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# Homework 4 Answers - ECO 301 Intermediate Microeconomics...

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ECO 301: Intermediate Microeconomics Marco A Castaneda Homework 4: Answers 1. ANSWER For the production function F(K,L) = 2K + L, we have the marginal products of labor and capital are MP L = 1 and MP K = 2 The marginal rate of technical substitution is 2 1 MP MP MRTS K L LK = = This implies the isoquants are linear. Graphically, the solution to this problem is as follows: Y Isoquants: MP L /MP K = 1/2 w L /w K = 1/3 Isocost lines (b): Isocost lines (a): w L /w K = 2/3 10 5 X 5 10 15 20 a) In this situation, we have L L K K w MP 10 1 15 2 w MP = > = This means the marginal output per dollar is always greater for capital than it is for labor. Therefore, only capital should be used in the production process. The optimal quantity of capital can then be determined by the equation q = 2K

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Therefore, we have q w K w L K* L* C 10 15 10 5 0 75 20 15 10 10 0 150 b) In this situation, we have L L K K w MP 5 1 15 2 w MP = < = This means the marginal output per dollar is always greater for labor than it is
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Homework 4 Answers - ECO 301 Intermediate Microeconomics...

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