The Evolution of the Sophisticated Quantity Theory: Marshall vs. Wicksell on Transaction Demand - Focus on Economic Theory

American Journal of Economics and Sociology, The,  Oct, 2001  by Michael J. Gootzeit

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Wicksell mainly described his concept of money demand when he analyzed the functions of money (22) for the straightforward pure-cash and the slightly more complicated simple-credit economy in a way that was very similar to Marshall's "cash-balance" approach. This was especially true since Wicksell specifically used the "Cambridge-k" to analyze how velocity would be formed, specifically calling it "the average interval of rest of money" (Wicksell 1898:52) and defining it as "the reciprocal of velocity" (ibid.). (23) Yet, Wicksell's concept of cash balances was not identical to Marshall's and the Cambridge school because he was not specifically analyzing the demand for real purchasing power. Instead, he was only describing how the holding by individuals of nominal money balances would vary as their preferences changed in the short period.

This has been called "the money-balance variant" as distinguished from "the real-balance variant of the cash-balance approach," although the latter was the one "derived directly from Marshall" (Eshag 1963:20-21), when he analyzed "short period price fluctuations" (ibid., p. 6). This "money-balance" was not as sophisticated as the "real-balance" view because it "was almost identical with the classical version of the quantity theory, [since] the stock of money is measured and expressed in terms of money transactions or money payments" (ibid., p. 21); the nominal transactions function of money was emphasized. There was no consideration of variations in real transactions because Wicksell assumed short run full employment, so the demand for cash balances could not be affected by changes in the level of real output, only the volume of nominal transactions could affect it.

Even though Wicksell's cash-balance version of money demand was essentially nominal, the importance he placed on the expansion of credit (a real variable blended into a nominal analysis) during the upward GP, allowed him to justify inflation by focusing on the pro-cyclic nature of V during the cycle, not on an increase in the money stock. This was part of Wicksell's analysis of the price-transmission process both for the pure and for the simple-credit economy. Marshall, on the other hand, did not theorize about increases in V during the short run CP when he justified inflation. V was therefore implicitly assumed to remain constant and Marshall focused instead on the extent to which the demand for real cash-balances would increase. (24) If this demand were constant because real income was stable, price increases were strongly associated with changes in the money stock; if it could increase because a growth in real income was predicted, price increases were less important and not associated as much with changes in the stock of money, no matter how large the increase in the volume of credit.

Omitting all consideration of the short run CP as a cycle, Marshall, like Wicksell, focused exclusively on nominal cash balances in the "classical version of the quantity theory ... used by him in explaining long-period, or secular, price changes" (ibid., p. 5). But, even here, Marshall did not assume a proportional relation between M and p. Such an analysis seemed to have been meant instead to describe how important were "changes in the supply of precious metals" (Marshall 1923:19; also quoted in Eshag 1963:5) relative to "changes in the methods of business and the amounts of commodities" (Keynes 1926:54; also quoted in Eshag:5-6) in causing long period price fluctuations. Because of these latter real influences, prices would not necessarily increase in proportion to the increase in precious metals. (25) The literature on Marshall focuses more on this longer run aspect of his quantity theory and neglects how he used the quantity theory to describe his short run analysis of cycles.