Week 5 Lecture_Consumer Surplus ch14

# Week 5 Lecture_Consumer Surplus ch14 - Week 5 Consumers...

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Week 5 Consumer’s Surplus

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Consumer’s Surplus Consumer’s Surplus is an exact dollar measure of utility gained from consuming commodity 1 when the consumer’s utility function is quasilinear in commodity 2.
Consumer’s Surplus U x x v x x ( , ) ( ) 1 2 1 2 = + Consider the special case when The consumer’s utility function is quasi-linear in x 2. Take p 2 = 1. Then the consumer’s choice problem is to maximize U x x v x x ( , ) ( ) 1 2 1 2 = + subject to p x x m 1 1 2 + = .

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Consumer’s Surplus That is, choose x 1 to maximize v x m p x ( ) . 1 1 1 + - The first-order condition is v x p '( ) 1 1 0 - = That is, p v x 1 1 = '( ). This is the equation of the consumer’s demand for commodity 1.
Consumer’s Surplus Individual demand curve p 1 p v x 1 1 = '( ) x 1 * x 1 ' p 1 '

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Consumer’s Surplus p 1 p v x 1 1 = '( ) x 1 * x 1 ' CS CS v x dx p x x = - '( ) ' ' ' 1 1 1 1 0 1 ) 0 ( ) ( ' 1 ' 1 ' 1 v x p x v - - = p 1 ' is exactly the consumer’s utility gain from consuming x 1 units of commodity 1.
Consumer’s Surplus p 1 x 1 * x 1 ' p 1 '

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Consumer’s Surplus p 1 x 1 * x 1 ' CS before p 1 (x 1 ) p 1 '
Consumer’s Surplus p 1 x 1 * x 1 ' CS after p 1 " x 1 " p 1 (x 1 ) p 1 '

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p 1 x 1 * x 1 ' x 1 " Lost CS p 1 (x 1 ), inverse demand curve for commodity 1. p
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## This note was uploaded on 09/06/2010 for the course FBE ECON2113 taught by Professor Franchsica during the Fall '09 term at HKU.

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Week 5 Lecture_Consumer Surplus ch14 - Week 5 Consumers...

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