Louis Makowski

General Equilibrium and Market Socialism:
Clarifying the Logic of Competitive Markets*

Louis Makowski                                  Joseph M. Ostroy

July, 1992

UCLA Department of Economics Discussion Paper No. 672

Abstract

We describe two versions of general equilibrium, each highlighting different features of the price system, the standard (Walrasian) version with its emphasis on the decentralization/information role of prices and another emphasizing what we call the appropriation/ incentive role of competitive prices. Through their different implications for market socialism, we illustrate the differences between these two approaches to general equilibrium.

JEL classification nos.: B20 and B24 (History of thought since 1925); D50 (General Equilibrium); D60 (Economic Welfare); P20 (Socialist systems)

1 Introduction

Since its inception, consensus has prevailed within general equilibrium theory. The line from Walras [1874, 1877] to Debreu [1959] and beyond has seen the gradual sloughing off of extraneous / erroneous details and accumulation of logical precision to provide a more comprehensive and translucent formulation of a vision found in Walras. Firmly rooted in a tradition widely regarded as the most mathematically mature, general equilibrium theory is one of the least controversial branches of economics. One may argue for or against its importance as a source of economic insight, but there is much less room for arguing about what general equilibrium theory is and it what it has to say.

We do not share this view. Our position is not that there has been a misapprehension of the Walrasian tradition. Quite the contrary, we shall take pains to point out its grip on general equilibrium. Rather, we want to loosen its hold—to distinguish between general equilibrium and its Walrasian representation (WGE), and to offer something else instead. To summarize, we claim that there are two images of a price system and, while they are by no means mutually exclusive, WGE captures only one.

Ordinarily, to point out the limitations of a theory, it is useful to call attention to a discrepancy between its predictions and some empirical phenomenon. We shall want, to do that here. Because general equilibrium theory is valuable as a conceptual tool with broad scope rather than an instrument with specific empirical content, contradictory empirical evidence is difficult to obtain. There was, however, one very important encounter between general equilibrium and an “empirical application” namely market socialism, where the ‘predictions’ based on WGE were not borne out by the facts.

In this essay, we critically examine the reciprocal influence between market socialism, most notably the work of Lange [1938] and Lerner [1944], and WGE. We shall argue that the Lange/ Lerner attempt to graft WGE onto a socialist economy was a logically compatible coupling: market socialism fit the image of the price sys tem emphasized by WGE remarkably well. Not only did the Walrasian model of competitive markets inspire market socialism, but in its encounter with market socialism important properties of the Walrasian tradition were highlighted, notably the decentralization/ information role of prices.

But the connection between general equilibrium and market socialism might have been otherwise: if another image of the price system had been incorporated, the principles of general equilibrium could have demonstrated that market socialism was much more problematic than Lange and Lerner believed. In other words, through their different implications for market socialism, we shall illustrate the differences between the Walrasian and another image of the price system.

2 Features of Walrasian General Equilibrium

ln describing WGE, we take care to separate the formal properties of the theory from those that, although crucial to its interpretation, can be logically dissociated from it. We highlight. three features: (1) price-taking, (2) tâtonnement, and (3) the decentralization/information role of prices. Only the first is unambiguously a component of its axiomatization; the other two are extensions and interpretations of it. Together, the three formed the seed for market socialism.

2.1 Price-taking: Encapsulating the economy

Households and firms take prices as given, and an explanation as to why they do is not a part of the formal theory. When justification is called for, appeal is made to background conditions not explicitly part of the theory. The most commonly invoked of these conditions is large numbers of buyers and sellers. Upon closer inspection, large numbers is supplemented by the assumption that the commodities traded are homogeneous rather than idiosyncratic and personalized—to rule out monopolistic competition. This leads to thick markets as the background condition from which the price-taking hypothesis is seen to follow.

The starting point for a general equilibrium model is the ‘basic data’ of the economy, listing the characteristics of the individual agents—their tastes, endowments, production possibilities, and ownership shares of firms. Without distinguishing between households or firms, call vi the characteristics of agent “I”. The economy is then given by ξ= {(Vi,)}. Price-taking is called upon to define the utility- or profit maximizing response Vi→ øi(p), the vector (or set of vectors) of commodities that the price-taking maximizer with characteristics vi would choose if the price vector were p.

The main consequence of price-taking is that it leads to the encapsulation of the basic data of the economy by demand and supply functions, i.e., as far as competitive analysis is concerned, ξ = {(Vi)} is effectively replaced by the reduced form{( øi(.)}. Even more succinctly, an equilibrium of E is a p for which 0 E Z q>,(p).

Encapsulation is a brilliant device.  lf the aim of general equilibrium is to provide a theory of relative prices in a thick markets environment, encapsulation is an efficient way of translating the basic data into an immediately usable form. Indeed, encapsulation is so compelling as to appear to be inevitable, as is the statement “the reduction of E =   to   is necessary for describing/defining competitive general equilibrium”.  There are formal tricks one can use to pin-point the zero of the aggregate excess demand function without using demand functions at all, e.g., Arrow and Hahn [1971, p. 114]; nevertheless, these devices are not taken as serious alternatives to Walrasian encapsulation.

Before going on we call attention to the fact that neither Jevons [1879] nor Edgeworth [1881] used Walras’ method of encapsulation to define equilibrium. Jevons used the notion of arbitrage plus the first-order calculus conditions for a utility maximizer to define equilibrium in a simple setting with two commodities and two types of individuals. His efforts have been criticized as incomplete because he did not follow Walras’ method of demand-and-supply/encapsulation in formulating general equilibrium. Edgeworth, formalizing some of Jevons’ insights, made a very conscious effort to avoid encapsulation because he regarded it as begging the question of how and why individuals would be price-takers. Edgeworth used the more primitive notion of contract and recontract, now known as the core, as his way of showing how competitive equilibrium would arise when markets are thick. Makowski and Ostroy [1991b] follow yet another approach to arrive at competitive equilibrium without Walras method of demand-and-supply. This will be discussed briefly in the concluding section; like; Edgeworth, we utilize some of Jevons’ insights, but in a somewhat different way.

2.2 Tâtonnement: Price-taking away from equilibrium

Even though the definition of Walrasian equilibrium is only a statement about a zero of the aggregate excess demand function, the overwhelming weight of the Walrasian tradition has been to see the economy ε through its encapsulation {(øi)}. Once demand and supply is taken as the ‘practical starting point’ for general equilibrium, price-taking takes on a life of its own as the behavioral rule describing the actions of a perfect competitor both in and out of equilibrium.

For Walras, tâtonnement was the (erroneously constructed) method of proof to demonstrate the existence of equilibrium. Whether Walras intended tâtonnement to be only a hypothetical adjustment process to demonstrate existence or whether he also thought of it as showing how markets actually came into equilibrium is not always clear. What is clear, however, is that tâtonnement fits the analytical perspective in which the basic data of the economy are encapsulated before describing either competitive equilibrium or the way the economy arrives at equilibrium.

To illustrate the extent to which encapsulation ε of {(øi)} is taken as the effective starting point for WGE, consider the following remarks by Arrow [1959] about tâtonnement:

In this essay, it is argued that there exists a logical gap in the usual formulations of the theory of the perfectly competitive economy, namely, that there is no place for a rational decision with respect to prices as there is with respect to quantities.

The standard development of the theory of behavior under competitive conditions has made both sides of any market take the prices as given by some outside agency.

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