¹ The idea of using chained, as opposed to direct, transactions is not new. A contemporary version is given in: K. Brunner, A. H. Meltzer, "The Uses of Money: Money in the Theory of an Exchange Economy", American Economic Review, December, 1971, p. 791. The idea is not without difficulties. Consider a simple, two-step exchange: good X (held by Trader X) for good Y (held by Trader Y), then Y for Z. X and Z cannot be traded directly because Trader Z does not want X and Trader Y does not want Z. In order for this sequences of trades to begin, it is necessary that Trader X knows that Trader Z wants Y and that Trader Y wants X. That is, Trader X must know the preferences of the other two. If this limited amount of information is lacking, indirect exchange is not possible and barter exchange must be confined to cases of one-to-one want coincidence.

It is possible to relax the condition that Trader X must know others' preferences. We can imagine Trader X encountering a series of traders until he finds one willing to buy X for something Trader X does not want. At this point, he becomes a speculator holding a commodity which is not in his utility function.

² Ibid., n. 4, p. 785.

³ See, for example: J. Nieghans, "Money and Barter in General Equilibrium with Transactions Costs", American Economic Review, December, 1971, p. 773; or Don Patinkin, Money, Interest, and Prices, New York, Harper and Row, 1965, pp. 3-12.

⁴ In other words, intertemporal exchange is hazardous; one always runs the risk of buying "a pig in a poke" when the goods to be exchanged are not on the table. The greater the number of variables that cannot be specified exactly in contracts, the greater the hazards attached to intertemporal exchange. A monetary unit does not remove all these hazards but it does reduce the possibilities of disputes over whether the deliveries specified in a contract are carried out. Thus, instead of specifying the future delivery of a basket of apples, one could require the delivery of ten dollars worth of apples. Systems of weights and measures, weigh scales, grading, etc. further reduce such hazards. In this connection see: John C. McManus, "The Costs of Alternative Economic Organizations", Canadian Journal of Economics, August, 1975, pp. 334-50. On the role of contract law and the courts in the exchange process, see: Paul Davidson, "Money and the Real World", Economic Journal, March, 1972, pp. 101-15.

⁵ K. Brunner, A. H. Meltzer, op. cit., p. 800.

⁶ Patinkin, op. cit., pp. 531-40, especially pp. 536-7.

⁷ For an experimental investigation of the efficacy of Walrasian tatonnement, see: W. D. Cook, E. C. H. Veendorp, "Six Markets in Search of an Auctioneer", Canadian Journal of Economics, May, 1975, pp. 238-57. The conclusion they draw from their experiments is: "the results offer little support for the Walrasian adjustment hypothesis" (p. 238). Cook and Weendorp, however, seem to have missed the spirit and point of Walras' theory. His problem, in a nutshell, was whether real world markets operate in a fashion sufficiently similar to the auction that the logic of his systems of equations is preserved. It was only necessary to establish that prices are adjusted in the real world by the same rules as prevail in the auction.

⁸ See, for example: J. R. Hicks, Value and Capital, 2nd ed., Oxford, The Clarendon Press, 1946, p. 129.

⁹ G. Stigler, "The Economics of Information", Journal of Political Economy, June, 1961, pp. 213-25.

¹⁰ The proposition that an individual might be prevented from engaging in the search by a lack of resources of course implies imperfect capital markets. Were this not so, it would be possible, through the banking system, for an individual to transform future income prospects into current resources.

¹¹ This is a central theme of chapter seventeen, "The Essential Properties of Interest and Money" in J. M. Keynes, The General Theory of Employment, Interest and Money, London, MacMillan, 1936. For a lengthy examination of this aspect of Keynes' work, see: T. M. Rymes, "Keynes and the Essential Properties of Interest and Money", a paper presented to the meeting of the Canadian Economics Association, June, 1974, Toronto, Canada. More generally, as T. M. Rymes has suggested to me, holding money permits one to postpone decision-making when available information is inadequate. Professor Rymes contrasts this Keynesian view of "waiting", that is, abstinence from spending until the time is ripe with the classical view of waiting. Our approach is more in tune with that of Rymes whose comments are deeply appreciated and, hopefully, not misconstrued.

¹² If this perception of money is accurate, it is nevertheless an ex post facto argument which must assume memory of past prices on the part of transactors, or else how could one thing become a "standard of value". Moreover, for standard of value status to emerge and be maintained, certain money prices must have been established and proven stable. If so, the attainment of general equilibrium must be an iterative rather than simultaneous process. In this connection, I have argued that the general determinacy of prices in fact requires that certain key prices be set either by historical precedent or by central authorities. See: A. K. Kelly, "A Comment on the Price Level in Classical Monetary Theory", Canadian Journal of Economics, May, 1974, pp. 321-25.

¹³ The process is straightforward enough: if we accept that there are very few commodities whose prices are subject to "higgling and haggling" between buyers and sellers and, further, that prices are put on goods by sellers (they attach price stickers), then it is the actions of sellers, in response to the activities of buyers, which cause prices to change. Buyers who detect and avoid high prices, or flock to low prices, will generate unexpectedly low or high sales for sellers setting prices high or low respectively. The former will set lower sticker prices; the latter will set higher sticker prices. As in a Walrasian world, quantity discrepancies will produce appropriate price adjustments. Clustering of prices, rather than a single price in a market, can be explained by diminishing returns to price searching by buyers and to price revisions by sellers. No violation of the principle of marginal cost pricing is involved; rather, costs and revenues are merely redefined.

¹⁴ These views were given eloquent expression by Karl Polanyi. See: "Our Obsolete Market Mentality", in George Dalton, ed., Primitive Archaic and Modern Economies, Essays of Karl Polanyi, New York, Anchor Books, 1968. This last characteristic of primitive societies was described by Polanyi as follows: "In effect, the individual is not in danger of starving unless the community as a whole is in a like predicament. It is this absence of the menace of individual destitution that makes primitive society … more humane than nineteenth-century society, and at the same time less economic". (p. 66).

¹⁵ In Patinkin's neo-classical reconstruction, for example, transactors simply have money balances "… carried over from the proceeding week" (Patinkin, op. cit., p. 14).

¹⁶ Within the ceteris paribus condition, we include individual differences in such things as intelligence.

¹⁷ These propositions—that the costs of procuring information about commodities are related to characteristics of the commodities; and that specialists in price information will emerge—are very similar to the first postulates employed by Brunner and Meltzer to explain the emergence of a medium of exchange. (See: Brunner and Meltzer, op. cit., p. 786).

¹⁸ Axel Leijonhufvud, On Keynesian Economics and the Economics of Keynes, London, Oxford, 1968.

¹⁹ R. Clower, "The Keynesian Counter-Revolution: A Theoretical Appraisal", in F. Brechling, F. Hahn, eds., The Theory of Interest Rates, London, Macmillan, 1965.

²⁰ In The Triumph of Conservatism (Chicago, Quadrangle, 1963), Gabriel Kolko argued that the growth of government regulation of the economy that characterized the Progressive era in the United States was really an effort by government on behalf of American business to preserve the status quo in the face of the threats of more intense competition, the growing radicalism of the labour movement and Populist political forces (p. 285-6).

²¹ J. F. Muth, "Rational Expectations and the Theory of Price Movements", Econometrica, 1961, vol. 29, pp. 315-35. T. J. Sargent, and Neil Wallace, "Rational Expectations and the Theory of Economic Policy", Journal of Monetary Economics, 1976, vol. 2, pp. 169-83.

²² T. K. Rymes, "Money, Efficiency and Knowledge", Canadian Journal of Economics, November, 1979, p. 579.