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Homework 2 Answers

Homework 2 Answers - Economics 111 Intermediate...

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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 ff erence curve that yields U = 5 ( fi 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 0 15 12.5 10 7.5 5 2.5 0 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 fi gure graph her budget set if p 1 = 1 , p 2 = 1 and m = 10 . 1
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15 12.5 10 7.5 5 2.5 0 15 12.5 10 7.5 5 2.5 0 X1 X2 d. Find her optimal consumption bundle ( x 1 , x 2 ) and draw it in the fi gure. The optimal consumption value satis fi 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 0 15 12.5 10 7.5 5 2.5 0 X1 X2 e. Find her optimal consumption bundle ( x 0 1 , x 0 2 ) if p 1 = 2 , p 2 = 1 and m = 10 and draw it in the fi gure. Solving with the new prices we get: ( x 1 , x 2 ) = (2 . 5 , 5) .
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