Question

Give a simple and brief proof that a utility-maximizing consumer would exchange the two commodities up to the point where the relative ratio of marginal utility between the two commodities exactly equals their relative price ratio. What is General Equilibrium? Explain how Walras set up the general equilibrium model. What difficulties did Walras have in order to demonstrate that market forces could automatically correct disequilibrium? (Relate it to Jehovan's demonstration in the History of Economic Though)

Answer 1

General equilibrium

general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts to the theory of partial equilibrium, which only analyzes single markets

the walras develope the general equilibrium theory to solve a much-debated problem in economics. Up to that point, most economic analyses only demonstrated partial equilibrium—that is, the price at which supply equals demand and markets clear—in individual markets. It was not yet shown that equilibrium could exist for all markets at the same time in aggregate.

General equilibrium theory tried to show how and why all free markets tend toward equilibrium in the long run. The important fact was that markets didn't necessarily reach equilibrium, only that they tended toward it. As Walras wrote in 1889, “The market is like a lake agitated by the wind, where the water is incessantly seeking its level without ever reaching it.”

General equilibrium theory builds on the coordinating processes of a free market price system, first widely popularized by Adam Smith's "The Wealth of Nations" (1776). This system says traders, in a bidding process with other traders, create transactions by buying and selling goods. Those transaction prices act as signals to other producers and consumers to realign their resources and activities along more profitable lines.

Walras, a talented mathematician, believed he proved that any individual market was necessarily in equilibrium if all other markets were also in equilibrium. This became known as Walras’s Law.

The general equilibrium theory considers the economy as a network of interdependent markets and seeks to prove that all free markets eventually move towards general equilibrium.

Deficulty in equilibrium

Research building on the Arrow–Debreu–McKenzie model has revealed some problems with the model. The Sonnenschein–Mantel–Debreu results show that, essentially, any restrictions on the shape of excess demand functions are stringent. Some think this implies that the Arrow–Debreu model lacks empirical content. At any rate, Arrow–Debreu–McKenzie equilibria cannot be expected to be unique, or stable.

A model organized around the tâtonnement process has been said to be a model of a centrally planned economy, not a decentralized market economy. Some research has tried to develop general equilibrium models with other processes. In particular, some economists have developed models in which agents can trade at out-of-equilibrium prices and such trades can affect the equilibria to which the economy tends. Particularly noteworthy are the Hahn process, the Edgeworth process and the Fisher process.

The data determining Arrow-Debreu equilibria include initial endowments of capital goods. If production and trade occur out of equilibrium, these endowments will be changed further complicating the picture.