Walrasian General Equilibrium
The basic problem that Walras wished to analyse was that of finding prices and the corresponding inputs and outputs of firms and allocations to consumers in a many goods economy such that all markets clear, that is that excess demand for every good is zero.
It was the passage from a single good to many goods that was the challenge. Before accepting any definition of equilibrium, one has to specify what motivates the choices made by the individuals in the economy or market. In other words, in the Walrasian context we have to specify the demands and supplies of all the agents in the economy. For firms the idea adopted by Walras in line with earlier writers is simply that they wish to increase the profitability of their activity and the same idea was often attributed to traders. However, the objectives of consumers are less clear and this was the subject of vigorous debate. Walras had in mind that consumption bundles yielded utility, a cardinal or measurable concept for which he was criticized by Poincare (1901) and Laurent (1900), and that individuals maximized their utility subject to their budget constraints. (Incidentally, both Laurent and Poincare disagreed with the idea that satisfaction or utility could be measurable. Walras cites Laurent as having said in his address to the Institut des Actuaires franςais in 1900, “How can one accept the notion that satisfaction can be measured? No mathematician could agree to this.” However, in his 1901 letter Poincare tried to soften what Walras regarded as being unjustifiably harsh criticism but still balked at the idea of utility as a measurable entity.) The latter was defined by the prices which individuals took as given. The informal justification for another assumption, that of price taking behaviour, as the number of individuals became large, had already been given by Cournot (1838) whose influence Walras acknowledged. (In fact within the Walrasian framework we had to wait until the 1960s when Aumann 1964 provided a rigorous argument for price taking behaviour by introducing a continuum of individually insignificant agents.) Having specified the choices made by individuals at any prices, the equilibrium was then simply defined as the vector of prices for the l goods in the economy for which the excess demand for all goods was 0. Since the level of prices is indeterminate in the Walrasian system we can fix one price so that it is the numeraire. Thus, we only need (l - 1) prices. However, if l - 1 markets clear, at equilibrium so must the remaining market. Thus we have a set of equations with the same number of equations as unknowns and this Walras claimed was enough to show that there was a solution. It was not (see below).However, before proceeding, what has just been described is part of the Walrasian legacy but does not correspond to what Walras really did. It would be convenient to assume that Walras adopted Cournot’s ideas and used them to justify price-taking behaviour. If so, then the question is where do the prices come from? The way to answer this has been to suggest that there is an auctioneer who cries out the prices and this figure is regularly referred to as the “Walrasian auctioneer”. However, if there is one thing that we owe to Donald Walker (1996), it is to insist on the fact that Walras never, in fact, saw the market or economy as one in which there was free competition, in the sense that all the participants were price takers. He argues, and even his opponents agree, that the agents in Walras’s models could not have been viewed as “price takers” since nothing was specified about whom they were supposed to be taking prices from. Rather, he argues, Walras had in mind a notion of free or perfect competition as corresponding to a situation in which large numbers of individuals interact with each other freely but they are not passive price takers since they themselves quote the prices at which they are prepared to buy or sell.
Walras also saw pure or perfect competition as an ideal rather than a reality. Walker quotes Walras, in a letter to Ladislaus von Bortkiewitz, as saying: “Free competition is the principle mode of exchange in the real economy, practiced on all markets with more or less precision and therefore with less or more efficiency” (Walras to von Bortkiewicz, 1891, letter 999, in Jaffe 1965).Hence Walras believed in the idea that individuals quoted prices and exchanged goods with each other and that this would drive prices to some sort of equilibrium. There is a major problem with this in that we have to know, or rather the agents in the economy have to know, when to stop. This requires a great deal of information and Alfred Marshall (1920) argued that this was implausible for the minor players in the economy.
De Vroey (2003) has put forward an alternative argument to explain the emergence of the Walrasian auctioneer as a standard idea in economic theory. He suggests that the only way of completing the Walrasian story convincingly is to introduce an auctioneer. Thus he claims that the auctioneer is a logical necessity rather than an assumption made directly by Walras. As he says, “the auctioneer hypothesis is part and parcel of Walrasian theory. Without it, the latter would lack any scenario about the institutional dimension of its price formation mechanism” (De Vroey 2003: 469).