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Unformatted text preview: 1 Ch 15 Market Demand This chapter is to add up individual choices to get market demand. Also, we will examine the relationship between demand and revenue. 15.1 From individual to market demand Let ( ) i j i m p p x , , 2 1 denote consumer i &s demand for good j . There are n consumers. Then, the market demand for good j is the sum of n individual demands: Clearly, this aggregate demand depends on the distribution of incomes over all consumers as well as the prices. The aggregate demand can be viewed as the demand of some representative consumer who is thought of as having an income equal to ) ( 1 M m n i i = = . Then, the market demand can be rewritten as ( ) M p p X j , , 2 1 . In figure 15.1, the market demand for good 1 is plotted as a function of p 1 by holding all other prices and income fixed as parameters, i.e., X 1 = X 1 (p 1 ). Parametric change : A rise in p 2 may shift X 1 (p 1 ) outward if goods 1 and 2 are substitutes; or shift it inward if both goods are complements. Any economic change that raises M will shift X 1 (p 1 ) outward if good 1 is a normal good. p 1 X 1 X 1 (p 1 ) ( ) ( ) = = n i i j i n j m p p x m m m p p X 1 2 1 2 1 2 1 , , ,..., , , , 2 Change the demand function X 1 = X 1 (p 1 ) to X = D(p) to make the notation neater; the inverse demand function is denoted by p = P(X) , measuring what p would have to be for X units to be demanded. Drawing the demand curve is based on p = P(X) , since all consumers are facing the same price for the good they demand. They will have the same MRS at their optimal choices. Recall that MRS p = if the other goods are treated as a composite good. Thus, we can horizontally sum all consumers& demand curves for a good to obtain the market demand for that good....
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- Spring '09