The Rationale of the Demand for Money and of ‘Money Illusion’

Abstract

Consider the following propositions: (1) Each individual maximizes a utility function that depends only on the amounts of various goods he will consume during a period that begins after the marketing date and during which no further exchanges takes place; (2) The numéraire (i.e., the thing whose price is fixed at unity) is neither a consumption nor a production good; (3) At least one individual has positive money stock. Condition (1) defines a ‘static’ or ‘uniperiod’ model; (2) defines paper money; (3) excludes the regimes of ‘money-of-account’.

Jointly, these three conditions imply: (4) Prices of consumption goods that would clear the (perfect) market are infinite. That is, market equilibrium is not compatible with (1), (2), (3) taken jointly. This was proved mathematically in Patinkin’s first article and verbally by Phipps. It is difficult to understand why either of them could think they disagree.

Now replace (3) by: (3′) All money stocks are zero. (1), (2), (3′) jointly imply: (4′) Prices (also called absolute prices) of consumption goods are indeterminate; their ratios (so- called relative prices) are determinate and finite. Leontief s paper consists, in effect, in describing such a system: the regime of money-of-account.

Since in the system (1), (2), (3′), (4′) money stocks are zero, this system cannot be supplemented by the so-called equation of exchange making positive absolute prices proportional to the total money stock. This contradiction is present in what Hickman described as the ‘classical’ combination of a theory of formation of relative prices (determined in the ‘commodity-sector’ where utilities are maximized and markets cleared) with the equation of exchange (or ‘monetary sector’), in a regime of paper money.

To reconcile finite and determinate absolute prices of consumers’ goods with positive stocks of paper money, one can drop the ‘static’ condition (1). Replace it by: (1′) Each individual maximizes a utility function which depends not only on present but also on future consumption flows; he will be able to exchange stocks of goods and of money at future marketing dates. If some but not all individuals expect the prices of all goods to fall, these individuals will demand positive money stocks; at the same time the prices of goods will be determinate, positive, and finite.

This implies sharp alternations between an individual’s bearish ‘flight into money’ and bullish ‘flight into (certain) goods’. More realistic, smooth fluctuations of stocks are obtained if we introduce market imperfection, including transaction costs. If barter is excluded, one can define ‘illiquidity’ of a good as the slope of the marginal money revenue and marginal money outlay curve of the individual considered, respectively, as a seller and a buyer of this good. The individual demand for stocks of various goods and of money, given expected shifts in that curve, will depend on their degrees of illiquidity: for speculative purchase to be followed by resale, a relatively ‘liquid’ good (and money in particular) is preferred.

It is neither necessary nor sufficient to introduce uncertainty in order to explain positive stocks of money and the smooth fluctuation of these stocks.

Any system that admits positive demand for paper money stocks has also to admit that a change in the absolute prices of goods (the cheapening or appreciation of paper money in terms of goods) induces the individual to change his holdings of money relative to his holding and consumption of goods. Hence, there is ‘money illusion’ in all systems except that of money-of-account.

Presented at the Meeting of Econometric Society in New York City, December 1949. Acknowledgments are due to Donald Fort for his valuable remarks in class discussions back in 1946; to Karl Brunner and William Hood for their comments on earlier versions of the present paper; and to Milton Friedman and Leonid Hurwicz for suggestions. Added in 1974. The recent work of Jurg Niehans is relevant.