Econ501aH3ansS07

# Econ501aH3ansS07 - The Ohio State University Department of...

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The Ohio State University Department of Economics Econ 501.02 Prof. James Peck Homework #3 Answers 1. (a) The MRTS is the ratio of the marginal products, so we have MRTS = MP L K = 5 K 2 ( K + L ) 2 5 L 2 ( K + L ) 2 = K 2 L 2 . (b) AP L = 5 KL K + L L = 5 K K + L L = 5 K 2 ( K + L ) 2 (c) This production function exhibits constant returns to scale, because f ( θK,θL )= 5( θK )( θL ) + = θ 5 K + L . 2. (a) First, we set up the Lagrangean for the cost minimization problem Lagr. = wL + rK + λ [ x 5 K + L ] . The f rst order conditions are ∂Lagr. ∂L =0= w λ 5 K 2 ( K + L ) 2 ∂Lagr. ∂K r λ 5 L 2 ( K + L ) 2 ∂Lagr. ∂λ x 5 K + L . Solving the f rst two equations for λ and setting them equal to each other, we have the condition that MRTS = w/r, K 2 L 2 = w r =4 , which can be written as K = r w r L =2 L. (1) 1

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To make the math easier, we have substituted w =4 and r =1 . Plugging (1) into the third condition yields x = 5(2 L ) L 2 L + L = 10 L 3 . Solving for L, we have L = 3 x 10 . From (1), we have K = 6 x 10 .
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## This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Spring '08 term at Ohio State.

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Econ501aH3ansS07 - The Ohio State University Department of...

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