This document deals with the following topics:
Consider the following statement: "I will assume all markets with the sole exception of the labour market are in equilibrium." This is a statement (assumption) often made by economists of the keynesian persuasion or by those attempting to model an economy along keynesian lines.
Some economists (in particular, economists familiar with General Equilibrium Theory) would object strongly to this statement. They would say, "either all markets are in equilibrium, or more than one is in disequilibrium, but we can't have a situation where only one market is in disequilibrium". Their argument is based on Walras Law (or, more fully, "Walras Law of Markets"). Walras Law states that if there is excess supply in one market (eg involuntarily unemployed labour) then there must be a 'matching' excess demand elsewhere (eg. an excess demand for commodities). This would seem to be in conflict with, and cause us to ponder the wisdom of, the keynesian claim (and Keynes' own claim) that excess supply in the labour market can be an "equilibrium" and thus a persistent state of affairs in a (free) market economy.
Marie-Esprit-Leon Walras (b.1834, d. 1910) was a French-born economist whose outstanding work Éléments d'économie politique pure (Elements of Pure Economics) published in 1874 was one of the first comprehensive mathematical analyses of general economic equilibrium. (The book was very mathematical and perhaps more so than most works in Economics at the time. One reviewer went so far as to say that it displayed "an exuberance of algebraic foliage".)
A Professor of Political Economy at the Academy of Laussane in Switzerland, Walras is generally credited with having founded the "Laussane School of Economics". This school was to flourish under Walras successor as Professor of Political Economy at Laussane, the Italian economist and sociologist, Vilfredo Pareto.
Walras described the economic system in mathematical terms. For each product there is a "demand function" that expresses the quantities of the product that consumers demand as depending on its price, the prices of other related commodities, the consumers' incomes, and their tastes. For each product there is also a "supply function" that expresses the quantities producers will supply as depending on their costs of production, the prices of productive services, and the level of technical knowledge. In the market for each product there is a point of "equilibrium" at which a single price will satisfy both consumers and producers. Since equilibrium in each market depends on what happens in all other markets, finding a "general equilibrium" solution involves the simultaneous determination of equilibria in all markets. In order to do this, Walras constructed a mathematical system of simultaneous equations reflecting demand and supply in all the markets. Assuming that market clearing was synonymous with market equilibrium, assuming also "a regime of perfect competition" and that the quantities of inputs and outputs and their prices all automatically adjust to their equilibrium values before any trades actually take place, he was able to show how such a system might generate a unique equilibrium set of prices and quantities. (Walras described the process by which equilibrium is established as tatonnement or 'groping', emphasising that equilibrium prices and quantities were established through repeated experiments.) His work laid the foundation for mathematical economics and led the historian of economic thought Joseph Schumpeter to call the system of equations set out in Walras Éléments d'économie politique pure "the Magna Carta of Economics" (Schumpeter, 1954, p 242).
In this section I set out an intuitive explanation of Walras Law. Click here for a formal proof of Walras Law using summation notation and summation calculus (it's not very hard, really). Indeed, you might like to look at the formal demonstration of Walras Law first, and then you can judge how successful I have been at summarising the essential features of Walras Law in words.
In a Walrasian economic model (and in many others as well) each trader will plan to dispose one way or another of all of the income they intend to receive from selling goods, their labour services, financial assets or whatever. Consequently, for each trader the total value of their planned supply must exactly equal the total value of their planned demands. If we now look at the relationship between aggregate value of all commodities demanded by all traders and the aggregate value of all commodities supplied by all traders, the two must be equal. This implies that, should there ever be an excess of demand over supply for any one commodity, there must be a corresponding excess supply over demand (an excess of supply over demand is also called "negative excess demand") for at least one other commodity, otherwise the aggregate value of amounts agents wish to supply could not be equal to the aggregate value of amounts agents wish to demand. Another way to put this, is to say that the sum of excess demands over all the markets in the economy must equal zero and that this applies whether or not all markets are in (general) equilibrium. This is Walras Law.
What is important for macroeconomic modelling is that Walras Law implies that if there is excess supply (negative excess demand) in one market, then there must, corresponding to this, be positive excess demand in at least one other market. As we shall see, this implication of Walras Law leads many to be concerned about the theoretical grounding of Keynes' theory of unemployment and to be worried when a macroeconomic modeller says "let us assume that all markets are in equilibrium except the labour market".
Walras versus Keynes
It is an implication of Walras Law that an excess supply in any one market (eg an excess supply of labour - and remember that if we say there is an excess supply of labour we are saying that there is involuntary unemployment) must be 'matched by' an 'equivalent' excess demand elsewhere (eg. an excess demand for commodities). Why is this? First, because we have just seen, as a matter of mathematics, that the sum of excess demands in a market economy must be zero. This implies that if one market has excess demand there must be at least one other market with a corresponding level of excess supply. Second, and more intuitively, the excess supply of labour must be accompanied by an offsetting excess demand elsewhere (eg for commodities) because the unemployed workers must have been intending to do ('buy') something with the wages they hoped to earn. As mentioned in the first section of this document, this would seem to be in conflict with, and cause us to ponder the wisdom of, the keynesian claim (and Keynes' own claim) that involuntary unemployment can be an "equilibrium" - and thus a persistent - state of affairs in a (free) market economy.
Why is there a conflict between Walras Law and Keynes' model of the economy?
Two reasons:
First, followers of Walras would say that it does not make sense (and so it is not scientific, it is not acceptable) to "assume that all markets are in equilibrium except the labour market". As I mentioned in the introduction to this document, they would say, "either all markets are in equilibrium, or more than one is in disequilibrium, but we can't have a situation where only one market is in disequilibrium".
Second, followers of Walras would say that involuntary unemployment cannot persist in a market economy with flexible wages and prices. They would argue that if the commodities market has excess demand then the prices of commodities will tend to rise and this will tend to reduce the level of excess demand in that market. In the labour market, where there is excess supply, they would assert that the money wage will tend to fall. The joint effect of the rising price level together with a falling money wage is that the real wage will tend to drop thus reducing (and eventually removing entirely) the excess supply in the labour market.
As a consequence of the above, many would see the pronouncements of Keynes that the economy could find itself with an excess supply of labour and yet, in all (other) respects be in "equilibrium" as being in conflict with Walras Law and therefore as wrong or 'bad' in theory and so inadmissible.
The attack on the relevance of Walras Law for modelling situations in which there is involuntary unemployment was developed by Robert Clower (from the University of South Carolina) and Axel Leijonhufvud (from the University of California at Los Angeles). References to the work of Clower and Leijonhufvud are given below.
They hold that Keynes must have had in mind that Walras Law was inapplicable to the problem he was studying. This argument, and a very interesting argument it is too (it has become the foundation for a whole new branch of macroeconomics variously called 'disequilibrium macroeconomics' and 'fix-price macroeconomics') goes something like this. Clower and Leijonhufvud would agree that it is correct to say that in the aggregate an excess of planned supply in one market must be matched by an excess of planned demand in at least one other market. BUT, they would draw our attention to the fact that the excess demands and supplies are measured as differences between planned (or notional) demands and supplies, and not actual (or "effective") demands and supplies. According to them, Keynes maintained that there can be conditions under which excess demands (or supplies) will not be "effectively" communicated so that, although certain prices (including wages) are at disequilibrium levels, no process of bidding them away from these inappropriate levels will get started. In particular, the excess demand for commodities is not 'effective' market failure. It persists because "the market signals, pre-supposed in general equilibrium analysis are not transmitted" (Leijonhufvud, 1981, p 70).
Surprisingly, very few introductory or intermediate macroeconomics textbooks discuss Walras Law. Those that do, include:
R Barro, Macroeconomics: Fifth edition, MIT Press, 1997, Ch 5.
R Crouch, Macroeconomics: New York, Harcourt Brace Jovanovitch, 1972, Sections 6.2 and 16.1.
R Levacic and A Rebmann, Macroeconomics: Macmillan, London, Second edition 1982, Ch 16.
D Colander, Macroeconomics: Theory and Policy: Scott, Foresman and Co., Glenview, Illinois, 1986, Ch 11.
'Income and Employment Theory', an unsigned article in the New Encyclopaedia Britannica: Vol 9, pp 262-4, Chicago, 1983. (The Encyclopaedia Britannica is an excellent and much under-utilised source of information about Economists and Economic Analysis)
A Leijonhufvud, Keynes and the Classics: Two Lectures Institute of Economic Affairs, London, 1969, reprinted in A Leijonhufvud, Information and Coordination Oxford University Press, New York, 1981.
J Schumpeter, History of Economic Analysis: London, George Allen and Unwin, 1954, passim.
L Walras, Elements of Pure Economics: George Allen and Unwin, London, 1954. (Translated by W Jaffe).
B Snowdon et al, A Modern Guide to Macroeconomics: Edward Elgar, Aldershot, 1995, Ch 3.
T Sargent, Macroeconomic Theory: Academic Press, Boston, 1987, passim.
R Clower, The Keynesian Counter-revolution: a theoretical appraisal', in F Hahn and F Brechling, The Theory of Interest Rates Macmillan, London, 1965, pp 103 - 25, reprinted in R Clower, Money and Markets: Cambridge University Press, Cambridge, 1984.
D Patinkin, 'Walras Law' in The New Palgrave, A Dictionary of Economics, Macmillan, London, 1987, Volume 4, pp 864 - 8.
C Benassi (et al), The New Keynesian Economics Balckwells, Oxford, 1994.
Fittingly, there is a Walras Home Page at the Université de Lausanne (in French).
Biographies of Walras
J Schumpeter, Ten Great Economists: London, George Allen and Unwin, 1952, pp. 74 - 9.
D Walker, 'Walras, Leon' in The New Palgrave, A Dictionary of Economics, Macmillan, London, 1987, Volume 4, pp 852 - 63.
Walras' Autobiography is available over the internet from the Centre d'Etudes Interdisciplinaires Walras-Pareto at the Université de Lausanne (in French).
A picture of Walras and some very brief biographical information may be found at the History of Economic Thought site maintained by the Department of Economics at The New School for Social Research in New York. (And by the way, the Federal Reserve Bank of San Francisco has a nice page titled: Great Economists and Their Times.)
Acknowledgment
The picture of Walras is from Centre d'Etudes Interdisciplinaires Walras-Pareto at the Université de Lausanne.
(c) Department of Economics, University of Melbourne
