The beast which John Stuart Mill let out of the cage, the "pure" quantity theory of Hume, was to be picked up first by Simon Newcomb (1885) and then, most famously, by Irving Fisher in his Purchasing Power of Money (1911). The theory can be succinctly stated by referring to the infamous "equation of exchange" these two economists introduced:
where M is money, V is velocity, P the price level and T the level of transactions. Behind the restatement of the old Quantity Theory by Newcomb-Fisher, then, we have three pillars: firstly, that V and T are fixed with respect to the money supply. Secondly, that the supply of money is exogenous. Thirdly, the direction of causation runs from left (MV) to right (PT). These last two pillars are the most crucial, for as we noted, Ricardo accepted the first proposition, but reversed the direction of causation and thus endogenized the supply of money. Smith, Thornton and Wicksell also had endogenous money. The story of the Quantity Theory then runs like this: since V and T are fixed and M is exogenous, then an increase in the supply of money will lead to an exactly proportionate increase in the price level. Thus, money supply expansions only cause price inflation. However, such a statement is largely without theoretical flavor and, as Cantillon asks, in our quote above, how exactly does this come about? In this respect, Fisher and Newcomb falter somewhat. Supply of commodities is given by the "real side" of the economy and, by Say's Law, is accompanied by the demand for commodities. We must suppose, however, that for some reason or another (they never say why), money is required for exchange. This is an "institutional" arrangement. Money is required for transactions, therefore agents will demand some amount of money to undertake their transactions. We can rewrite the equation of exchange so M/P = T/V, where T/V is now the demand for money necessary to fulfill the transactions T given the institutional constraint V. Because output is given by the real side and the demand for money is an institutional arrangement, then V and T are more or less fixed. The only variables which remain, then, are M and P. If the equation above holds at all times, then if M rises, we necessarily need P to rise by the same amount. This is the restatement of the Quantity Theory. But there is already something wrong. We still have not addressed Cantillon's question: how exactly does this happen? In fact, an acceptable answer to this question would not be given until much later. Fisher, however, gave a rather loose idea of it. If M increases and T/V are fixed, then M/P > T/V, i.e. the money supply is greater than the money demand. People get rid of their excess supplies of money by demanding more of every good, thus the prices of all goods rise, i.e. P rises, until this extra demand is siphoned off. Note that recurrently, the real value of money supply is brought back down to the level of real money demand (T/V) and we get equilibrium once again. This explanation, then, provides a theoretical rationale for the left-side causation: money supply increases will be met by an exactly proportionate increase in prices. This is what Fisher (1911: p.29) identifies as the Quantity Theory of money. We can note a few important things. Firstly, we need a stable T/V for this to work. In other words, we need a stable demand function for money, couched in terms of transactions demand. Indeed, Milton Friedman and Anna J. Schwartz's famous 1963 study is dedicated precisely to unearthing this stable relationship empirically (see our discussion of Monetarism). Secondly, Irving Fisher stresses repeatedly the issue of dichotomy between the real and monetary sides: money does not have real effects. But did he really believe this? In a sense, he could not. Indeed, did not a rise in the supply of money lead to a rise in the demand of goods? Thus, the "real" demand for goods must be affected by "nominal" money. But is this not what Fisher derided as "money illusion"? Fisher's story is nice, but wrong - because he presumed Say's Law applied. We will have more to say on this later when discussing the Patinkin Controversy. However, we can still note a few important things here. Early Quantity Theorists, as the case of Mill shows, they did attempt to grapple with arguments of disparities of distribution, sectoral excess capacity and financial intermediaries. To a large extent, the strict Quantity Theory was viewed only as a long run theory dependend upon "helicopter drops" of money. Fisher, in particular spent much effort discussing "the temporary effects during the period of transition separately from the permanent or ultimate effects [which] follow after a new equilibrium is established - if, indeed, such a condition as equilibrium may be said ever to be established." (Fisher,, 1911: p. 55-6). He finds, simply, that "the `quantity theory' will not hold true strictly and absolutely during transition periods." (Fisher, 1911: p.161). In this sense, then, Fisher was not as strict about "dichotomies" as Hume was and later Neoclassical economists interpreted him to be. Among Fisher's most famous findings is, of course, his theory of the credit cycle which incorporates a variety of effects (although his ignorance of the effect of all his wonderful details on aggregate demand and output remains the largest drawback). The main part of Fisher's tale is that cycles are created largely by slow-adjusting interest rates (relative to inflation). In this story, the strict quantity theory does not hold for there are real effects on velocity and real interest rates (as well as minor output effects). However, again, the idea he presents is for transitional phenomena. In the long-run, where adjustment lags are overcome, the quantity theory comes back into its own. Note the conclusion that the so-called Fisher's Law must hold in the long-run: changes in interest follow changes in price on a one-to-one basis otherwise, credit cycles ensue and the quantity theory breaks down. Finally, we should stress Fisher's argument for the demand for money:
i.e. it is solely demanded for its medium of exchange role, its "transactions demand". Other motives to hold money - speculative, store-of-value, precautionary, etc. - are simply not a part of his story.
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