02aGE - Econ 251a Fall 2006 GENERAL EQUILIBRIUM So far we...

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Econ 251a Fall 2006 GENERAL EQUILIBRIUM So far we have concentrated on one market at a time, leaving all the rest unmodeled. Now we turn to a study of general equilibrium, in which di f erent markets interact. Our thinking was that money could substitute for the vast array of alternative choices that consumers and f rms face. From a purely logical standpoint, it is certainly true that when an agent chooses to buy more of the commodity under study, that will reduce her stock of money. She will therefore be right in comparing the marginal utility of a dollar spent on the commodity with the marginal utility of a dollar spent elsewhere. But if we describe the elsewhere as precisely as we do the commodity itself, we might learn more about the value of the commodity. Changes in the demand and supply of one commodity will typically have e f ects on the demand and supply of other commodities. If the commodities interact in the utility functions of consumers, as when the goods are substitutes or complements, then a price change in one commodity will obviously a f ect demand for the other. But even if the utilities of all commodities are separable, the consumption of one commodity still might a f ect the consumption of all other commodities through the agents’ budget sets. We did not have occasion to mention the budget set so far, but clearly any potential consumer has limited resources, and will therefore have to adjust his demand for many goods if his income changes, or if the price of one of the goods changes. In our previous analysis, we implicitly assumed that expenditures by each consumer would be taken out of his stock of money, and so would not a f ect the consumption of other goods that were already budgeted. That behavior can indeed be justi f ed by a special welfare function which assigns constant marginal utility to one of the goods. But with almost any other utility function, the budget set will force interactions between di f erent consumption markets. General equilibrium is a situation in which every agent is aware of the prices of all the goods, and buys or sells whatever he wants of every good at those prices, and the total buying of each good just equals the total selling. In short, in general competitive equilibrium, agents optimize and markets clear. How does the "market" discover the equilibrium prices? More fundamentally, how can we be sure there even are equilibriium prices that allow agents to optimize simultaneously, while matching supply and demand? When changing a price in one market a f ects demand in all the other markets, the simultaneous market clearing problem becomes highly nontrivial. In the following sections we indicate that equilibrium prices do indeed exist, and we illustrate how a central planner, who knew the preferences and endowments of every agent, could use a computer to f nd them. Of course in reality there is no central planner who knows everything, yet the market somehow still manages to f nd what looks like equilibrium
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This note was uploaded on 12/08/2009 for the course ECON 251 at Yale.

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02aGE - Econ 251a Fall 2006 GENERAL EQUILIBRIUM So far we...

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