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Unformatted text preview: Economics 101—Lecture 8 Consumer Surplus and Revealed Preference George J. Mailath February 8, 2011 In our last episode 1 We studied the labor/leisure decision of a worker, as an illustration of substitution and income effects. 2 Compensating variation of a change from p to p is ( u = V ( p , I ) ) given by CV ( p → p ) = e ( p , u ) − e ( p , u ) (suppose only the price of good 1 changes and p 1 > p 1 ) = p 1 p 1 ∂ e ( p , u ) ∂ p 1 dp 1 = p 1 p 1 x c 1 ( p , u ) dp 1 . 3 What if p 1 < p 1 ? Elasticities Consider a demand function x i ( p , I ) . How does expenditure p i x i ( p , I ) respond to a change in price p i ? ∂ p i x i ( p , I ) ∂ p i = x i + p i ∂ x i ∂ p i = x i 1 + p i x i ∂ x i ∂ p i = x i { 1 − η i } , where η i is the (own) price elasticity of demand (for good i ): η i = − p i x i ∂ x i ∂ p i . unit elasticity if η i = 1, so revenue unchanged, Demand is elastic if η i is big, so revenue ↓ , Demand is inelastic if η i is small, so revenue ↑ . Returning to compensating variation CV ( p → p ) = p 1 p 1 x c 1 ( p , u ) dp 1 . Some intuition Suppose compensated demand is very inelastic. Some intuition Suppose compensated demand is very elastic. Consumer Surplus...
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 Spring '08
 DANNICATAMBAY
 Microeconomics, Consumer Surplus, Consumer price index, Revealed preference, ηi, p1 p1 p1, pi ∂xi xi

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