Chapter 6 - Aggregation

Chapter 6 - Aggregation - Chapter 6 Aggregation and market...

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Chapter 6 Aggregation and market demand This chapter is really more of a sub-chapter, and just outlines a few issues in aggregation, by which is meant the process of developing a market demand curve from an individual demand curve. Really, what we want to be able to do is apply the results we have so painstakingly described for individual demand and utility at a market level. We wish to do this for both theoretical and practical reasons. Theoretically speaking, prices and quantities are usually thought to be determined by interactions in a market, and therefore we want to have a description of market demand. Moreover, we would like most of the work we have done in developing things such as compensated demands and expenditure functions to carry over to the analysis of events at the market level. Practically speaking, aggregating to the market level is important because data often comes in this form, and quantities such as consumers’ surplus, compensating variation, and equivalent variation can only be analyzed at the market level. We really do nothing special to make market demand out of individual demands - we simply add them up. 1 Suppose that we have N total agents in the market, numbered i = 1 , 2 , 3 ,...,N . To get a market demand, add up 1 Thus, we do not have what John Maynard Keynes called “the fallacy of composition,” which is the idea that the whole behaves diFerently than the sum of its parts. 157
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158 CHAPTER 6. AGGREGATION AND MARKET DEMAND all the individual demands for good x , say: X = N s i =1 x i ( p x ,p y ,I ) (6.1) There is nothing odd about doing this, and most of the properties of indi- vidual demand functions should carry over to the market demand function (6.1); market demand is increasing in income and decreasing in prices if each individual demand function is, and retains the homogeneity properties of its components. Thus, there is no diFculty in making statements like “as the price of good x goes up, the market quantity of good x demanded falls.” Potential problems surface, however, if one is interested in talking about elasticity of demand, and other things like compensated demands, expendi- ture functions, and indirect utility functions at the market level . That is, we wish to avoid having to consider the situation of every consumer separately, and a common device is to instead discuss things from the perspective of the representative consumer . The thought experiment is something like the following: what if we took the average of income levels and preference parameters, described these “average decisions,” and then scaled the size of these average decisions up to the size of the market? That is, what we do is we get rid of the wealthy consumers, the poor consumers, the consumers
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This note was uploaded on 11/13/2009 for the course ECONOMICS 721 taught by Professor Partha during the Fall '09 term at CUNY Hunter.

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Chapter 6 - Aggregation - Chapter 6 Aggregation and market...

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