Universidade de Brasília Instituto de Ciências Humanas Departamento de Economia

Programa de Seminários Acadêmicos

PATINKIN ON INVOLUNTARY UNEMPLOYMENT AND THE AGGREGATE SUPPLY CURVE Mauro Boianovsky Departamento de Economia, UnB

Seminário nº 24/01 - 5/10/01 Brasília, DF 2001

1 Patinkin, the Cowles Commission, and the theory of unemployment and aggregate supply

Mauro Boianovsky Universidade de Brasilia [email protected]

Preliminary draft. Prepared for presentation at the “Patinkin Conference”, Lausanne, 20-22 September 2001.

“For a long period before the writing of the first edition [of Money, Interest and Prices] I had been puzzled by the apparent contradiction between the intuitive feeling, on one hand, that there was a connection between a firm’s product-output and its labor-input, and the traditional demand curve for labor, on the other hand, that did not depend explicitly on output and whose sole independent variable was the real wage rate.” (Patinkin, 1989, p. xvi)

Introduction This paper offers an account of Don Patinkin’s quest for a model of the analytical relationship between the labor market and the commodity market, as revealed by his essays on unemployment produced at the Cowles Commission in Chicago from 1946 to 1948 and by the 1953 draft of his 1956 classic Money, Interest and Prices (henceforth MIP). According to Patinkin’s reading of Keynesian economics in the late 1940s, there was a missing piece in the unemployment literature at the time, that is, the concept of an aggregate supply function in the market for commodities. This was the subject-matter of his 1949 Economic Journal article, which was the final version of earlier drafts discussed with members of the Cowles Commission, among them Lawrence Klein, Trygve Haavelmo and Jacob Marschak, director of research of the Commission between 1943 and 1948 (see Patinkin, [1949a] 1981, p. 155). Marschak was also chairman of Patinkin’s PhD thesis committee at the University of Chicago. Patinkin’s doctoral dissertation “On the consistency of economic models: a theory of involuntary unemployment” was submitted in the spring of 1947. It consisted of two parts, dealing respectively with the “mathematical consistency of a general-equilibrium system with money” and with “unemployment interpreted as the manifestation of an inconsistent system”, as described by Patinkin (1995, p. 379). The second part was published in revised form as the 1949 EJ unemployment article, while the first part came out in two Econometrica articles (Patinkin, 1948a, 1949b). There was a common theme running through the dissertation: overdetermination of systems with homogeneous equations. As recalled by Klein (1987, p. 352), the “Patinkin problem” was intensively discussed at the Commission. In 1949 Patinkin moved to Jerusalem to work at the department of economics of the Hebrew University and in few years became engaged in “the writing of a book

2 on monetary theory which will, among other things, ‘translate into English’ my preceding articles” (letter to D. H. Robertson, October 9, 1953). By the end of 1953 the first draft of MIP was written, including a chapter on “Monetary Theory under the Assumption of Unemployment”. As discussed below, that unpublished chapter featured a diagrammatic formulation of the aggregate supply function distinct from the first sections of the 1949 unemployment article, and, more importantly, introduced the notion that demand for labor is influenced by the entrepreneurs’ expectations of prices. Apart from that, the 1953 draft kept the basic description of unemployment put forward by Patinkin in the 1940s as points off the supply curve of labor. The expectational analysis of 1953 did not survive in the published version of that chapter (see Patinkin, 1965 [1956], ch. XIII), which proposed that workers are off their labor supply curve because firms are off their commodity supply curve when faced with inadequate aggregate demand. That disequilibrium notion was not part of the original framework of the Cowles Commission, although it could also be interpreted as a manifestation of an overdetermined system, as suggested by Haavelmo (1960). In 1948 Marschak introduced in his Chicago lectures the notion of aggregate supply and demand curves drawn within the output-price coordinate system (see Marschak, 1951). That was probably the first appearance of what is nowadays called the “AS-AD model”, with its distinction between “classical” and ‘Keynesian” theories depending on the slope of the aggregate supply curve, which was not the approach of Patinkin’s 1956 book.

Overdetermination and Unemployment Patinkin’s standard model in his unpublished essays “Unemployment in Keynesian Systems” (December 1946) and “A Reconsideration of the Theory of Unemployment” (March 1947, both held in the Special Collections Library, Duke University) consists of an economy with three commodities: labor, claims to labor (i.e. money) and leisure, all measured in terms of hours. The variables are Xd (demand for labor hours), Xs (supply of labor hours), S (savings), T (leisure), Y (national income) and the Lagrange multiplier. The individuals (who are at the same time workers and consumers) maximize the utility function u(Xd, S, T) subject to the budget restraint Xd + S = Xs = K - T, where K is the total number of hours in the period under discussion, that is, Xs + T = K. The price is expected to remain the same in the future. Further to those two equations, the model provides three equations describing the equality between the marginal utility of the variables in the utility function and the Lagrange multiplier, plus two definitions of national income Y = Xd and Y = Xs. The system is, therefore, overdetermined, since there are 7 equations and 6 variables. Patinkin simplifies further by eliminating the Lagrange multiplier to give two equations expressing the equality between the marginal utilities, which are functions of Xd, S and T. He then expresses S and T in terms of Xs and Xd, so that the system has just three variables Xs, Xd and Y. Finally, two of the three variables can be expressed in terms of the third to yield Xs = g(Y) and Xd = f(Y), which are respectively the “supply function” and the “expenditure function”. Together with the two definitions of national income Y = Xd and Y = Xs, the derived system has now 4 equations in 3 variables. The overdetermination is expressed by the fact that the pair of equations Xd = f(Y) and Y = Xd determine a value for Y, and the pair Xs = g(Y) and Y = Xs determine another one that is not necessarily the same. Hence, the system is inconsistent.

3 As pointed out by Patinkin, the problem did not arise in the classical system because of the assumption of Say’s law that F(y) is identically equal to Y. Alternatively, the classical economists assumed that an additional variable “rate of interest” affected the expenditures of individuals, which in principle could render the system consistent. However, the additional condition that the rate of interest is nonnegative may overdetermine the system. Furthermore, “Keynesian theory has really never dealt explicitly with the overdeterminacy of the system; the supply function is just not introduced at all” (Patinkin, 1947a, p. 4). In order to explain how overdetermination can be removed and the equilibrium value of Y determined in the “real world”, Patinkin next assumes that workers (suppliers) and consumers can be treated as separate groups, as represented by the functions Xs = g(Y) and Xd = f(Y), respectively, when they are subject only to the technological restraint and to the budget restraint. This leads to the definition of the “full-employment level of income” as represented by “the amount suppliers are willing to provide when they are free to work as much as they desire”, subject only to the technological restraint Xs + T = K and the market conditions Y = Xd and Y = Xs. The actual level of Y depends on the “relative bargaining power” of workers and consumers, which decides the extent of involuntary unemployment and provides the missing link in Keynesian economics.1 If the consumers are able to assert themselves completely, the workers maximize utility subject to the additional restraint that the total amount of labor they supply must equal the given amount of Xd decided by consumers. Patinkin (1946, p. 6) writes the new Lagrangean under these conditions and shows that Xs is completely determined by the technological restraint and the demand restraint, that is, the worker cannot anymore vary Xs and T in order to maximize utility. The upshot is that “the overdeterminess is now obviously removed” and that “the rigorous theoretical economist must adhere to the definition of unemployment as being off the supply curve of labour” (1946, pp. 6 and 20). Patinkin (1946, section II) also discussed a model with firms, with the same conclusions about overdetermination. The general equilibrium model consists of R industries (= number of commodities), M firms (Mi in each industry) and N workers, with 2R + 2M + 2N +1 equations (demand function, production function, equality between marginal productivity and real wage, time constraint of workers, equality between real wage and marginal utility of leisure in each industry and firm, plus the equilibrium conditions that the supply and demand of every commodity and labor must be equal). The variables are 2R + 2M + 2N (demand, employment and production in each firm, real wage in each industry, leisure time and work time by each worker in each industry), which means overdetermination, since aggregate employment is decided in two ways in the system.2 In case firms “have their way completely”, the 2R + 2M equations (demand function, production function, equality between marginal productivity and real wage and equilibrium in the commodities markets) determine the 2R + 2M variables (demand, employment and production in each firm, real wage in each industry). The equation expressing equality between the sum of work done by each worker and the total number of workers employed is automatically satisfied, since “we assume that the workers will supply any work demanded from them” (p. 11). The conclusion again is that, because of the additional constraint represented by the output level decided by firms (which is equal to aggregate demand), workers are not able to maximize their utility. That was not the first time in the literature that involuntary unemployment was defined as points off the labor supply curve, but it was the first attempt to formalize the concept as the outcome of an inconsistent system.3

4 Patinkin submitted his 1946 unemployment paper for publication, which raised strong reaction from Marschak, who asked him a letter of January 16, 1947 to “stop the editorial processing...until your article has been thoroughly discussed on our group”. Marschak invoked the “collective responsibility” of the Cowles Commission and pointed out that “Haavelmo also considers the article a very provisional result of some games at the blackboard...I do not understand the hurry. The matter is too important”. Patinkin apparently withdrew the paper and in the winter of 1948 submitted a third version, entitled “Inconsistent Systems and Involuntary Unemployment” (Patinkin, 1948b), to the Journal of Political Economy. As he informed on a letter of March 18, 1948 to Marschak, the paper was rejected for being “too technical for their purposes”. In another letter of November 10, 1948, Patinkin wrote to Marschak about the “extensive revisions” of the paper compared to the form in which it appears in the thesis, and in December the revised paper, with the new title “Involuntary Unemployment and the Keynesian Supply Function”, is successfully submitted to the Economic Journal (Patinkin, [1949a] 1981). It was also reprinted, together with Haavelmo (1950), as Cowles Commission Paper no. 38 (“Two Papers on Involuntary Economic Decisions”), with the addition of a mathematical appendix originally excluded from EJ (see Patinkin, [1949a] 1981, pp. 175-179). The first sections of Patinkin’s 1949 EJ article present a criticism of the “Keynesian cross” type of diagram used to illustrate the determination of income. The diagram was extensively used at the time, as shown by Patinkin’s student notebook of Oskar Lange’s course on “Business Cycle Theory” at the University of Chicago on the summer of 1945. Patinkin’s main criticism was that, in the absence of a supply function for commodities, the Keynesian cross is not able to explain the movement toward equilibrium income through changes in price and output. Accordingly, an “aggregate desired-supply function” of the form Xs = g(Y), as discussed above, is added to the Keynesian cross as an almost horizontal line reflecting Patinkin’s assumption that the price of commodities is always proportionate to the price of productive services (constant real wages).4 Following along the lines of the argument of the 1946 manuscript, the income level that equilibrates the demand side is not necessarily the same one that equilibrates the supply side. Patinkin ([1949a] 1981, p. 161) concludes that “the inconsistency created by the explicit introduction of the aggregate supply function into Keynesian systems provides the key to the theory of involuntary unemployment implicit in Keynesian economics”. It should be noted that, although sometimes Patinkin mentions “firms” in sections II and III of the article, the “suppliers” represented by his supply function are the workers, just like the standard model of earlier versions of the paper discussed above. Hence, he states that “suppliers must be employed to the full extent they desire” at the income level decided by the supply function and the 45o line (p. 164). Patinkin’s ambiguity on that score was noticed by de Jong (1954) as part of a critical reaction that set off an intense discussion about the role of supply functions in Keynesian economics between de Jong, Hawtrey (1954), Robertson (1955) and Weintraub (1957) - see King, 1994. As suggested by de Jong (1954, pp. 7-8), Patinkin’s “desired-supply function” should be redefined as the value of output resulting from the substitution of the supply function of labour into the aggregate production function. Throughout most of the manuscripts on unemployment Patinkin assumes that the functions are homogeneous. Building on an unpublished note by L. Hurwicz circulated among members of the Cowles Commission in June 1945, Patinkin

5 ([1949b] 1981, pp. 132-33) established the following theorem: “If every equation of a system of K independent equations in K variables is homogeneous of some degree t in the same set of variables, then the system possesses no solution (i.e., it is inconsistent), with the possible exception of the one which sets each of the variables equal to zero”. The inconsistency is derived from the fact that the homogeneity assumptions leads to the reduction of the number of dependent variables by one, for the functions depend on the ratios of these variables and not on their individual values. As recalled by Klein (1987, pp. 351-52), At the Cowles Commission we worried about the problem of homogeneous systems...we worried a lot because homogeneous functions really throw away one variable. We wondered about the system being overdetermined or undetermined. This gave rise to the Patinkin question. The whole Patinkin problem grew out of our daily discussions at the Cowles Commission. Haavelmo, Patinkin, Rubin, Marschak, I, and others, were always around the blackboard puzzling about these issues. Haavelmo had a great idea: he said that there are systems that have a solution when they are dynamic and they are inhomogeneous, but when you stop them at a point of time and you try to take them to the steady state you force them to be homogeneous. So you say rational behaviour of an equilibrium sort has no money illusion...but the dynamic process is inhomogeneous.5 Apparently, Patinkin was aware of Haavelmo’s “great idea”, since he mentioned in the 1946 manuscript (p. 20) the possibility that “non-homogeneity can be introduced through speculative and dynamic considerations introduced into the model”. He did not pursue that line of research though, in contrast with Klein himself. Klein (1954, pp. 285-87; see also 1947a, p. 116) suggested the following closure of the labor market in order to bring out Haavelmo’s idea and remove overdetermination from a Keynesian macroeconomic model: ND = ND (w/p); NS = NS (w/p); dw/dt = f(NS - ND ), with 0 f(0). The last equation is added to express the notion that, while both entrepreneurs and workers are assumed to behave without money illusion in the static model, bargaining is made in terms of money-wages reflecting a lag between price movements and wage adjustment. Klein’s dynamic wage bargaining anticipating some aspects of the Phillips curve formulation - introduces money illusion, so that “the fundamental characteristic of the system is that it contains nonhomogeneous behaviour functions when in motion but homogeneous functions in the static form” (1954, p. 286). In a footnote to his well-known 1948 AER article on “Price Flexibility and Full Employment” Patinkin ([1948c] 1972, p. 27, n. 34) writes the equation dw/dt = f(NS - ND ) to express the fact that a system with price flexibility cannot be in equilibrium if there is unemployment, but he apparently did not realize that the equation assumed money illusion implicitly. Another “solution” to the homogeneity problem, rejected as ad hoc by both Patinkin ([1949b] 1981, pp. 14344) and Klein (1987, p. 351; 1947a, pp. 115-16), is the introduction of a nonhomogeneous equation of the form NS = h(w) expressing money illusion of workers. Patinkin’s own complete solution to the ‘Patinkin problem” came only in 1949, when he inserted in galley proof the ten last paragraphs of his Econometrica article (see Patinkin [1949b] 1981, pp. 144-47; 1995, p. 381) after realizing that the economically meaningful way for the commodity demand equations to depend on the absolute price level was to include real money balances as variables in the equations. Elements of that solution can be found already in his articles in AER and

6 EJ in 1948 and 1949, albeit in the underdeveloped form of the inclusion of the price level instead of real money balances in the equations. In any event, the mathematical notion that the equations are non-homogeneous - and the corresponding economic notion that changes in the price level shift the expenditure function until it meets the “desired-supply function” at full-employment income level remove the inconsistency of the static system, which has a unique full-employment solution. At first sight, the introduction of the real balance effect appears to seriously damage Patinkin’s former explanation of unemployment as a manifestation of a static overdetermined system. Nevertheless, Patinkin claims that his description of involuntary unemployment as points off the labor supply curve still applies in the realm of dynamic analysis, that is, “the existence of a consistent equilibrium position for the static system is a necessary, but not a sufficient condition for the elimination of involuntary action within the economy” ([1949a] 1981, p. 174). In order to bring this out, Patinkin set out in section V of his EJ article a model of a consistent system featuring equations of supply, demand and market equilibrium for three aggregate markets (commodities, labor and money). The equations for the commodity market are: E = ¥(y, r, p), Y = ø(Nd) and E = Y, that is, the expenditure function and the “new comer” production function respectively. Of course, the equilibrium in the commodity market is not necessarily a full-employment equilibrium. The demand equation for the labor market is the usual one Nd = f(w/p), which, when substituted into the production function, yields the “familiar aggregate supply function” (p. 172). Differently from the “desired-supply function”, it depends on the (variable) real wage rate. As pointed out by Patinkin (pp. 172-73), there were at the time several models in the literature similar to his (e.g., Modigliani, 1944), but the aggregate supply function is generally only implicit in those models and, more importantly, is not used to bring out the concept of involuntary unemployment. Under the assumption that the equilibrium in the commodity and money markets is “quickly re-established”, Patinkin argues that an exogenous shift in the expenditure function brings about involuntary unemployment while the system “tries to correct the disequilibrium in the labor market” (p. 173) by means of the (real balance) effect of falling prices and wages on aggregate demand. The crucial assumption now is that the adjustment process “takes time” (p. 174), which forcefully introduces disequilibrium dynamics and expectations into the analysis, as discussed next.

Expectations, Aggregate Supply and the Demand for Labor When Patinkin set off to write the first draft of MIP in Jerusalem in 1953, the 1949 ambiguous “desired-supply function” was gone, replaced by the “familiar aggregate supply function”. In chapter VII (“Macroeconomics and Full Employment”) of the 1953 draft, the aggregate supply function is based on on the supply function of a profit-maximizer representative firm in perfect competition. As Patinkin would emphasize in the published book ([1956] 1965, pp. 11-12 and 209), the function describes the outcome of an “individual-experiment”, not a “market-experiment”. As explained at the end of his 1949 article, it results from the substitution of the aggregate demand curve for labour, now written as Nd = Q(w/p, Ko), into the aggregate production function Y = ø(N,Ko), to yield Y = ø[Q(w/p, Ko), Ko], which gives the aggregate supply function Y = S(w/p, Ko) (cf. [1956] 1965, ch. IX). Correspondingly, the function is now represented in the Keynesian cross diagram by

7 a vertical line drawn at the level of output yielded by function S for any given real wage rate. As noticed by Dennis Robertson in correspondence of January 14, 1956 (a few months before the book came out), Patinkin’s new supply function, in contrast with the 1949 “desired-supply function”, does not yield a unique (full-employment) equilibrium: I can’t see what happens to your diagram now that you draw your S as a vertical not as a horizontal straight line. There is an infinity of such straight lines, each corresponding to a point on the DY axis, and I don’t see how we know which to use until we have determined y. But the determination of Y is the object of the exercise. Robertson’s letter was a reply to an unpublished note by Patinkin on “Keynes and Supply Functions: a Comment” written in 1955 as a reaction to de Jong (1954) and Robertson (1955). In the note (p. 3) Patinkin clarifies that “I no longer consider my original graphical representation of the aggregate supply function to be correct. In particular, I would now dispense with the assumption that this function is even slightly dependent on Y. In addition, I would now represent it as a vertical line”, which is the form employed in “my forthcoming” book (cf. [1956] 1965, fig. IX-3, p. 212). The relation between the redefined supply curve and the labour market during periods of unemployment is the focus of chapter IX of the 1953 draft of MIP. Patinkin carries to that chapter the assumption, implicitly made in the 1949 EJ article, that firms are always on their labor demand curve and, therefore, on their commodity supply curve: It is assumed that the amount of labor employed always corresponds to the amount demanded. That is, it is assumed that throughout the dynamic process of adjustment the economy is to be found at a point on the demand curve for labor. Clearly, only if the economy returns to equilibrium will this also be a point on the supply curve [of labor]. (Patinkin, 1953, p. IX-4). The notion that firms are always in their demand curves for labor was ingrained in the models of the Cowles Commission in the late 1940s. In his discussion of how to solve the overdetermination problem Klein (1947a, pp. 110-111) pointed out that “there is little that can be done to either the production function or to the demand for labor” and that “there is no relation that is more stable than the demand for labor”. Likewise, in his mathematical formalization of the Keynesian system, Klein (1947b, p. 203) wrote that “regardless of the shifting adjustments, the demand curve for labor will hold”. In 1953 Patinkin was, therefore, still firmly in the tradition of the Cowles Commission in his assumption about the demand curve for labor, but, as we shall see presently, he added on that occasion a new element to that function: price expectations of entrepreneurs. Patinkin (1953, pp. IX-4 and IX-5) first describes the effects of an exogenous downward shift of the expenditure function E = F(Y, r, M/p) under the assumption that the “period of adjustment” of the economy back to its original equilibrium is “sufficiently short”, so that inventories are accumulated for a brief period only and, more importantly, falling prices do not affect price expectations of firms. The initial downward shift of the expenditure function creates a deflationary gap in the commodity market, which moves prices downward and raises the real wage rate. The ensuing excess supply in the labor market drives money-wages down “instantly

8 in the same proportion as the price level”. Hence, the real wage rate remains constant at its original full-employment level, but the commodity market still features excess supply. Prices keep falling, which brings about a positive real balance effect in both the commodity and bond markets that shifts the expenditure function back to its original position (cf. [1956] 1965, pp. 230-232). Things change, however, if the dynamic process of adjustment takes a significant amount of time: Assume now that the aggregate demand curve does not react quickly to the changes in interest rates and real balances. Then the preceding smooth process of adjustment is no longer possible. First, firms will not be willing to let their inventories accumulate for any protracted period. Second, throughout the period of excess supply prices are falling. Hence firms will discover that they are continuously making losses. For they hire labor and undertake production at one price level, and sell it later at a lower one. After this happens over a period of time, firms realize that they must plan their production on the assumption that the future price level will be lower than the present one. Correspondingly, firms will hire labor in accordance not with the existing nominal real wage rate, but with the anticipated effective rate. Thus even if the existing real wage rate remains the same, or even falls, the effective rate may rise. Hence firms will decrease the amount of labor they employ. (1953, pp. IX-5 and IX-6; italics added) Patinkin had discussed price expectations before, but in connection with the expenditure function, not the supply function ([1948c] 1972, pp. 22-23; [1949a] 1981, p. 174). The influence of dynamic expectation factors on aggregate demand raises the issue of the “stability of the dynamic system ”, that is, the ability of the economy to return to a full-employment equilibrium through falling prices and wages “within a reasonable time” ([1948c] 1972, p. 28; italics in the original). These effects (together with the “distributional effects” represented by the impact of lower prices and wages on the real debt burden) are also discussed later on in the 1953 draft (p. IX-12), but the crucial point of that chapter is the introduction of endogenous adaptative price expectations to explain why firms reduce their demand for labour even under the assumption that money-wages fall “instantaneously” with the price level. The standard assumption about price expectations in macroeconomic models in the 1940s and early 1950s was of “static expectations”, defined by Lange (1944, p. 20) in the Cowles Commission Monograph no. 8 as the notion that “all decisions are based on the expectation that current prices will continue during that part of the future which is relevant to present decisions”. It corresponds to John Hicks’s ([1939] 1946) concept of “unity elasticity of expectations”, which, according to Hicks, was introduced into the literature for the first time as part of Knut Wicksell’s ([1898] 1936) famous “cumulative process” of price change. The assumption of “static expectations” was adopted, among others, by Modigliani (1944, p. 45) and by Patinkin himself in MIP ([1956] 1965, pp. 61, 200), where he wrote that “for simplicity, it is assumed that these future prices are expected - with certainty - to be identical with current ones”.6 Furthermore, he decided in the book to abstract from the “complications” produced by discrepancies between actual and expected prices. He was aware that “what we disregard here as ‘complications’ forms the basis of Hick’s dynamic analysis” of temporary equilibrium, but defended the abstraction on the grounds that it would allow a “dynamic analysis” of the stability of the market

9 process of the kind set off by L. Walras and P.A. Samuelson and “taken for granted” by Hicks (MIP, p. 67; cf. E.R. Weintraub, 1979, ch. 4). As pointed out by Stanley Fischer (1993, p. 20), Patinkin deployed in MIP “atemporal stability analysis” to examine the forces bringing the economy into equilibrium within each week, which differs not only form the more recent modelling practice but also from the Wicksellian tradition of Hicks and others. The argument of chapter IX of the 1953 draft about the labor demand curve is somewhat reminiscent of the Wicksellian cumulative process, with the important difference that Patinkin assumed an elasticity of price expectation higher than one in a downward process, while Wicksell’s discussion of elastic price expectation was restricted to an upward process. Wicksell’s influence in this regard is hardly surprising, since Patinkin had published a year before an essay on the Wicksellian cumulative process (Patinkin, 1952a; see also Boianovsky, 1998). As pointed out by Patinkin (1953, p. IX-6), the notion of “anticipated effective” real wage can be used to show how the level of aggregate demand affects the employment and output decisions of firms: It should be emphasized that this description of how unemployment begins differ only semantically from the familiar Keynesian analysis. The latter presents the decrease in employment as a result of the deflationary gap - the inability of firms to find buyers for the fullemployment output. In our model, however, anticipated sales are not one of the explicit factors which influence the demand for labour. But their implicit influence is fully reflected by an increase in the effective real wage rate. It follows that to say that firms will not be able to sell all their output is to say that this wage rate will go up, so that the employment policies of firms will be affected accordingly. Apparently, Patinkin believed that the inclusion of anticipated sales as an argument in the demand for labor function is not consistent with the perfect competition assumption, as opposed to the notion that competitive firms form expectations about the market prices of their commodities. Falling prices cause an increase in the real wage anticipated by firms (despite falling money-wages), followed by a reduction of employment on the redefined labor demand curve. Correspondingly, the aggregate supply function of commodities drawn in the Keynesian cross diagram is shifted to the left, but (by assumption) not enough to eliminate the deflationary gap. Prices, therefore, keep falling, which affects the aggregate demand curve (via real balance effect) and the anticipated real wage, leading to a gradual reduction of the excess supply of commodities. The economy will eventually reach an “unemployment equilibrium” in the commodity and bond markets, described by the absence of forces in these markets working to change prices or the interest rate. However, as pointed out by Patinkin (1953, p. IX-8), the excess supply of labor exerts a downward pressure on money-wages, which reacts back on the commodity and bond markets. The movement of the anticipated real wage rate is now downwards, which shifts the aggregate supply curve to the right and creates a deflationary gap followed by falling prices and a positive real balance effect that pushes the expenditure curve upwards. “If the process is successful, a new full-employment equilibrium position is reached with money-wages, prices and interest rate all lower than in the original equilibrium position, but with the real wage rate unchanged” (1953, p. IX-8; cf. [1956] 1965, p. 326, first paragraph). During the whole process there is involuntary unemployment measured by excess supply of labor, according

10 to Patinkin. He is, however, silent about the price expectation of workers. The tacit assumption seems to be that workers have the same price expectation as firms, for Patinkin (1953, fig. 30, p. IX-2) measures involuntary unemployment in the labor market diagram at an anticipated real wage rate common to both workers and firms. Patinkin’s 1953 model can be interpreted as assuming implicitly that money-wages are set one period in advance to equalize demand and supply of labor at the expected price level. This (adaptative) price expectations will be, however, frustrated by the actual price movement, which brings about excess labor supply and further changes in prices and wages until disequilibrium is eliminated from all markets (cf. the aggregate supply-aggregate demand rational expectations model of Blanchard and Fischer, 1989, pp. 518-19, where the money-wage is set to equalize the rationally expected labor demand and labor supply in the next period, and employment, determined by labor demand, depends on unexpected movements in the price level). As pointed out above, there are almost no traces of the 1953 expectational model of labor demand in MIP, where stationary expectations are assumed throughout. This can be in part explained by the fact that Patinkin had not put forward in 1953 a model explaining how price expectations are formed; the adaptative process is only implicit in the draft. Hence, he referred in section XI.3 of the first edition of the book to the “Pandora box” of expectations and uncertainty. In the second edition, reflecting the publication of adaptative expectation models by P. Cagan (1956) and others, Patinkin ([1956] 1965, p. 311) mentioned that “expectations are not pulled out of the air, but are related to past price experience” in order to point out that the stability results of his monetary model remain valid under “dynamic” expectations as well. The influence of price expectations on labor demand is discussed in a brief paragraph in MIP (1956, pp. 234-35, 1965, p. 337), which repeats the central argument of the 1953 draft: The anticipation of a lower future price level has the same effects on the amount of labor demand as a rise in the current real wage rate. For, in making their plans, firms will compare the wage paid for current input with the lower price that will subsequently be received for its resulting output. [Footnote: Note that though in comparing future with present prices it is the rate of decline which is relevant, in comparing future prices with the present wage rate it is the level of these prices that must be considered.] ([1956] 1965, p. 337). The main reason, however, why the expectational model of 1953 is largely absent from MIP is that ch. XIII of the published version of the book offers an interpretation of the behaviour of firms that, in contrast with the draft version, claims that firms are off their labor demand curves and their aggregate commodity supply curve. Involuntary unemployment means, in the 1956 book, disequilibrium not only in the labor market (as in the 1949 EJ article and in the 1953 draft) but also in the commodity market.

Disequilibrium and Real Wages

11 The “central message” (to use a term dear to Patinkin; see 1982, ch. 4) of MIP is expressed in the introductory chapter of that book [919560 1965, p. xxv), and can be split in two propositions: (i) the long-run neutrality of money result of the quantity theory of money is valid even under the usual Keynesian aggregate demand and liquidity-preference functions, and is based on price and wage flexibility and on the assumption of absence of ‘money illusion”; (ii) Keynesian unemployment theory remains valid for the formulation of full-employment policy. The second proposition can be found already in Patinkin [(1948c) 1972)], written during his period at the Cowles Commission, whereas the former one was put forward in his 1954 essay on “Keynesian Economics and the Quantity Theory” (Patinkin, 1954). As recalled by Patinkin (1995, p. 384), “it was in the process of writing that article that I decided to write my 1956 book” (cf. 1954, p. 125, n. 7, where reference is made to his work in progress). As an implication of those two propositions, one can infer that the theoretical contribution of Keynesian economics cannot be described as the claim that money is not neutral or that it may not be neutral under certain circumstances. In particular, Patinkin ([1956] 1965, ch. XII, sections 1 and 2) showed that, using the framework of the quantity theory of money as formulated in his book, money is not neutral if prices or money-wages are rigid, and, more importantly, if money illusion is introduced. In the presence of money illusion in the labor supply function written as Ns = T(w), a downward shift of the expenditure function (caused by a reduced quantity money) brings about a fall in prices and, to a lesser extent, in the equilibrium value of money-wages. As a result of this increase in the real wage rate, the aggregate supply curve shifts to the left and brings the economy to a new fullemployment equilibrium with a lower output and employment than in the initial position. This reduction of employment cannot, of course, be described as “involuntary unemployment” in J.M. Keynes’s (1936, ch. 2) or Patinkin’s sense, since the labor market is in equilibrium and all people willing to work at the existing money-wage and price level get jobs. A similar result was reached in Marschak’s (1951, p. 64) lectures on Income, Employment, and the Price Level , a book that will be further discussed below. Patinkin’s model of involuntary unemployment in ch. XIII of MIP represented an attempt to “give precise expression” to two “intuitive, common-sense ideas which have all too frequently been unjustifiably rejected as violating the precepts of rigorous economic analysis”, not only at the Cowles Commission. “First, we see that involuntary unemployment can exist even in a system of perfect competition and wage and price flexibility...Second, we see that a deficiency in commodity demand can generate a decrease in labor input without requiring a prior increase in the real wage rate” ([1956] 1965, pp. 323-24). The first point was already present in the 1949 EJ article and in the 1953 draft, but not the second. The empirical evidence (presented by Dunlop, 1938 and Tarshis, 1939, and discussed also by Tsiang, 1947, at the time Patinkin was working on his dissertation; see also Abraham and Haltiwanger, 1995, for the more recent literature) that changes in real wages are not countercyclical represented a challenge to the traditional Keynesian assumption that firms are always on the demand curve for labor. The contradiction was noticed by Klein (1947b, pp. 106-107), who, despite the remark that “it appears that Keynes was backing the wrong horse”, did not elaborate on the problem. Patinkin was also probably influenced by the 1946-1947 controversy in AER on marginal productivity theory between Richard Lester on one side and F. Machlup and G. Stigler on the other. According to Lester’s empirical article (1946, p. 63), there was a “gap between marginal theory of the firm” and “theories of employment and business

12 cycle”. In particular, in Lester’s view, Keynes “fails to reconcile his continued adherence to the marginal-productivity theory with his new theories of employment determination, based on effective demand”. In correspondence of February 4, 1950 to Milton Friedman, Patinkin complained that “Machlup and Stigler dispense with [Lester’s empirical] findings much too glibly” and that they do not clarify “under what circumstances” they would reject the marginal productivity theory (quoted by Leeson, 1998, p. 443).7 From a theoretical perspective, Patinkin’s most important piece of analysis en route to ch. XIII of MIP was his 1952 article on the “Limitations of Samuelson’s Correspondence Principle”, which introduced into the literature the notion of “spillover effects”. The article was a generalization of an earlier short report presented at the 1947 meetings of the Econometric Society. Patinkin (1947b, p. 172) criticized Samuelson’s dynamic equation dp/dt = ø(XD - XS) on the grounds that the behaviour described by the equation “is not localized in any specific behaviour unit (e.g., firm) except in a few markets where there is an official auctioneer”. However, instead of investigating the process of price adjustment by suppliers in disequilibrium (as K. Arrow, motivated by a similar criticism of Samuelson’s approach, would do a few years later), Patinkin (1952b, p. 40) focused the argument on the notion that “the rate of adjustment in one market may depend on the excess demand in other markets”. This reflected earlier discussions with M. Friedman, as pointed out by Patinkin (1952b, p. 41). [Samuelson’s] equation attempts to describe the dynamic pressures making for changes in the price pi. But surely, as Professor Milton Friedman pointed out to the writer some years ago, the excess demand functions which appears on the right hand side of [the equation] cannot be taken as a complete measure of this pressure. For this function measures the net amount demanded on the assumption that the individuals who constitute the market are able to buy or sell as much as they desire at the prevailing set of prices. But this is precisely the situation that does not obtain under dynamic conditions; for then, by assumption, there are unsatisfied buyers and sellers. According to Patinkin (1952b, pp. 42-43), this means that the determinant is different from the one established by Samuelson and, by that, in contrast with the “correspondence principle”, the conditions for dynamic convergence will not generally be able to provide useful information about comparative statics. The role of this result in the framework of MIP is somewhat ambiguous, since, despite calling attention to spillover effects in ch. X.2, Patinkin ([1956] 1965, pp. 235-36) decided to disregard their implications for the stability of the system on the assumption that the intermarket pressures are never “strong enough” to change the directions of the market forces described by Samuelson’s equation. “Hence the system remains stable. But this stability is now a matter of assumption - not of proof”. Nevertheless, the dynamic intermarket pressures expressed by spillover effects are essential to Patinkin’s suggested reformulation of the demand curve for labor in disequilibrium. While still rejecting, as in the 1953 draft, the notion that expected sales should be an argument in the labor demand function of competitive firms, Patinkin’s solution now is to capture the influence of commodity output on labor input “not in the variables on which the labor demand function is dependent, but in its form “ ([1956] 1965, p. 319). Because of inadequate aggregate demand (which, by assumption, is not

13 quickly stimulated by the positive real balance effect brought about by falling prices and wages), firms face a quantity constraint on the amounts they can sale at prevailing prices. The reactions by Patinkin’s former colleagues of the Cowles Commission to Patinkin’s disequilibrium analysis can be illustrated by Haavelmo (1960) and Arrow (1957). According to Haavelmo (1960, ch. 32), if an additional constraint is put on a variable (e.g., an exogenous rate of interest) in the classical macroeconomic model, a “fundamental overdeterminacy emerges” and the economy operates under a different model that does have a solution. Producers will adopt different “strategies” according to whether the exogenous interest rate is equal, higher or lower than its endogenous equilibrium level. The additional variable “strategy” would solve the overdeterminacy problem. Haavelmo (p. 204) considers two different strategies for a producer, corresponding to the classical and depression cases, respectively: (a) maximize profit with regard to the inputs by maximizing profits for any given level of output and choose that output which gives the largest among the relative profit maxima; (b) maximize profit with regard to to the inputs by maximizing profit for an assumed given volume of output (the volume to be determined by somebody else). Although Haavelmo did not refer to Patinkin in that connection, there is little doubt that his treatment was influenced by ch. XIII of MIP. This is clear from his statement that The important lesson of our analysis [is that] there is no reason why the form of a realistic model (the form of its equations) should be the same under all values of its variables. We must face the fact that the form of the model may have to be regarded as a function of the values of the variables involved. Thus, for example, it is obviously absurd to maintain a supply equation which presupposes free quantity adaptation to given prices if the actual market situation is characterized by selling difficulties (Haavelmo, 1960, p. 205).8 Arrow reviewed MIP for the Mathematical Reviews in 1957. Most of the review is about part one (“Microeconomics”) of the book, but in his brief discussion of the macroeconomic part we can find the comment that ch. XIII examines the behaviour of the model “under conditions of unemployment (i.e., in disequilibrium or with rigid prices). A number of interesting problems as to the significance of the usual demand and supply functions under these circumstances are raised, though not resolved” (Arrow, 1957, p. 706). Arrow’s own solution to some of the microeconomic adjustment problems raised by ch. XIII of MIP can be found a couple of years later in his well-known 1959 piece “Toward a Theory of Price Adjustment”, which introduces the concept that perfect competition applies only to markets in equilibrium, while transitory imperfect competition should be assumed when prices are changing under the pressure of excess supply and firms face an elastic demand curve for their commodities (see also Gogerty and Winston, 1964). It is worth noting that Patinkin ([1949a] 1981, p. 169, n. 11) acknowledged discussion with Arrow at the Cowles Commission when assuming in the 1949 EJ article that equilibrium in the market for goods is quickly restored through price changes (so that perfectly competitive firms are on their supply curves all the time), in contrast with his assumption about the labor market. Patinkin ([1956] 1965, p. 323, n. 9) was aware that there was a flaw in the argument of ch. XIII of MIP, since the assumption of perfect competition could not be consistent with the notion that firms face a quantity constraint. Many years later, in a letter of February 12, 1974 to Axel Leijonhufvud,

14 Patinkin pointed out that “I did not succeed in achieving in [ch. XIII] (and this I admitted in that footnote on p. 323) an integration of my economic intuition with my formal economic analysis” and expressed his intention to “examine recent developments in the theory of unemployment in order to see it it provides an answer to [those] difficulties”. Apparently, Patinkin did not find in the then new literature on disequilibrium macroeconomics an answer to his problem, which eventually led him to suggest that the “assumption of imperfect competition” could be used to show how aggregate demand can affect output and employment (Patinkin, 1989, p. xix). Patinkin’s disequilibrium analysis in MIP was partly motivated by the attempt to show that, in contrast with traditional Keynesian theory and closer to empirical evidence, reductions in unemployment are not generally associated with falling real wages ([1956] 1965, pp. 340-41; see also Grossman, 1972). He was not able, however, to put forward a hypothesis about the cyclical behaviour of real wages, which is an indetermined variable in the model of ch. XIII. Such an indetermination goes back to his 1946 essay, where Patinkin (1946, pp. 16-17) advanced a bargaining model between firms and workers for both employment and real wages, based on the notion of “compromise coefficients”.9 In his 1948 AER Patinkin had already pointed out that the relation between money and real wages is ambiguous in Pigou (1943), although only the reduction of money-wages only, not of real wages, mattered for the eventual convergence to full-employment income. The classical school holds that the existence of long-run unemployment is prima facie evidence of rigid wages. The only way to eliminate unemployment is, then, by reducing real wages. (Since workers can, presumably accomplish this end by by reducing their money wage, this position has implicit in it the assumption of a constant price level - or at least one falling relatively less than wages). Pigou now recognizes that changing the relative price of labor is not enough, and that the absolute price level must vary. In fact, a strict interpretation of Pigou’s position would indicate that unemployment can be eliminated even if real wages remain the same or even rise...for in any case the effect of increased real value of cash balances is still present. [Footnote: The role of real wages in Pigou’s system is very ambiguous. At one point he assumes that reduced money wages will also decrease real wages...At another no such assumption seems to be involved.] (Patinkin, [1948] 1972, p. 17). In his 1949 EJ article, as discussed above, Patinkin simply assumed, in traditional fashion, that real wages are decided by the marginal productivity of labor. This reflected the tacit assumption that the market value of the real wage rate is determined by its demand price, as claimed by L. Klein in his Keynesian Revolution. According to Klein (1947b, p. 203), under conditions of a fall in employment caused by inadequate aggregate demand, “it is not meaningful to assume that employed workers move downward along their supply schedule of labor, for they would be accepting a smaller real wage than employers would be willing to pay. But it is meaningful to assume that they move upward along the demand curve for labor and get the highest possible real wage offered for the amount of labor corresponding to the reduced level of income”. Over the years, however, Patinkin remained unconvinced by Klein’s solution to the real wage bargaining problem, which was the same one implicitly adopted by Keynes. In an unpublished note written in the early 1990s and intended as a revision of his 1987 New Palgrave entry on Keynes,

15 Patinkin elaborated on Alfred Marshall’s general influence on the framework of the General Theory and suggested that “Keynes’s basic assumption that any instant of time employed workers receive a real wage equal to their marginal product even though there are unemployed workers willing to work for less is a reflection of Marshall’s fish-market analysis, in which the market price equals the demand price, even though there are sellers willing to sell for less”. This was, however, an incorrect application of Marshall’s fish-market analysis, since “in pure case there is no reservation demand there, whereas there is one in labor market, so supply curve of labor not vertical but upward sloping”. Keynes’s assumption, that under unemployment conditions the real wage rate paid by firms exceeds the rate (measured by their marginal disutility) upon which workers insist in order to supply that amount of labor, was noticed elsewhere by Patinkin (e.g., 1982, p. 134), although not discussed on that occasion. The real wage rate indetermination problem, as clarified in a letter of January 12, 1987 to Tom Rymes about Patinkin’s entry on “Walras’s Law” in the New Palgrave, could be interpreted with the help of the concept of “constrained supply of labor”, as opposed to the virtual or “notional” supply of labor.10 Under the assumption of passive adjustment by workers of the amount of labor they supply to the amount demanded by firms (which can be found already in Patinkin, 1946; see also 1987, p. 867; MIP, passage added in the second edition, p. 333, n. 22), Patinkin wrote to Rymes that the “constrained excess demand for labor is always zero...and the [real] wage rate is, strictly speaking, then indeterminate”. In the New Palgrave entry on Walras’s Law, however, ‘I simply accept Keynes’ assumption that the real wage rate is always equal to the marginal product of labor...One can, however, rightly ask why this is so - and this question is related to the ‘basic analytic problem’ of footnote 9 of chapter XIII” of MIP. A way out of the indetermination problem is provided by the “efficiency wage” and insideroutsider” models of real wage rigidity developed in the 1980s. Together with the assumption of imperfect competition in the commodity market, real wage rigidity can then be interpreted as reflecting a horizontal demand curve for labor, with the actual level of employment determined by aggregate demand for output. As suggested by Patinkin (1989, p. xix), “this would accord with my ‘more Keynesian that Keynes’ interpretation of involuntary unemployment described on pp. 340-41” of MIP, but would also imply the rejection of the off aggregate supply curve analysis advanced in that book.

Keynes, Marschak and the AS-AD model Marschak’s reaction to Patinkin’s use of the concept of an aggregate supply function in his 1947 “Reconsideration of the The Theory of Unemployment” is illustrative of the neglect of the supply side in Keynesian theory at the time. Marschak asked Patinkin in March of that year: “Has this concept [of a supply function] ever been used? What is its counterpart in the Keynesian system? It cannot be an investment function...nor can this be the production function, I think”. Marschak’s bewilderment with the aggregate supply function concept did not last long, though, for in his 1948 lectures at the University of Chicago - where he had replaced Oskar Lange as professor of macroeconomics - he was already discussing the “Supply Curve for All Goods” (Marschak, 1951, lecture 19). However, whereas Patinkin usually formulated his aggregate supply function as the result of an “individual experiment” based on labor demand only, Marschak deployed a “market experiment” where the aggregate

16 supply function reflects the assumption made about equilibrium (or disequilibrium) between labor demand and labor supply. Marschak’s supply function is, therefore, a “reduced form” in the price-output coordinates that results from the “structural equations” of the labor market. His “supply sub-set” is described by 5 equations: the labor demand function nd = (W, P); the labor supply function ns = (W, P); the equilibrium conditions in a “free (i.e., non-unionized) labor market” n = nd = ns; and the short run production function y = (n). As explained by Marschak (p. 55), “with the help of these 5 equations we can, in general, eliminate 5 out the 6 variables involved (n, nd, ns, W, P. y). By eliminating all variables but P and y we obtain a ‘supply curve for all goods’, under conditions of free labor market”: y = ¥(P; ; ; ). The position of the curve depends on the values of , and , while its slope depends on the assumptions made about money illusion in the labor supply and demand functions. As suggested by George Horwich (1997, p. 8), Marschak (1951) presented the first formulation of what would become known a few decades later as the “ASAD model”. Marschak’s “demand curve for all goods” was advanced in lecture 18, where he developed the “demand sub-set” of the model. It consists of 3 equations (private aggregate demand as a function of income, interest rate, money stock and tax rate; the equality between income and the sum of private demand and government expenditure; and the equality between the money stock and money demand as a function of interest, income and the tax rate) in three endogenous variables (private aggregate demand D, income Y and interest rate r), all measured in nominal terms. He then writes Y as a reduced form function of all the exogenous variables of the demand sub-set and introduces the key assumption that at least one group of individuals suffers from “money illusion” in their expenditure decision (consumers or government etc), which assures that the price level enters the system of behaviour equations and, by that, brings about a negative functional relation between y (= Y/P) and P. As pointed out by Marschak (p. 54), the “demand curve for all goods” involves two endogenous variables, y and P. “It is not a reduced form. It does not explain by itself how either y or P is determined by outside conditions. There must exist a further relation between these same variables”, which is the aggregate supply function. Marschak’s complete model consists of the aggregate demand and supply functions, which decide simultaneously real output and the price level. If both labor supply and demand functions are free of money illusion [that is, nd = (W/P) and ns = (W/P)], they determine n and W/P, which means that the aggregate supply curve is horizontal (since Marschak puts P and y on the horizontal and vertical axes, respectively) and employment is not affected by price changes. This is the “classical” theory of the labor market (p. 58). Generally, the aggregate supply curve will be upward-sloping if employers are “relatively more price-conscious” than workers (p. 59), which includes as a special case the assumption that nd = (W/P) and ns = (W, P) or ns = (W) . Under these circumstances, a shift of the aggregate demand curve would affect both output and price level; in particular, the model would not feature money-neutrality.Nevertheless, as Marschak is at pains to clarify, the condition n = nd = ns still applies, which means that an upward-sloping supply curve is not theoretically associated with involuntary unemployment. The model does not account for involuntary unemployment “in the sense that not all people willing to work at at existing W and P get jobs. They all do.” In order to introduce the possibility of involuntary unemployment, Marschak replaces the equilibrium condition in the labor market for n = Min(nd, ns), that is, “employment is equal to

17 either the demand for or the supply of labor, whichever is smaller” (p. 64). This was probably the first appearance of the “short-side” rule in the literature.11 The replacement of the two equations n = nd = ns by the equation n = Min(nd, ns) introduces overdeterminacy into the model, which leads Marschak to include the equation W = W o expressing the action of trade unions. As explained by Marschak, the equation W = W o is not a “labor supply function of the unions”, since labor supply is still expressed by the ns function. “The failure of labor demand and supply quickly to become equal to each other is explained by the fact that the wage-bargaining is done by unions rather than by individuals” (p. 64). This is different from L. Klein’s (1954) notion discussed above that there is money illusion in the dynamic bargaining equation only, but it plays a similar role. The supply sub-set of the model consists now of the labor supply and demand functions, the production function and the equations n = Min(nd, ns) and W = W o. Patinkin neither mentioned Marschak (1951) in MIP nor usually deployed a reduced aggregate supply function a la Marschak. There is a brief mention in MIP (p. 211) to the representation of Patinkin’s supply function Y = S(w/p, Ko) within the (p, Y) (which stands for real income in Patinkin) coordinate system. The curve is upward-slopping, since “the higher the price level, the lower the real wage rate, the greater the input of labor, and the greater, therefore, the aggregate amount of commodities supplied”. It is clear enough that, in Patinkin’s individual experiment, money-wages are taken as given by firms. Although this is the supply function concept used in ch. XIII of MIP, it is possible to find a different supply function in the book, which, like Marschak’s, reflects the behaviour of suppliers as a whole, including workers. So, in a footnote added on p. 42 of the second edition as part of a discussion of the stability of the price level (originally developed for an “exchange economy”), Patinkin claims that the argument remains valid for a “production economy”, since supply depends only upon relative prices in system without money illusion and the supply curve is accordingly vertical within (p, Y) coordinates (see also pp. 76-77). He further notices that stability analysis of the price level would not be affected if supply (not only demand) was assumed to depend on real balances, provided it was a decreasing function of such balances and, therefore, it featured a positive slope.12 Furthermore, Patinkin ([1956] 1965, p. 211) also mentions the representation of his aggregate demand function E = F(Y, r, Mo/P) within (p,Y) coordinates, reflecting the direct (on the commodity market) and indirect (on the bonds market) real balance effects of a change of the price level. Although the formulation is apparently similar to Marschak’s, it should be noted that the influence of the price level on aggregate expenditure, called “money illusion” by Marschak, is an expression of rational behaviour and by no means an “illusion” in Patinkin’s framework (cf. MIP, p. 627, n. 35). Marschak’s “short-side” rule for the labor market can be found many years later in Patinkin’s last formulation of his general-equilibrium macroeconomic model, as an appendix to an article on Israel’s stabilization program of 1985 (Patinkin, 1993). It is noteworthy that there are no equations in ch. XIII of MIP (in contrast with the previous chapters of the book), except for a model of a fix-price, fix-wage economy in section 4, also discussed in the mathematical appendix ([1956] 1965, pp. 330 and 510-514). The model in Patinkin (1993, pp. 122-23) is formally similar to the one presented in ch. X of MIP, with the crucial difference that output is an endogenous variable, in contrast with the full-employment model of ch. X. Patinkin’s 1993 model reads (excluding the equation for foreign exchange): F(Y, r, M/P) -Y = 0

18 Nd(w/p, Ko) - Ns(w/p) = 0 B(Y, r, M/p) = 0 L(Y, R, M/p) - M/p = 0 Y = ø[N•(w/p, Ko)] where ø[ ] is the production function and N•( ) is “the lesser of Nd( ) and Ns( ).” The equation for Y is the new-comer in the model, since it differs from the previous supply equation adopted in MIP by including explicitly the “short-side” rule. In contrast with the off supply curve analysis of ch. XIII, the new equation states that firms will be on their labor demand curves under conditions of excess supply in the labor market. The 1993 system consists of 4 independent equations in 4 endogenous real variables (r, w/p, M/p, Y). Taking into account the nominal variables, there are two real variables r and Y, and 3 unknown nominal variables (w, p, M). Patinkin then fixes the value of one nominal variable (M) in order to determine the value of the other nominal variables w and p. The equilibrium of the system, described as “a situation in which every agent is on his demand and/or supply curve, is, by definition, a position of full-employment at which Y = Yo. It should be noted that, as opposed to Marschak (1951), Patinkin’s use of the short-side rule is not associated with an exogenously given money-wage, which is endogenously determined in the model.13 The AS-AD model has become, since the 1970s, a workhorse in the macroeconomic literature. Patinkin used the model in his lectures for undergraduates in the 1970s and 1980s, which, however, he based on Dornbusch and Fischer 1978 textbook, instead of his own MIP. In his lecture notes of spring 1979 for a macroeconomic course delivered at the University of Chicago Patinkin followed Dornbusch and Fischer (and many other textbooks) in the derivation of the aggregate demand curve as the locus of intersection pints in the IS-LM diagram as the price level changes. As in Marschak (1951), but differently from Patinkin’s own construction of the aggregate demand curve within (p,Y) coordinates in MIP, the textbook curve represents the relation between two endogenous variables (p, Y) when the commodity and money markets are in equilibrium. Patinkin also followed Dornbusch and Fischer in the derivation of an upward-slopping aggregate supply curve based on the assumptions of mark-up pricing and constant average productivity of labor (which, by the way, implies that real wages do not move countercyclically). The short-run aggregate supply curve shifts over time to the extent that money-wages adjust to disequilibrium in the labor market according to a Phillips curve relation. In his 1990 “Defense of IS-LM” Patinkin (1990a, p. 124) suggested a specification of the aggregate supply curve consistent with Keynes’s (1936) assumptions about price level determination under perfect competition. Using Keynes’s assumptions that the “second classical postulate” (equality between real wage and marginal disutility of employment) should be rejected and the “first classical postulate” (equality between real wage and marginal product of labour) accepted, Patinkin argued that an upward-slopping aggregate supply curve could be derived for a fixed money-wage rate. This would provide the missing relation to determine the price level and output together with the aggregate demand curve derived from the IS-LM framework.14 Although consistent with Keynes’s construction, “needless to say, these curves are not the same as those which respectively bear these names in chapter 3 of the General Theory (Patinkin, 1990a, p. 124). Patinkin’s reference to the use of aggregate supply and aggregate demand concepts in Keynes’s General Theory reflected his long time struggle on how to

19 interpret the meaning of “aggregate demand price” and, especially, “aggregate supply price” on pp. 24-26 of that book. In his unpublished 1948 manuscript, Patinkin (1948a, p. 32, n. 17) suggested that by “aggregate supply price” Keynes meant output Y, not a supply function. In a letter of May 12, 1952 to de Jong, replying to the criticism that he had overlooked Keynes’s aggregate supply analysis in his 1949 EJ article, Patinkin wrote that “I have been puzzled...as to the meaning of Keynes’ pages 24-5...I must confess that I simply do not understand these pages in Keynes”. The publication of Patinkin ([1949] 1981) and Keynes’s obscurity on that score raised a debate between 1954 and 1962 in the Economic Journal (see King, 1994), but Patinkin neither took part nor removed from MIP the charge that there is no supply analysis in the General Theory. This change after the publication of the first volumes of Keynes’s Collected Writings in the early 1970s, which led Patinkin to embark on a comprehensive investigation of the development of Keynes’s macroeconomic thought (see Patinkin, 1976, 1982). Ch. 9 of Patinkin (1976, p. 84, n. 3) was his first attempt to “amend [the] error” of his 1949 contention and come to terms with Keynes’s “aggregate supply price”. Patinkin (1976, p. 91, n. 12; 1982, p. 131, n. 9) eventually concluded that Keynes’s (implicit) formulation of the supply function was very close to Patinkin’s own presentation in MIP, although marred by some mistakes in the discussion of the mathematical properties of the function. Part of the difficulties were caused by the fact that Keynes usually described his aggregate demand and supply functions as functions of the employment level (instead of output) and measured in wage units. Furthermore, he did not deploy diagrams to represent them. A diagrammatic representation of Keynes’s aggregate supply price function Zw = ø(N) would show, because of the assumption of diminishing returns, rising prices and declining real wage along the curve. As pointed out by Patinkin (1976, p. 91, n. 12), Keynes’s procedure of “associating different points on his upward sloping aggregate supply curve with different levels of the real wage rate” is “analytically much the same” as its representation as a vertical function drawn as of a given real wage rate, which shifts when the real wage rate changes, as in MIP. This means that the 45o line in the Keynesian-cross diagram can be interpreted as a representation of the amount produced and supplied by firms as they move along their labor-demand curves, with the real wage rate declining as they move rightwards along the 45o line (cf. Patinkin, 1987, p. 866). However, even granting the formal correctness of Keynes’s concept of “aggregate supply price”, there remained, according to Patinkin (1976, p. 94), the problem of Keynes’s assumption that firms are always on their aggregate supply functions. As I have argued elsewhere, the planned labor input specified by this demand curve reflect the firms’ profit-maximizing behaviour on the assumption that at the designed real wages they will be able to sell in the market all of their corresponding planned output. Why, then, should this curve continue to be relevant for a situation of disequilibrium in which, by definition, this assumption is not fulfilled? In brief, despite Keynes’ declared objective of integrating monetary and value theory, he did not really develop a theory of the demand for labor consistent with the state of unemployment qua market disequilibrium that was his major concern in the General Theory. Patinkin did not repeat that criticism in his further discussion of Keynes’s principle of effective demand a few years later (see Patinkin, 1979, 1982). This can be explained by the fact that, whereas in 1976 (following the framework of MIP) he

20 adopted a Walrasian perspective on the labor demand function, in 1979 and after the formulation is Marshallian, which of course accords better with Keynes’s own approach. The distinction between the Marshallian and Walrasian experiments in the derivation of the labor demand curve was pointed out by Leijonhufvud (1974, pp. 166-68). Keynes’s Marshallian firms decide the amount supplied based on their (uncertain) expectation of market price for their commodity at the start of the production period, whereas Walrasian firms calculate their demand for labor and supply of output on the belief that this volume of output can be sold at the announced price. Hence adding an independently specified “sales-expectation” means that the Walrasian experiment becomes “overdetermined”, in contrast with the Marshallian formulation. From this perspective, the locus of solution points for w/p and N is formed through the effect of changes in effective demand on market equilibrium prices under the assumption of diminishing returns (see also Davidson, 1967; Casarosa, 1981). As pointed out by Patinkin (1982, p. 19), Though [Keynes’s] new theory retained the classical inverse relation between real wages and employment, it reversed its causal direction: it was not the real wage rate which determined the level of employment, but the level of employment which determined the real wage rate. Thus, under conditions of unemployment and a given level of effective demand, a reduction of money-wages generates an initial decline in the real wage rate, which increases the level of employment and output, generating an excess of aggregate supply and bringing the price level down until the original real wage and employment levels are restored (see Patinkin, 1982, p. 142). As stressed by Patinkin (p. 132), the double fact that the slope of Keynes’s aggregate supply function (dZw/dN) is higher than one (because of diminishing marginal productivity)15 and that the slope of the aggregate demand function is less than one (because of the consumption function) assures that a fall in output caused by excess aggregate supply will reduce supply more than demand and bring the economy to its equilibrium level of output, which constitutes - together with Keynes’s discussion of the uncertain effects of falling money-wages on aggregate demand in ch. 19 of his book, previously discussed by Patinkin in his 1948 AER article - the “central message” of the General Theory.

Concluding Remarks There is one important macroeconomic concept conspicuously absent from Patinkin’s writings on unemployment and aggregate supply: the Phillips curve. There is no reference to Phillips (1958) in the 1965 edition of MIP, and only very few ones in the rest of Patinkin’s books and articles. Part of the explanation can be found in Patinkin’s criticism of M. Friedman’s well-known 1974 interpretation of the quantity theory of money and Keynesian economics. According to Friedman (1974, p. 32), Keynesian models in the 1950s lacked an equation for the determination of prices, provided by the discovery of the Phillips curve. Patinkin (1974, p. 129) disagreed with Friedman’s suggestion of a “missing equation” and pointed out that “first of all, an economic analysis of wage movements was already provided by the General Theory. Indeed, the Phillips curve theory itself is foreshadowed in chapter 19 and 21 of this book. Second, even before the flourishing of the Phillips curve, Keynesian econometric models generally treated the wage and price level as endogenous variables of the system”. He referred on that occasion to the macroeconometric

21 estimations carried out by L. Klein and others at the Cowles Commission and after. More importantly, according to Patinkin, the concern of Keynesian econometric models with the determination of prices and wages was a by-product of their focus on disequilibrium states. “In the Keynesian system there is no equilibrium equation for the labor market, but rather a dynamic wage-adjustment equation determining the rate of change of the nominal wage rate in response to the state of excess supply in this market”. Patinkin’s contribution to that literature, particularly in the late 1940s and in the 1950s, was the investigation of the causes of market disequilibrium, instead of an attempt to establish the determinants of the pace of wage and price changes brought about by such an state of disequilibrium. This has become since the early 1970s the focus of the literature on the microfoundations of the Phillips curve, which Patinkin (1982, p. 158) described as “the most fruitful contributions to the theory of aggregate supply during the past decade”. This was particularly the case of the analysis of the effects of incomplete information on the determination of money-wage and prices, which, as Patinkin (1982, pp. 137-38) pointed out, should not be interpreted as “money illusion”. It is clear from the preceding discussion that Patinkin changed his mind throughout his long quest for the correct specification of the aggregate supply function and interpretation of the analytical relationship between the labor and commodity markets. His ambiguous “desired-supply function” was replaced in 1949 by the “familiar supply function”, while keeping the hypothesis (made by L. Klein and others at the Cowles Commission) that firms are on their labor demand curves. The overdetermined system of his 1947 thesis was replaced by a system featuring the real balance effect, but the original association between unemployment and points off labor supply curve was kept. The introduction of the real balance effect in 1949 led Patinkin to examine carefully the disequilibrium dynamics when prices and wages are changing, which he did in the 1953 draft of MIP by introducing the notion of “effective anticipated real wage rate” and its influence on labor demand. However, he assumed “static expectations” in the published version of MIP , when the notion that perfect competitive firms face quantity constraint was advanced for the first time. Although Haavelmo interpreted ch. XIII of MIP positively in terms of the old overdetermination problem of the Cowles Commission, others (like Arrow) realized the analytical problems involved in the assumption of perfect competition in disequilibrium, of which Patinkin was aware. After his initial surprise with Patinkin’s notion of an aggregate supply function, Marschak put forward what was probably the first AS-AD model in the literature. In the process, he introduced the “short-side” rule, which Patinkin deployed in his last statement of the aggregate supply function in 1993. By that time, it was clear to Patinkin that Keynes’s original concept of “aggregate supply price” could be applied to the determination of the equilibrium level of output under the assumption that firms are on their labor demand curves, associated, though, with its unattractive implication that real wages are countercyclical.

Notes I would like to thank the staff of the Special Collections Library of Duke University for their kind help with the Patinkin files. Research funding from CNPq (Brazilian Research Council) is gratefully acknowledged.

22 1. Patinkin (1946) suggested a model of “compromise” between consumers and suppliers according to their bargaining power. However, in the 1949 EJ article he assumed something like the “short-side” rule by stating that “it is difficult to conceive of demanders buying more than they desire” ([1949] 1981, p. 167). 2. In a footnote to p. 11, Patinkin (1946) writes the corresponding macro system: (a) Xd = [(w/p)N, Y - (w/p)N] (b) Y = ø(N, Ko) (c) ND = f(w/p) (d) NS = g(w/p) (e) ND = NS = N (f) Xd = Y

demand for goods production function demand for labor supply of labor

which gives 7 equations in 6 variables (Y, w/p. N, ND, NS, Xd). 3. The first diagrammatic discussion of involuntary unemployment as points off the labor supply curve was probably provided by Joan Robinson (1937). See Boianovsky, 2000. 4. As pointed out by Patinkin in a note added to the 1981 reprint of his article, this assumption contradicts the law of diminishing returns. For a correct derivation of the “desired-supply curve” see Edwards, 1959. 5. “Consider a dynamic economic system which is such that, if we omitted all the dynamic elements in it, we should have an overdetermined static system. Then the dynamic system may have a solution, but it can have no stationary solution. The economic interpretation of this is that the time-motion of prices and quantities may serve as an outlet for the forces that press for the fulfilment of the impossible conditions for stationariness” (Haavelmo, 1960, p. 207). On the importance of inhomogeneities in Klein see also Ball (1981). 6. As explained by Lange (1944, p. 29, n. 1), “this does not imply perfect knowledge. The expected prices may differ from the prices which are realized subsequently.The certainty of the expectations is merely subjective “. 7. Many years later, Patinkin (1989, p. xvi) commented on “la condition scientifique of our discipline: its inability in all too many cases to reach definitive conclusions about theoretical questions on the basis of empirical studies”. He did not believe that the Cowles Commission’s careful estimation of structural equations based on firm probabilistic principles yielded more accurate predictions than other methods and was in general skeptical about the ability of econometricians to derive empirical macroeconomic structural relations “which will stand up under the test of time” (1995, p. 387). 8. It is unlikely that Haavelmo influenced directly Patinkin’s off demand for labor curve analysis, since in his previous discussion of overdetermination in the classical system Haavelmo (1949-1950, p. 79. n.) mentioned only points off labor supply curve.

23 9. Patinkin eventually gave up his 1946 “compromise model”, apparently because of its outcome is uncertain if the participants refuse to adjust their compromise coefficients in the necessary manner, which can lead to a “revolution” and the breaking down of the whole system until “the new realignment of power is settled” (1946, p. 17). 10. Patinkin (1987) criticized Robert Clower’s well-known argument that Walras’s Law does not hold in disequilibrium, on the grounds that the “law” is always valid if the excess-demand equations consistently reflect the influence of quantity constraints. See Rhodes (1984) for a similar criticism. 11. The short-side rule is based on the principle of voluntary action, which is “a fair description of our institutions” (Marschak, p. 64). 12. Dixon (1995, pp. 59-63) has suggested that Patinkin’s discussion of the labor market in MIP (pp. 202-205) contains implicitly the first formulation of the fullemployment vertical supply curve of the AS-AD model, under the assumption of absence of real balance effects in the labor market. However, full employment is only a “bench mark” in MIP (p. 205). Furthermore, Dixon has overlooked Marschak’s explicit derivation of a vertical AS curve. 13. As pointed out by Patinkin ([1949] 1981, pp. 163-64), “those workers unable to find jobs because of the union wage policy might be said to be ‘involuntary’ unemployed; but this involves a completely different usage from the customary one, which implies that workers are unemployed neither through their fault, nor through that of their brethren”. 14. Patinkin (1990b, p. 220) clarified that Hick’s original 1937 formulation of IS-LM, as opposed to the usual textbook presentation, included the production functions and prices of consumption and investment goods. 15. This can be seen in the following derivation by Patinkin (1982, pp. 131-32; see also Casarosa, 1981). The production function Y = ø(N) in wage units is given by Yw = [pø(N)/w]. Upon substitution from the profit maximizing condition w/p = ø’(N), Yw becomes the aggregate supply function Zw = [ø(N)/ø’(N)], with dZw/dN > 1, since ø’’(N) < 0. Apparently, Klein (1947, p. 203) was the first one to derive the expression above for Zw, but he did not develop its mathematical properties.

References A) By Don Patinkin Patinkin, D. 1946. Unemployment in Keynesian Systems. Unpublished manuscript. Special Collections Library, Duke University. Patinkin, D. 1947a. A Reconsideration of the Theory of Unemployment. Unpublished manuscript. Special Collections Library, Duke University.

24 Patinkin, D. 1947b.. Market-adjusting and inventory equations. Econometrica. 15 (April): 172-73. Patinkin, D. 1948a. Relative prices, Say’s Law and the demand for money. Econometrica. 16 (April): 135-54. Patinkin, D. 1948b. Inconsistent Systems and Involuntary Unemployment. Unpublished manuscript. Special Collections Library, Duke University. Patinkin, D. 1948c. Price Flexibility and Full Employment. American Economic Review. 38 (Sept): 543-64. As reprinted in Patinkin 1972, ch.2. Patinkin, D. 1949a. Involuntary Unemployment and the Keynesian Supply Function. Economic Journal. 59 (Sept): 360-83. As reprinted in Patinkin 1981, ch. 7. Patinkin, D. 1949b. The Indeterminacy of Absolute Prices in Classical Economic Theory. Econometrica. 17 (Jan): 1-27. As reprinted in Patinkin 1981, ch. 5. Patinkin, D. 1952a. The Limitations of Samuelson’s “Correspondence Principle”. Metroeconomica. 4 (Aug): 37-43. Patinkin, D. 1952b. Wicksell’s “Cumulative Process”. Economic Journal. 62 (Dec): 835-47. Patinkin. D. 1953. “Money, Interest and Prices”. Unplublished draft. Special Collections Library, Duke University. Patinkin, D. 1954. Keynesian Economics and the Quantity Theory of Money. In K. Kurihara, ed. Post-Keynesian Economics. Rutgers: Rutgers University Press, 12352. Patinkin, D. 1956. Money, Interest, and Prices: An Integration of Monetary and Value Theory. Evanston: Row, Peterson. Patinkin, D. 1965. Money, Interest, and Prices: An Integration of Monetary and Value Theory. 2nd edition. New York: Harper and Row. Patinkin, D. 1972. Studies in Monetary Economics. new York: Harper and Row. Patinkin, D. 1974. Friedman on the Quantity Theory and Keynesian Economics. In R. Gordon, ed. 1974, 111-31. Patinkin, D. 1976. Keynes’ Monetary Thought - A Study of its development. History of Political Economy. 8 (Spring): 1-150. Patinkin, D. 1981. Essays On and In the Chicago Tradition. Durham, NC: Duke University Press. Patinkin, D. 1982. Anticipations of the general Theory? And other essays on Keynes. Oxford: Basil Blackwell.

25 Patinkin, D. 1987. Walras’s Law. In J Eatwell et al, eds. The New Palgrave - A Dictionary of Economics. Vol. 4: 863-868. London: Macmillan. Patinkin, D. 1989. Money, Interest, and Prices: An Integration of Monetary and Value Theory. 2nd. edition, abridged, with a new Introduction. Cambridge, Mass.: MIT Press. Patinkin, D. 1990a. In Defense of IS-LM. Banca Nazionale del Lavoro Quarterly Review. No. 172 (March): 119-34. Patinkin, D. 1990b. On Different Interpretations of the General Theory. Journal of Monetary Economics. 26 (2): 205-43. Patinkin, D. 1993. Israel’s Stabilization Program of 1985, Or Some Simple Thruths of Monetary Theory. Journal of Economic Perspectives. 7 (Spring): 103-28. Patinkin, D. 1995. The Training of an Economist. Banca Nazionale del Lavoro Quarterly Review. No. 195 (Ded): 359-95. B) Other references (to be completed)

Universidade de Brasília Instituto de Ciências Humanas Departamento de Economia

Programa de Seminários Acadêmicos Os seminários acadêmicos do Departamento de Economia são geralmente realizados às sextas-feiras no Auditório do Instituto de Ciências Humanas ou no Anfiteatro nº 16, das 16 às 18hs. A partir de novembro de 1998 os textos passaram a ser sistematicamente reproduzidos e catalogados. A partir de março de 2000 os textos passaram a ser incluídos na página do Departamento na internet: http://www.unb.br/ih/eco/ecosum.htm. Os seminários apresentados a partir de 1 de setembro de 2000 foram: Número Data

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Mauro Boianovsky ECO/UnB

Patinkin on Involuntary Unemployment and the Aggregate Supply Curve

Mini-cursos de Abertura do Semestre A partir do primeiro semestre letivo de 1999, cada período letivo tem sido aberto com um mini-curso envolvendo tópicos avançados que geralmente não são abordados nas disciplinas tradicionais do curso de Economia. O mini-curso é ministrado por especialistas de amplo conhecimento na área e é aberto à comunidade acadêmica em geral. Os mini-cursos proferidos foram: Semestre

Data

Apresentador

Título

I/1999

19-22/4/1999

Marilda Sotomayor ECO/USP

Mercados de Matching de Dois Lados

II/1999

31/8-3/9/1999

Marcos Lisboa EPGE/FGV

Mercados Sequenciais e Ativos Financeiros em Modelos de Equilíbrio Geral

I/2000

27-31/3/2000

Naércio Menezes Filho ECO/USP

Microeconometria

II/2000

21-24/8/2000

Fábio Kanczuk ECO/USP

Modelos Econômicos de Processos Políticos

I/2001

16-24/4/2001

Arilton Teixeira IBMEC-Rio

Introdução à Teoria dos Ciclos Econômicos Reais

I/2001 (extra)

12-15/6/2001

John Seater North Carolina St. Univ.

Bank Regulation

Para maiores informações sobre como obter os textos favor comunicar-se com: Richard Renz Maurício Soares Bugarin Secretário do Programa de Seminários Coordenador de Pesquisa e Extensão E-mail: [email protected] E-mail: [email protected] Departamento de Economia, Universidade de Brasília ICC Norte, Asa Norte, 70910-900 Brasília/DF/Brasil Telefone: 61-2723548, Fax: 61-3402311