hw3_soln

hw3_soln - Solution Homework Assignment 3 Econ 150b....

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Solution Homework Assignment 3 Econ 150b. Intermediate Microeconomics Fabian Duarte * February 5, 2008 1. Consider a consumer whose utility function is given by u ( x 1 , x 2 ) = ( α x ρ 1 +( 1 - α ) x ρ 2 ) 1 ρ (1) where ρ ε ( 0 , 1 ) is a parameter. Using any of the three methods we’ve seen in class, find the optimal consumption bundle as a function of prices ( p 1 , p 2 ) and income m . Plot the demand and Engel curves. (a) First method: We use two equations: MRS = - p 1 p 2 p 1 x 1 + p 2 x 2 = m So, first we calculate MRS , for that we need to calculate first partial derivatives u x 1 = 1 ρ ( α x ρ 1 +( 1 - α ) x ρ 2 ) 1 ρ - 1 ( αρ x ρ - 1 1 ) and u x 2 = 1 ρ ( α x ρ 1 +( 1 - α ) x ρ 2 ) 1 ρ - 1 (( 1 - α ) ρ x ρ - 1 2 ) then MRS = - α x ρ - 1 1 ( 1 - α ) x ρ - 1 2 = - p 1 p 2 (2) * fabian.duarte@yale.edu 1
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then x 1 = ( 1 - α ) p 1 α p 2 · 1 ρ - 1 x 2 (3) Now, we replace x 1 in the second equation p 1 x 1 + p 2 x 2 = m and we get m = p 1 ( 1
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This note was uploaded on 04/11/2008 for the course ECON 150 taught by Professor Eduardofaingold during the Spring '08 term at Yale.

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hw3_soln - Solution Homework Assignment 3 Econ 150b....

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