation of the interest rate to price changes - should concentrate on the natural rate of interest. 1. Irving Fisher, The Rate of Interest (New York, 1907), chap. v, xiv; idem, Purchasing Power of Money, pp. 56-59.	F.M. Fisher I Franklin M. Fisher Disequilibrium Foundations of Equilibrium Economics (Econometric Society Monographs) Cambridge 1989 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Measurements	Solow	Harcourt I 7 Capital/Measurements/return on investment/Fisher/SolowVsFisher/Solow/Harcourt: Solow [1963a⁽¹⁾, 1966⁽²⁾, 1967⁽³⁾, 1970⁽⁴⁾]: Solow's purpose was, in part, to get away from the obstacles of the measurement of capital and its related problems by developing instead the concept of the rate of return on investment. His own contributions were to graft technical progress on to Fisher's analysis and to apply the resulting concepts empirically, in order to obtain estimates of the orders of magnitude of the rates of return on investment in post-war U.S.A. and West Germany. >Irving Fisher. Joan RobinsonVsSolow: It is argued that neither in theory nor in empirical work has Solow been able completely to escape from the need to define and measure aggregate capital and to work within the confines of a one-commodity model. >Aggregate Capital. Harcourt I 116 Measurements/Solow/Harcourt: Realized expectations and perfect foresight are needed strictly to justify all Solow's results. >Expectations. Capital, rates of profits, etc., cannot be measured unless this is so, for past investments could not be weighted by their appropriate [values] (which themselves might no longer be appropriate). The calculations of the man of words would have irretrievably - and forever - parted company with those of the man of deeds, as Joan Robinson would say. >Joan Robinson. Comparisons taken from pseudo-production functions bear not at all on the out-of-equilibrium processes that have occurred. >Pseudo-production function, >Aggregate production function, >Cobb-Douglas production function. Harcourt: This approach to analysis is not, of course, confined to one side alone. And it should also be pointed out that the calculations are carefully hedged round with appropriate qualifications and a fine sense of the empirical orders of magnitude involved. Harcourt I 117 HarcourtVsSolow: Nevertheless, the analysis is an illegitimate extrapolation of results that hold only for a one commodity, malleable capital world in which the short run and the long run collapse into one and perfect foresight and realized expectations are guaranteed. >One-commodity model. With social rates of return somewhere in between, the inevitable implication is that something or someone needs to give a nudge to bring them all closer together. Otherwise the divergencies between social and private risks will continue to have unfortunate consequences for the social wellbeing of the economies concerned. >Return on investment/Solow. 1. Solow, R. M [1963] 'Heterogeneous Capital and Smooth Production Functions: An Experimental Study', Econometrica, xxxi, pp. 623-45. 2. Solow, R. M., Tobin, J., von Weizsacker, C. C. and Yaari, M. [1966] 'Neoclassical Growth with Fixed Factor Proportions', Review of Economic Studies, xxxm, pp. 79-115. 3. Solow, R. M. [1967] 'The Interest Rate and Transition between Techniques', Socialism, Capitalism and Economic Growth, Essays presented to Maurice Dobb, ed. by C. H. Feinstein (Cambridge: Cambridge University Press), pp. 30-9. 4. Solow, R. M [1970] 'On the Rate of Return: Reply to Pasinetti. Economic Journal, LXXX, pp.423-8.	Solow I Robert M. Solow A Contribution to the Theory of Economic Growth Cambridge 1956 Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972
Money	Mises	Parisi I 269 Money/Institutions/Mises: In the same spirit of Menger’s explanation for the emergence of money, Mises attempted to explain the emergence of legal rules. Mises argued that property law originally arose from recognition of simple possession, and contract law from primitive acts of exchange within localized areas. While the former may have had as its primary motive the avoidance of violence and the creation of peaceful conditions, the latter was almost bound to arise under conditions of de facto property in order to pursue the gains from exchange. >Carl Menger. But ultimately the world created by these early efforts produced institutions that could be viewed as “a settlement, an end to strife, an avoidance of strife” and thus “their result, their function” is to produce peace within a community (Mises, 1981/1922⁽¹⁾, p. 34). Mises built on the argument made much earlier by Adam Smith, though Smith’s focus is not on violence but on trade. For Smith, individuals have a natural propensity to “truck, barter and exchange” (Smith, 1981/1776⁽²⁾, p. 15). >Ludwig von Mises. 1. Mises, L. v. (1981/1922). Socialism: An Economic and Sociological Analysis. Indianapolis, IN: Liberty Fund. 2. Smith, A. (1981/1776). An Inquiry into the Nature and Causes of the Wealth of Nations, Vols. I–V. Indianapolis, IN: Liberty Fund. Rajagopalan, Shruti and Mario J. Rizzo “Austrian Perspectives on Law and Economics.” In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. Rothbard IV 13 Money/Marginal Utility/Mises/Rothbard: Ludwig von Mises set out to repair [the] split [between money, “price levels,” “national product,” and spending], and to ground the economics of money and its purchasing power (miscalled the “price level”) on the Austrian analysis of the individual and the market economy: to arrive at a great integrated economics that would explain all parts of the economic system.⁽¹⁾ >Austrian School. Rothbard IV 14 Individuals/MisesVsFisher, Irving: At last, economics was whole, an integrated body of analysis grounded on individual action; there would have to be no split between money and relative prices, between micro and macro. The mechanistic Fisherine view of automatic relations between the quantity of money and the price level, of “velocities of circulation” and “equations of exchange” was explicitly demolished by Mises on behalf of an integrated application of the marginal utility theory to the supply and demand for money itself. >Irving Fisher. Specifically, Mises showed that, just as the price of any other good was determined by its quantity available and the intensity of consumer demands for that good (based on its marginal utility to the consumers), so the “price” or purchasing power of the money-unit is determined on the market in the very same way. In the case of money, its demand is a demand for holding in one’s cash balance (in one’s wallet or in the bank so as to spend it sooner or later on useful goods and services). The marginal utility of the money unit (the dollar, franc, or gold-ounce) determines the intensity of the demand for cash balances; and the interaction between the quantity of money available and the demand for it determines the “price” of the dollar (i.e., how much of other goods the dollar can buy in exchange). Quantity theory: Mises agreed with the classical “quantity theory” that an increase in the supply of dollars or gold ounces will lead to a fall in its value or “price” (i.e., a rise in the prices of other goods and services); but he enormously refined this crude approach and integrated it with general economic analysis. >Quantity theory. Rothbard IV 15 Marginal utility/Mises: (…) [von Mises] showed that this movement is scarcely proportional; an increase in the supply of money will tend to lower its value, but how much it does, or even if it does at all, depends on what happens to the marginal utility of money and hence the demand of the public to keep its money in cash balances. Furthermore, Mises showed that the “quantity of money” does not increase in a lump sum: the increase is injected at one point in the economic system and prices will only rise as the new money spreads in ripples throughout the economy. If the government prints new money and spends it, say, on paper clips, what happens is not a simple increase in the “price level,” as non-Austrian economists would say; what happens is that first the incomes and the prices of paper clips increase, and then the prices of the suppliers of the paper clip industry, and so on. So that an increase in the supply of money changes relative prices at least temporarily, and may result in a permanent change in relative incomes as well. >Money supply/Mises. Rothbard IV 16 Marginal utility/Money/Mises/Rothbard: In applying marginal utility to money, Mises had to overcome the problem which most economists saw as insuperable: the so-called “Austrian circle.” Economists could see how the prices of eggs or horses or bread could be determined by the respective marginal utilities of these items; but, unlike these goods, which are demanded in order to be consumed, money is demanded and kept in cash balances in order to be spent on goods. No one, therefore, can demand money (and have a marginal utility for it) unless it already was in existence, commanding a price and purchasing power on the market. But how then can we fully explain the price of money in terms of its marginal utility if money has to have a pre-existing price (value) in order to be demanded in the first place? Regression theorem: In his “Regression theorem,” Mises overcame the “Austrian circle” in one of his most important theoretical achievements; for he showed that logically one can push back this time component in the demand for money until the ancient day when the money commodity was not money but a useful barter commodity in its own right; in short, until the day when the money-commodity (e.g., gold or silver) was demanded solely for its qualities as a consumable and directly usable commodity. >Regression theorem. Not only did Mises thus complete the logical explanation of the price or purchasing power of money, but his findings had other important implications. For it meant that money could only originate in one way: on the free market, and out of the direct demand in that market, for a useful commodity. And this meant that money could not have originated either by the government proclaiming something as money or by some sort of one-shot social contract; it could only have developed out of a generally useful and valuable commodity. Menger had previously shown that money was likely to emerge in this way; but it was Mises who established the absolute necessity of this market origin of money. Value of money/Rothbard: But this had still further implications. For it meant, in contrast to the views of most economists then and now, that “money” is not simply arbitrary units or pieces of paper as defined by the government: “dollars,” “pounds,” “francs,” etc. Money must have originated as a useful commodity: as gold, silver, or whatever. The original money unit, the unit of account and exchange, was not the “franc” or the “mark” but the gold gram or the silver ounce. Rothbard IV 17 Gold standard/Central Banks/Mises/Rothbard: This analysis, combined with Mises’s demonstration of the unmitigated social evils of the government’s increase of the supply of arbitrarily produced “dollars” and “francs,” points the way for a total separation of government from the monetary system. For it means that the essence of money is a weight of gold or silver, and it means that it is quite possible to return to a world when such weights will once again be the unit of account and the medium of monetary exchanges. A gold standard, far from being a barbarous fetish or another arbitrary device of government, is seen able to provide a money produced solely on the market and not subject to the inherent inflationary and redistributive tendencies of coercive government. A sound, non-governmental money would mean a world where prices and costs would once more be falling in response to increases in productivity. >Gold standard/Mises, >Marginal Utility/Austrian School. 1. Ludwig von Mises. 1912. The Theory of Money and Credit (Theorie des Geldes und der Umlaufsmittel, Translated by H.E. Batson in 1934; reprinted with “Monetary Reconstruction» (New Haven, Conn.: Yale University Press, 1953). Reprinted by the Foundation for Economic Education, 1971; reprinted with an Introduction by Murray N. Rothbard, Liberty Press Liberty Classics, 1989.	EconMises I Ludwig von Mises Die Gemeinwirtschaft Jena 1922 Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Money Supply	Keynesianism	Mause I 222f Money Supply/Keynesianism/KeynesianismVsFisher: From the perspective of recent Keynesian approaches, the commercial banking sector (...) could provide the money supply that is needed from the right side of the equation... M x V = Y ^real x P ^Y = Y ^nom. M: Money supply - V: Speed of circulation - P: Price level - T: Transactions - Y: Gross domestic product ... - i.e. from the amount produced and the prevailing prices - by reducing or expanding the production of bank deposits accordingly. In this case, the causal chain is completely reversed; it now runs from right to left in Fisher's traffic equation. If this is the case, other explanations for observable economic or inflation fluctuations must be provided and the direction of monetary policy must be adjusted accordingly.	Mause I Karsten Mause Christian Müller Klaus Schubert, Politik und Wirtschaft: Ein integratives Kompendium Wiesbaden 2018
Price Level	Fisher	Rothbard III 837 Price level/Fisher/Rothbard: Fisher, attempting to find the causes of the price level, has to proceed further. Cf. Equation of exchange/Fisher. MV = PT. M - Money supply V - Velocity of circulation P – Price level T (or Q) - Expenditures RothbardVsFisher: (…) even for the individual transaction, the equation p = (E/Q) (price equals total money spent divided by the quantity of goods sold) is only a trivial truism and is erroneous when one tries to use it to analyze the determinants of price. (This is the equation for the price of sugar in Fisherine symbolic form.) Fort he whole community: How much worse is Fisher's attempt to arrive at such an equation for the whole community and to use this to discover the determinants of a mythical "price level"! Rothbard: for simplicity's sake, let us take only the two transactions of A and B, for the sugar and the hat. Total money spent, E, clearly equals $ 10.70, which, of course, equals total money received, pQ + p'Q'. Average price level: But Fisher is looking for an equation to explain the price level; therefore he brings in the concept of an "average price level," P, and a total quantity of goods sold, T, such that E is supposed to equal PT. But the transition from the trivial truism E = pQ + p'Q' ... to the equation E = PT cannot be made as blithely as Fisher believes. Indeed, if we are interested in the explanation of economic life, it cannot be made at all. RothbardVsFisher: For example, for the two transactions (or for the four), what is T? How can 10 pounds of sugar be added to one hat or to one pound of butter, to arrive at T? Obviously, no such addition can be performed, and therefore Fisher's holistic T, the total physical quantity of all goods exchanged, is a meaningless concept and cannot be used in scientific analysis. Problem: If T is a meaningless concept, then p must be also, since the two presumably vary inversely if E remains constant. And what, indeed, of P? Here, we have a whole array of prices, 7 cents a pound, $ 10 a hat, etc. Price level: What is the price level? Clearly, there is no price level here; there are only individual prices of specific goods. But here, error is likely to persist. Solution/Fisher: Cannot prices in some way be "averaged" to give us a working definition of a price level? This is Fisher's solution. Prices of the various goods are in some way averaged to arrive at P, then P = (E/T), and all that remains is the diffcult "statistical" task of arriving at T. Average: RothbardVsFisher: However, the concept of an average for prices is a common fallacy. It is easy to demonstrate that prices can never be averaged for different commodities; we shall use a simple average for our example, but the same conclusion applies to any sort of "weighted average" such as is recommended by Fisher or by anyone else. Rothbard III 838 What is an average? Reflection will show that for several things to be averaged together, they must first be totaled. In order to be thus added together, the things must have some unit in common, and it must be this unit that is added. Only homogeneous units can be added together. E.g., 7 cents/1 pound of sugar + 1000 cents/1 hat. Can these two prices be averaged in any way? Can we add 1,000 and 7 together, get 1,007 cents, and divide by something to get a price level? Obviously not. Simple algebra demonstrates that the only way to add the ratios in terms of cents (certainly there is no other common unit available) is as follows: (7 hats + 100 pounds of sugar) cents/(hats) (pounds of sugar). RothbardVsFisher: Obviously, neither the numerator nor the denominator makes sense; the units are incommensurable. Weighted average/Solution/Fisher: Fisher's more complicated concept of a weighted average, with the prices weighted by the quantities of each good sold, solves the problem of units in the numerator but not in the denominator: P = pQ + p’Q‘ + p‘‘Q‘‘ / Q + Q‘ + Q‘‘ RothbardVsFisher: The pQs are all money, but the Q's are still different units. Thus, any concept of average price level involves adding or multiplying quantities of completely different units of goods, such as butter, hats, sugar, etc., and is therefore meaningless and illegitimate. Even pounds of sugar and pounds of butter cannot be added together, because they are two different goods and their valuation is completely different. And if one is tempted to use poundage as the common unit of quantity, what is the pound weight of a concert or a medical or legal service?⁽¹⁾ Equation of Exchange/RothbardVsFisher: It is evident that PT, in the total equation of exchange, is a completely fallacious concept. While the equation E = pQ for an individual transaction is at least a trivial truism, although not very enlightening, the equation E = PT for the whole society is a false one. Neither P nor T can be defined meaningfully, and this would be necessary for this equation to have any validity. We are left only with E = pQ + p'Q', etc., which gives us only the useless truism, E =E.⁽²⁾ >Equation of Exchange/Fisher, >Velocity of circulation/Fisher, >Quantity theory. 1. For a brilliant critique of the disturbing effects of averaging even when a commensurable unit does exist, see Louis M. Spadaro, "Averages and Aggregates in Economics" in on Freedom and Free Enterprise, pp. 140-60. 2. See Clark Warburton, "Elementary Algebra and the Equation of Exchange," American Economic Review, June, 1953, pp. 3 58-61. Also see Mises, Human Action, p. 396; B.M. Anderson, Jr., The Value of Money (New York: Macmillan & Co., 1926), pp. 154-64; and Greidanus, Value ofMoney, pp. 59-62.	F.M. Fisher I Franklin M. Fisher Disequilibrium Foundations of Equilibrium Economics (Econometric Society Monographs) Cambridge 1989 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977
Return on Investment	Solow	Harcourt I 7 Capital/Measurements/return on investment/Fisher/SolowVsFisher/Solow/Harcourt: Solow [1963a⁽¹⁾, 1966⁽²⁾, 1967⁽³⁾, 1970⁽⁴⁾]: Solow's purpose was, in part, to get away from the obstacles of the measurement of capital and its related problems by developing instead the concept of the rate of return on investment. His own contributions were to graft technical progress on to Fisher's analysis and to apply the resulting concepts empirically, in order to obtain estimates of the orders of magnitude of the rates of return on investment in post-war U.S.A. and West Germany. >Irving Fisher. Joan RobinsonVsSolow: It is argued that neither in theory nor in empirical work has Solow been able completely to escape from the need to define and measure aggregate capital and to work within the confines of a one-commodity model. >Aggregate Capital. Harcourt I 94 Return on investment/Solow/Harcourt: What, then, is the rate of return on investment? Consider a planned economy which has a stock of heterogeneous capital goods, produces a certain volume of one consumption good and is at full employment with its inputs efficiently allocated. (Efficient means only that it is impossible to have more of anything without less of something else.) Compare this situation with possible neighbourhood efficient arrangements in which there is a little less consumption and therefore more capital goods (in physical, not necessarily in value terms). Now change over to an alternative arrangement by saving, i.e. reducing consumption. This allows a one-period gain (the next) in consumption over what it would have been. Make sure that the biggest gain is chosen for a given reduction in consumption now. Finally suppose that in the period after the next the economy reaches the position that it intended to be at by that period anyway. That is, the economy over the three periods has had decided for it - we are all technocrats now - a consumption stream C₀ -h, C₁+j, C2, .. . instead of one of C₀, C₁, C₂, . . . Then a natural definition of the one-period rate of return on investment (R1) is R₁ = j-h/ h = j/h -1 . . .perfectly natural usage. For „technocrats“ see >Capital theory/Solow. Harcourt I 95 Saving/prices/implicit assumptions/Harcourt: We should note the vital importance in all these definitions of an implicit assumption either that saving may be transformed into investment without affecting relative prices or that we are analysing a one-commodity model. Without these assumptions, saving, in the sense of consumption forgone, will not necessarily add the additional consumption because, depending on how prices change, it will be associated with different amounts and types of investment. Hence Solow concentrates on small changes - the notional changes of the neoclassical procedure – and the prices corresponding to a switch-point rate of profits: see Solow [1967⁽⁵⁾, 1970⁽⁶⁾]. Measurements: Solow claims that calculating the rate of return requires no measure of the stock of capital, not even necessarily a mention of it, although in some of his theoretical examples and in his empirical work he is unfaithful to himself. He also claims that neoclassical theory, in so far as it centres around the rate of return, can escape from the malleability assumption and 'can accommodate fixity of form and proportions both' (p. 27). Malleability: As an aside but very much related to the malleability assumption, he comments that J. B. Clark's jelly assumption (see Stigler [1941]⁽⁷⁾, chapter xi, and Samuelson [1962]⁽⁸⁾) makes the analysis easier (…). Substitution: Moreover it contains the important kernel of truth that substitution possibilities are easier over longer periods of time even though at any moment of time capital goods may be highly specific and substitution possibilities ex post (if not ex ante) limited: see Hicks [1932]⁽⁹⁾, pp. 19-21. Harcourt I 96 SalterVsSolow: This seems to be literally true only if we are considering the working out in actual time of the possibilities which exist at the beginning of a Marshallian long period, while not allowing anything to change, other han what was expected to change at the start of the period. The application of results from this analysis to real-world happenings is, therefore, suspect, as Salter [1960⁽¹⁰⁾, 1965⁽¹¹⁾], for example, has so clearly shown. >Return on investment/Neo-Keynesianism. Harcourt I 96 SolowVsNeo-Keynesianism: Rates of return on investment are calculated by Solow for two 'poles apart' models of planned economies. The first is an all-purpose onecommodity model with a smooth, well-behaved, constant-returns-toscale production function; the second is Worswick's stockade dictator version of Joan Robinson's model of accumulation (see Worswick [1959]⁽¹²⁾). One-period and perpetuity rates of return are obtained and these are shown, in the neoclassical case, to equal the net marginal product of capital. Harcourt: The two extreme cases are chosen in order to show '. . . that the rate of return . . . does not depend for its existence and meaning on the possibility of defining "marginal productivities" or having smoothly variable proportions between the factors of production' (Solow [1963a],⁽¹³⁾ p. 30). Harcourt I 97 Saving/investments: These results are offered as the answer (or, rather, an answer) to the important question: What is the pay-off to society from an extra bit of saving transformed into capital formation? Harcourt I 110 Return on investment/Solow/Harcourt: Solow uses a Ricardo-Sraffa system with circulating capital; (…) he shows that the rate of interest is an accurate measure of the social rate of return on investment, provided only that the economy is at full employment and uses competitive pricing, and that we are comparing one stationary state with another which has the same labour force but uses, at the given rate of profits, a different equi-viable technique, namely one that requires more circulating capital, commodity by commodity. Both stationary states are in long-run competitive equilibrium; their net products consist entirely of consumption goods. In order for one economy to move (technocratically) from its technology to the other's, consumption must be cut in one period (or for a number of periods in more complicated cases). Solow shows that the extra consumption per period obtained in perpetuity as a result of this move, when expressed in terms of the common set of prices at the given rates of interest (and wages) and as a proportion of the consumption forgone, similarly measured, equals the rate of interest. Harcourt I 111 This ratio, (…) is Solow's measure of the rate of return in perpetuity, R_∞= p/h. 1. Solow, R. M [1963] 'Heterogeneous Capital and Smooth Production Functions: An Experimental Study', Econometrica, xxxi, pp. 623-45. 2. Solow, R. M., Tobin, J., von Weizsacker, C. C. and Yaari, M. [1966] 'Neoclassical Growth with Fixed Factor Proportions', Review of Economic Studies, xxxm, pp. 79-115. 3. Solow, R. M. [1967] 'The Interest Rate and Transition between Techniques', Socialism, Capitalism and Economic Growth, Essays presented to Maurice Dobb, ed. by C. H. Feinstein (Cambridge: Cambridge University Press), pp. 30-9. 4. Solow, R. M [1970] 'On the Rate of Return: Reply to Pasinetti. Economic Journal, LXXX, pp.423-8. 5. Solow, R. M. [1967] 'The Interest Rate and Transition between Techniques', Socialism, Capitalism and Economic Growth, Essays presented to Maurice Dobb, ed. by C. H. Feinstein (Cambridge: Cambridge University Press), pp. 30-9. 6. Solow, R. M [1970] 'On the Rate of Return: Reply to Pasinetti. Economic Journal, LXXX, pp.423-8. 7. Stigler, George J. [1941] Production and Distribution Theories: The Formative Period (New York: Macmillan). 8. Samuelson, P. A. [1962] 'Parable and Realism in Capital Theory: The Surrogate Production Function', Review of Economic Studies, xxix, pp. 193-206. 9. Hicks, J. R. [1932] The Theory of Wages (London: Macmillan). 10. Salter, W. E. G. [1960] Productivity and Technical Change (Cambridge: Cambridge University Press). 11. Salter, W. E. G. [1965] 'Productivity Growth and Accumulation as Historical Processes', Problems in Economic Development, ed. by E. A. G. Robinson (London: Macmillan), pp. 266-91. 12. Worswick, G. D. N. [1959] 'Mrs. Robinson on Simple Accumulation. A Comment with Algebra', Oxford Economic Papers, xi, pp. 125-41. 13. Solow, Robert M. [1963a] (Professor Dr. F. De Vries Lectures, 1963) Capital Theory and the Rate of Return (Amsterdam: North-Holland).	Solow I Robert M. Solow A Contribution to the Theory of Economic Growth Cambridge 1956 Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972
Velocity of Circulation	Fisher	Rothbard III 840 Velocity of Circulation/Fisher/Rothbard: Equation of Exchange/RothbardVsFisher: It is evident that PT, in the total equation of exchange, is a completely fallacious concept. While the equation E = pQ for an individual transaction is at least a trivial truism, although not very enlightening, the equation E = PT for the whole society is a false one. Neither P nor T can be defined meaningfully, and this would be necessary for this equation to have any validity. We are left only with E = pQ + p'Q', etc., which gives us only the useless truism, E =E.⁽²⁾ >Equation of Exchange/Fisher. Equation of exchange: MV = PT. M - Money supply V - Velocity of circulation P – Price level T (or Q) - Expenditures Cf. >Price level/Fisher. Velocity: Let us consider the other side of the equation, E = MV, the average quantity of money in circulation in the period, multiplied by the average velocity of circulation. V is an absurd concept. Even Fisher, in the case of the other magnitudes, recognized the necessity of building up the total from individual exchanges. He was not successful in building up T out of the individual Q's, P out of the individual p's, etc., but at least he attempted to do so. But in the case of V, what is the velocity of an individual transaction? Velocity is not an independently defined variable. Fisher, in fact, can derive V only as being equal in every instance and every period to E/M. If I spend in a certain hour $ 10 for a hat, and I had an average cash balance (or M) for that hour of $200, then, by definition, my V equals 1/20. I had an average quantity of money in my cash balance of $200, each dollar turned over on the average of 1 /20 of a time, and consequently I spent $ 10 in this period. RothbardVsFisher/RothbardVsVelocity of circulation: But it is absurd to dignify any quantity with a place in an equation unless it can be defined independently of the other terms in the equation. Fisher compounds the absurdity by setting up M and V as independent determinants of E, which permits him to go to his desired conclusion that if M doubles, and V and T remain constant, p - the price level - will also double. But since V is defined as equal to E/M, what we actually have is: M x (E/M) = PT or simply, E = PT, our original equation. Thus, Fisher's attempt to arrive at a quantity equation with the price level approximately proportionate to the quantity of money is proved vain by yet another route. >Price level/Fisher. Solution/Pigou/Robertson: A group of Cambridge economists - Pigou, Robertson, etc. - has attempted to rehabilitate the Fisher equation by eliminating V and substituting the idea that the total supply of money equals the total demand for money. RothbardVsPigou/RothbardVsRobertson: However, their equation is not a particular advance, since they keep the fallacious holistic concepts of P and T, and their k is merely the reciprocal of V, and suffers from the latter's deficiencies. Cf. >Neo-Fisher-Effect. Rothbard: In fact, since V is not an independently defined variable, M must be eliminated from the equation as well as V, and the Fisherine (and the Cambridge) equation cannot be used to demonstrate the "quantity theory of money." And since M and V must disappear, there are an infinite number of other "equations of exchange" that we could, with equal invalidity, uphold as "determinants of the price level." Thus, the aggregate stock of sugar in the economy may be termed s, and the ratio of E to the total stock of sugar may be called "average sugar turnover," or U. This new "equation of exchange" would be: SU = PT, and the stock of sugar would suddenly become a major determinant of the price level. Or we could substitute A = number of salesmen in the country, and x = total expenditures per salesman, or "salesmen turnover," to arrive at a new set of "determinants" in a new equation. And so on. >Quantity theory.	F.M. Fisher I Franklin M. Fisher Disequilibrium Foundations of Equilibrium Economics (Econometric Society Monographs) Cambridge 1989 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977

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