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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
MICHAEL J. GOOTZEIT (*)
ABSTRACT. When the money supply increased exogenously, Marshall's vs. Wicksell's versions of short run inflation transmission are shown to be different because of their ideas on money demand. During the approach to monetary equilibrium, the implication was that the demand for transactions cash balances would have to increase in order for inflation to stop. Marshall focused on the real, while Wicksell focused on the nominal, demand for such balances; Marshall assumed velocity of money was constant, while Wicksell assumed it to be pro-cyclic. These assumptions about money demand caused them to make different predictions on how much prices would eventually rise: Marshall described a price-undershoot, while Wicksell described a price-overshoot mechanism.
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Introduction
THE EVOLUTION OF THE (CAMBRIDGE) "CASH-BALANCE" version of the quantity theory focused on the role of real income ([Y.sub.R]) or velocity (V) in affecting prices. If these two variables were assumed to remain constant, then the simple quantity theory would predict the price level to change in proportion to a change in the money supply (M). If a more "sophisticated" version of the quantity theory were to be considered, one in which [Y.sub.R] or V was allowed to change, then the price level could be predicted to change in a different proportion than the change in the money supply. This type of result, which may be traced back to the late part of the 19th century, would be much more realistic and it would conform to the predictions of more modern macro models.
This paper will show that both Marshall and Wicksell constructed such a sophisticated version of the quantity theory. It will be shown that Marshall allowed a direct connection between M and [Y.sub.R] not so much in his major writings, but in his Parliamentary testimony, so the conclusion he gave that allowed prices (P) to increase less than in proportion to a change in M after a period of deflation has not been emphasized in the literature. It will also be shown that Wicksell's treatment of the "simple credit" economy allowed him to show a direct relation between M, V, and P, although [Y.sub.R] remained constant at its full employment level. P will thus be shown to be capable of increasing more than in proportion to the M increase. This type of model is also not emphasized in the literature, which prefers instead to discuss the "pure cash" and the "pure credit" models, two extremes and both "imaginary" cases. (See Laidler 1991:128-29, his use of the term "imaginary" is quoted from Wicksell 1898:70. (1)) By default, the simple credit model (one that uses cash or gold and convertible bank-notes and rudimentary credit instruments) is the one case in Wicksell that illustrates a more of a realistic relation between M, V, and P. But, it is also the case Wicksell spent less time and care to describe in his major works.
Both of these writers integrated the "Cambridge cash balance" version of transaction money demand into their predictions about how prices would change in response to a change in M. This implies that they had a concept of monetary equilibrium, where money supply equals money demand, and that (M, V, [Y.sub.R], P) would change as the economy adjusts toward this level, even if it never gets there. But, they did not describe the same versions of money demand. Marshall used a "real" and Wicksell used a "nominal" balance version of this concept. This accounts for their predictions about how money demand would adjust to changes in money supply and their differences on how the macro variables listed above would change during this monetary transmission process. It will be shown that Marshall's predictions of price changes during an upward cycle were more realistic than Wicksell's, partly because of this theoretical difference on what caused money demand to change.
II
The Role of SQT in Late 19th-Century Explanations of Price Variation
HOW DID THE QUANTITY THEORY EVOLVE in the late 19th century? This question has not been satisfactorily answered by writings in the history of economics. It seems clear that the quantity theory was generally invoked to explain price changes and it also appears that most uses of it did not attribute such variation simply to changes in the money stock, however defined. Therefore, besides changes in M, variations in V and [Y.sub.R] had become potential explanations of changes in P. This idea has become known as the "sophisticated quantity theory" (SQT) in the 20th century and it has been used extensively in theoretical and empirical expositions related to the explanation of price variation. Moreover, SQT examines the role that changes in (V,[Y.sub.R]) play in causing price fluctuations by describing the concept of the transaction demand for money ([M.sub.D]). If the money market tends to remain in equilibrium, an increase in M would have to be matched by an equal increase in [M.sub.D]. If the percent increase in [M.sub.D] equals the percent increase in nominal income (Y), V will remain constant. Moreover, whether V is constant or not, P need not increase in proportion to the increase in M.
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