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Economics Reflections on the Quantity Theory: Pigou In ECONOMICS REFLECTIONS ON THE QUANTITY THEORY: PIGOU IN 1917 AND PARETO IN 1920-21 by Michael McLure Business School University of Western Australia DISCUSSION PAPER 13.24 REFLECTIONS ON THE QUANTITY THEORY: PIGOU IN 1917 AND PARETO IN 1920-21 by Michael McLure* Business School University of Western Australia DISCUSSION PAPER 13.24 Abstract: In 1917, Pigou published his classic article on “The Value of Money” in the Economic Journal. In 1920-21, Pareto wrote a manuscript on monetary theory, ‘Note Critiche di Teoria Monetaria’, but it was not published until 2005 when some fragments of that manuscript were located by Fiorenzo Mornati. In both these papers the authors reflected on the quantity theory of money and both established the conditions that must be met for the theory to hold. Yet the rhetoric of Pigou in light of his analysis was very moderate, cautious and broadly supportive of the theory; whereas the rhetoric of Pareto in light of his analysis was far more direct, unequivocal and critical of the theory. In this study the analysis of Pigou and Pareto is compared and that analysis is used to explain the difference in their rhetoric pertaining to the quantity theory. It is concluded that this case is illustrative of a more general difference between Cambridge and Lausanne economics during the second generation of these two respective ‘schools’ of thought. * University of Western Australia, Business School Economics Program. I would like to thank Ken Clements for his very helpful comments on an earlier draft of this paper. The names Pareto and Pigou are primarily united by their legacies in welfare economics, though the differences between the two scholars in this field are so significant that many, such as David Collard (2011), differentiate Paretian welfare economics from Pigouvian welfare economics. Indeed, the contrasts, and similarities, between Pareto and Pigou over aspects of welfare economics and income distribution have been the subject of present author’s recent studies (McLure 2010 and 2013). For the history of economic ideas, it is also relevant that Pareto and Pigou were representatives of wider bodies of mainstream economic thought, with Pareto the second generation leader of the ‘Lausanne School’ and Pigou the second generation leader of the ‘Cambridge School’. Of course, these schools have been contrasted at an even more general level, with Lausanne economics being primarily associated with Walrasian general equilibrium and Cambridge school’s economics being primarily associated with Marshallian partial equilibrium (Hicks 1946, De Vroey 1999 Donzelli 2008). But within each of these two schools the relationship between money and the real economy was also of considerable importance. The Cambridge school’s legacy in monetary economics is recognised as an episode of the first order of importance to the history of economics, with the subject well studied by monetary economists and historians of economics (Bridel 1987). The Lausanne school’s legacy in this area has been far less influential, but is still of considerable importance. For example, by the 1930s the originality of Walras’s approach was highlighted to the English speaking world by Arthur Marget (1931, 1935), was revived and critically considered by Don Patinkin (1965) and the relationship between money and Lausanne general equilibrium in the works of Walras and Pareto has been historically investigated by Pascal Bridel (1997, 2000). The purpose of this paper is to extend the comparison and contrast of the work of Pareto and Pigou beyond the field of strict welfare economics and income distribution to a core issue in monetary theory: the validity of the quantity theory of money and the mechanisms for expressing that theory. The scope of the study is limited to near contemporary papers: Pigou’s influential “The Value of Money” (Pigou 1917), which provides the first formalisation of the Cambridge equation for the demand for money in reaction to the quantity theory of money in its Fisherian form; and Pareto’s manuscript ‘Note Critiche di Teoria Monetaria’ (Pareto 2005), which was drafted, but not published, in 1920-21 as a criticism of the quantity theory of money.1 Pigou’s Illustration of the Quantity Theory A. C. Pigou formally introduced, for the first time (Collard 2002, p. xxv), the ‘Cambridge equation’ for the demand for real cash balances. He did so in a form that could be readily 1 Fragments of Pareto’s manuscript were discovered in the University of Lausanne archives by Fiorenzo Mornati, who published them in the final volume of Pareto’s Opera Omnia in 2005. 1 reconciled with the Fisher exchange equation, and the associated quantity theory of money; and yet provide the apparatus for illustrating that the power of a unit of currency to purchase real goods changes in response to factors other than the quantity of money. Given the comparative objectives of this paper, it is useful to work backwards from the Fisher equation to highlight the difference between Pigou’s approach and the standard presentation of the quantity theory of money. The simplified Fisher equation is the product of the quantity of money in terms of units of legal tender (M) and the velocity of circulation for money (V) is equal to the product of the nominal price level (Pn) and an index of the volume of transaction (T): MV = PnT (1) But Pigou’s notion of price does not concern the nominal price level (Pn); rather, he treats the real price of money as the quantity of wheat that a unit of legal tender can purchase (Pw). In other words, wheat is the numeraire by which value within the real economy is measured, and (Pw) is the purchasing power of money, as represented by the quantity of the numeraire that a unit of legal tender can command. Consequently, Pigou’s notion of price is the inverse of Fisher’s, with Pw = 1/ Pn. Pigou also presents the real price of money as the dependent variable. Consequently, the Fisherian equivalent of the Pigouvian notion of the purchasing power of a unit of legal tender is: T Pw = (2) MV But Pigou’s basic contention is that Pw depends on the demand for real balances, where real balances are titles to legal tender (legal tender, deposits and notes issued by banks) which are measured by the product of: total resources enjoyed by the community at any given moment, expressed in terms of the numeraire good wheat, (Rw); and the proportion of those real resources that the community wishes to hold as titles to legal tender (k). Consequently, Pigou specified the real price of a unit of legal tender as: kRw Pw = (3) M But Pigou also demonstrates the equivalence of his approach with that of Fisher by suggesting that the right hand side of equation (2), and the right side of equation (3), both represent the value of real balances. This is because the value of real balances, (kRw), is the equivalent of the ratio of T to V because the proportion of real resources that the community holds as titles to legal tender (k) is the inverse of the velocity of circulation2 (V) and transactions (T) are the sum of real quantities of goods weighted by real value (i.e. the quantity of each good is weighted in the transaction index by the quantity of the numeraire 2 Pigou notes that when people halve their holdings of titles to legal tender the velocity of circulation is doubled (Pigou 2002 [1917], p. 209). 2 good wheat that it could purchase). When equations (2) and (3) are expressed as percentage changes, and the value of the T to V ratio in equation (2) is constant between periods, and the real balances kRw in equation (3) is constant between periods; and the quantity theory emerges. %ΔPw = -%ΔM (4) That is, the relative change in the value of a unit of money is negatively related to the relative change in the quantity of money when: the value of real cash balances kRw is constant between periods (i.e. when equation 4 is derived from equation 3); or, to say the same in another way, the ratio T/V is constant between periods (i.e. when deriving equation 4 from equation 2). Pareto’s Illustration of the Quantity Theory The form of Pareto’s method of formalising the quantity theory is most closely linked to the Fisher equation, though it is unclear if Pareto had read Fisher’s work on this subject and his inspiration appears to be Walras’s early work on monetary theory (McLure 2012).3 The similarity is due to Pareto, like Fisher, setting his equation in terms of nominal prices. The difference is that Pareto isolates the transaction price for the numeraire good from that of the transaction prices for all other goods. As a consequence, Pigou’s focus on the purchasing power of money, and its relationship to the numeraire (wheat in Pigou’s analysis), is also evident from Pareto’s money equation. Pareto starts his monetary analysis in his ‘Note Critiche di Teoria Monetaria’ (1920- 21) by attempting to derive the value of transactions from the following Walrasian equation of exchange of goods and productive services for an individual. However, he does so by isolating the numeraire good from other economic goods: Τ ap00+=∑( apττ )0 (5) τ =1 a0 quantity of the numeraire good p0 nominal price of the numeraire good aτ quantities exchanged of goods and services 1, 2 ... Τ pτ nominal exchange prices of goods and services 1, 2 ... Τ 3 To date the author has found no reference in Pareto’s works to Fisher’s classic The Purchasing Power of Money, and it is uncertain if he ever read it.
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