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Unformatted text preview: Chapter 7 Competitive Markets and Partial Equilibrium Analysis Up until now we have concentrated our e f orts on two major topics - consumer theory, which led to the theory of demand, and producer theory, which led to the theory of supply. Next, we will put these two parts together into a market. Speci f cally, we will begin with competitive markets. The key feature of a competitive market is that producers and consumers are considered price takers. That is, individual actors can buy or sell as much of the output as they want at the market price, but no one can take any unilateral action to a f ect the price. If this is the case, then the actors take prices as exogenous when making their decisions, which was a key feature in our analysis of consumer and producer behavior. Later, when we study monopoly and oligopoly, we will relax the assumption that f rms cannot a f ect prices. Our main goal here will be to determine how supply and demand interact to determine the way the market allocates societys resources. In particular, we will be concerned with: 1. When does the market allocate resources e ciently? 2. When, if the government wants to implement a speci f c allocation, can the allocation can be implemented using the market (possibly by rearranging peoples initial endowments)? 3. Why does the market sometimes fail to allocate resources e ciently, and what can be done in such cases? The third question will be the subject of the next chapter, on externalities and public goods. For now, we focus on the f rst and second questions, which bring us to the f rst and second fundamental 185 Nolan Miller Notes on Microeconomic Theory: Chapter 7 ver: Aug. 2006 theorems of welfare economics, respectively. 7.1 Competitive Equilibrium The basic idea in the analysis of competitive equilibrium is the law of supply and demand. Utility maximization by individual consumers determines individual demand. Summing over individual consumers determines aggregate demand, and the aggregate demand curve slopes downward. Pro f t maximization by individual f rms determines individual supply, and summing over f rms determines aggregate supply, which slopes upward. Adam Smiths invisible hand acts to bring the market to the point where the two curves cross, i.e. supply equals demand. This point is known as a competitive equilibrium, and it tells us how much of the output will be produced and the price that will be charged for it. Notation We are going to be dealing with many consumers, many producers, and many commodities. To make things clear, Ill denote which consumer or producer we are talking about with a superscript. For example, u i is the utility function of consumer i, x i is the commodity bundle chosen by consumer i , and y j is the production plan chosen by f rm j . For vectors x i and y j , Ill denote the l th component with a subscript. Hence x i = x i 1 , ..., x i L , and y j = x j 1 , ..., x j L . So x j L refers to consumer j s consumption of good L . This di f ers from MWG, which uses double subscripts. But, I think that ers from MWG, which uses double subscripts....
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This note was uploaded on 09/21/2011 for the course ECON 3022 taught by Professor Wer during the Spring '11 term at UC Irvine.
- Spring '11