Leon Walras and General Equilibrium Theory, Leon Walras Biography

Walras's use of marginal analysis was only a part of his contribution to modern economics. His work on marginalism was in many ways more sophisticated than that of Jevons and Menger, but because it was in French it did not have the same impact. We devote an entire chapter to Walras because of his general equilibrium theory. That work has had an enormous impact on the economics profession, and it places Walras with Marshall as a candidate for father of one of the two branches of neoclassical economics.

What Is General Equilibrium Theory?
General Equilibrium Notes, General Equilibrium Economics

General equilibrium model is an analysis of the economy in which all sectors are considered simultaneously. Thus, one considers both the direct and the indirect effects of any shock to the system, and one considers the cross-market effects simultaneously with the direct effects. This interrelationship of the sectors of the economy is relatively simple to conceptualize, but it is an enormously compli­cated idea to put down formally. Walras's contribution was to model the general equilibrium system in a formal manner.

Early Precursors of General Equilibrium Theory

Because general equilibrium is relatively easy to conceptualize, it shouldn't be surprising that it was not a new idea in 1874 when Walras published Elements of Pure Economics. Earlier writers had had a clear vision of an economy consisting of many interconnected parts. For example, Quesnay had given this vision form in his economic table, which traced the flow of annual production among the various sectors of the economy. Similarly, in vivid descriptions' of market processes, Adam Smith showed deep insight into the relationships among the various parts of the economy. But although these writers explained the interconnection, they did not formally model it.

In 1838, A. Cournot (1801-1877) made an enormous advance in formalizing the interrelatedness of the economy while analyzing certain microeconomic problems. He was able to express some of the problems of the theory of the firm
in mathematical form, and he used calculus to prove that profits are maximized when marginal cost is equal to marginal revenue. In doing so, he did for the theory of the firm what Jevons and Menger did for choice theory: he formulated
it in marginal terms. In addition, Cournot went beyond Jevons and Menger, whose heuristic and arithmetical expositions had limited their insights. Cournot's abstract mathematical orientation assisted him considerably in comprehending
relationships within the economy and helped him to anticipate Walras. Cournot correctly concluded that "for a complete and rigorous solution of the problems relative to some parts of the economic system, it [is] indispensable to take the
entire system into consideration.

Cournot felt, however, that mathematical analysis was not sufficiently devel­oped to permit the formulation of a general equilibrium model. J. H. von Thiinen (1783-1850) also applied calculus to the solution of problems in economic theory; and as with Cournot, this mathematical orientation led him to see the possibility of presenting a general equilibrium model as a system of simultaneous equations. Perhaps because they were better mathematicians than Walras (Walras had not been accepted into the prestigious Ecole Polytechnique in France because he failed the mathematics section of the entrance exam, whereas Cournot was considered a brilliant mathematician), Cournot and von Thiinen did not attempt

to address the complicated interrelationships of general equilibrium theory because of the many assumptions that were required to make the problem tractable and the inability to measure the concepts.

For whatever reason, Walras forged ahead where others feared to tread; so it was Leon Walras who was first able to give the general equilibrium vision clarity and precision by formulating a model of an economy through the use of mathematical notation. For this accomplishment' he is justly praised as an important predecessor of modern economic theory, with its heavy emphasis on abstract model building and the use of mathematics.

We will describe a Walrasian model in words and discuss some of the theoretical issues it raises. Before we do that, however, it is helpful to consider the difference between a general and a partial equilibrium model.