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Unformatted text preview: Economics 111: Intermediate Microeconomics Spring 2008 Homework 2 Answer Key Professor: Pedro Dal Bó 1. Consider the following utility function: U = x 1 2 1 x 1 2 2 . a. Draw the indi f erence curve that yields U = 5 ( f nd x 2 as a function of x 1 with U = 5 ). x 2 = 25 x 1 15 12.5 10 7.5 5 2.5 15 12.5 10 7.5 5 2.5 X1 X2 X1 X2 b. Find the MRS for every consumption bundle. Is the MRS decreasing in x 1 ? MRS = MU 1 MU 2 = x 2 x 1 It is decreasing in x 1 . c. In a new f gure graph her budget set if p 1 = 1 , p 2 = 1 and m = 10 . 1 15 12.5 10 7.5 5 2.5 15 12.5 10 7.5 5 2.5 X1 X2 X1 X2 d. Find her optimal consumption bundle ( x ∗ 1 , x ∗ 2 ) and draw it in the f gure. The optimal consumption value satis f es the following two conditions: x 1 x 2 = 1 (MRS= p 1 p 2 ) x 1 + x 2 = 10 (budget constraint). Solving we get: ( x ∗ 1 , x ∗ 2 ) = (5 , 5) . 15 12.5 10 7.5 5 2.5 15 12.5 10 7.5 5 2.5 X1 X2 X1 X2 e. Find her optimal consumption bundle ( x ∗ 1 , x ∗ 2 ) if p 1 = 2 , p 2 = 1 and...
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This note was uploaded on 02/13/2011 for the course ECON 111 taught by Professor Dalbo during the Spring '08 term at Brown.
 Spring '08
 DALBO
 Economics, Utility

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