Econ302-hw3-solutions-spring08 - 1 Econ302 Homework...

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Econ302 Homework Assignment 3 Solution 1. Trisha's Fashion Boutique production function for dresses is ( 29 1 1 3 2 , , = y K L K L where K is the number of sewing machines and L is the amount of labor hours employed. Trisha pays $15 per labor hour and sells each dress for $87.50. Also, Trisha currently has 4 sewing machines. Fill in the table below. How many units of labor will Trisha employ before the value of the marginal product of labor is less than the cost of a labor hour? y L L MP ( 29 $87.50 L MP 1 20 40 60 80 Solution: 1/ 2 (1/3) 1 1/ 2 2/3 1/ 2 2/3 2/3 1 1 3 3 3 3 L y MP K L K L L K K L L - - = = = = = y L 2 3 . 3 = L K MP L ( 29 $87.50 L MP 2 1 0.666667 58.33333 5.428835 20 0.09048 7.917 6.839904 40 0.05700 4.9874 7.829735 60 0.04350 3.80612 8.617739 80 0.03590 3.14188 To find the number of units of labor that Trisha will employ, we need to find L such that the value of the marginal product of labor is at least as much as the wage rate. 87.5*MPL >= 15 2 3 4 15* 15. 3 L K We get L = 7. 1
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2. In Example 6.3 in the textbook, wheat is produced according to the production function q = 100K 0.8 L 0.2 . a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. For fixed labor and variable capital: K = 4 q = (100)(4 0.8 )(49 0.2 ) = 660.22 K = 5 q = (100)(5 0.8 )(49 0.2 ) = 789.25 MP K = 129.03 K = 6 q = (100)(6 0.8 )(49 0.2 ) = 913.19 MP K = 123.94 K = 7 q = (100)(7 0.8 )(49 0.2 ) = 1,033.04 MP K = 119.85. For fixed capital and variable labor:
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This note was uploaded on 08/26/2009 for the course ECON 302 taught by Professor Toossi during the Spring '08 term at University of Illinois at Urbana–Champaign.

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Econ302-hw3-solutions-spring08 - 1 Econ302 Homework...

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