Lecture_12_Market_Demand

Lecture_12_Market_Demand - Lecture 12: Market Demand c 2008...

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Lecture 12: Market Demand c 2008 Je/rey A. Miron Outline 1. Introduction 2. From Individual to Market Demands 3. The Inverse Demand Curve 4. Extensive Versus Intensive Margins 5. Elasticity 6. Elasticity and Demand 7. Elasticity and Revenue 8. Constant Elasticity Demands 9. Elasticity and Marginal Revenue 10. Marginal Revenue Curves 11. The Income Elasticity of Demand 1 Introduction So far, we have derived and characterized individual demand curves. Now we want to aggregate these to form market demand curves. We also will de&ne and characterize the concepts of elasticity, revenue, and mar- ginal revenue. This will be useful for later analysis of market equilibrium. 1
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2 From Individual to Market Demands Let x 1 i ( p 1 ; p 2 ; m i ) represent consumer i good 1 is de±ned as X 1 ( p 1 ; p 2 ; m 1 ; : : : ; m n ) = n X i =1 x 1 i ( p 1 ; p 2 ; m i ) That is, the market demand for good 1 is the sum of the individual demands. Note that in general market demand depends on the distribution of income. In particular, transferring income from one person to another, with the total ±xed, could change overall demand. Most of the time, however, it is a reasonable approximation to think in terms of representative consumers, each earning the average income. In this case, we can just sum all the incomes and write the market demand curve as X 1 ( p 1 ; p 2 ; M ) where M is the sum of all the incomes. In this case, the demand curve is just like that of an individual with income M . We can illustrate the market demand curve in the standard way: 2
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Graph: A Market Demand Curve y = 10 x 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 p q Geometrically, the market demand curve is the horizontal sum of the underlying individual demand curves: 3
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Graph: Summing up Individual Demand Curves y = 9 3 x y = 12 2 x 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 p q B C A D1 D2 Market Demand A = B + C the curve. For example, an increase in p 2 , assuming goods 1 and 2 are substitutes, shifts demand for good 1 outward. An increase in income shifts the demand in or out in the same direction, assuming good 1 is a normal good. 3 The Inverse Demand Curve The standard demand curve relates the quantity demanded to price. Then, annoy- ingly, standard presentations plot the demand curve with price on the vertical axis and quantity on the horizontal axis - the opposite of the standard convention for plotting y = f ( x ) : 4
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This note was uploaded on 09/16/2009 for the course ECONOMICS 1010A taught by Professor Jeffreya.miron during the Fall '09 term at Harvard.

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Lecture_12_Market_Demand - Lecture 12: Market Demand c 2008...

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