# 1st_Midterm_Practice_Answer - Econ 352 Intermediate...

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Econ 352 YiLi Chien Intermediate Macroeconomics Spring 2010 1 st Midterm Practice Answers Part One (40 pts) Instruction: answer the following questions using analytical frameworks. Depict appropriate diagrams if needed. 1. (15 points) Consider a Cobb-Douglas production function with K(capital), L(labor). The production function is Y=AK 0.4 L 0.6 . a) (5 pts) Derive expression for the marginal product of capital and labor. MP K = ә Y/ ә K = 0.4 AK 0.4-1 L 0.6 = 0.4 AK -0.6 L 0.6 = 0.4 A(L/K) 0.6 Similarly, MP L = ә Y/ ә L = 0.6AK 0.4 L 0.6-1 = 0.6AK 0.4 L -0.4 = 0.6A(K/L) 0.4 b) (5 pts) Show that this Cobb-Douglas production function exhibits constant returns to scale. Suppose we scale up capital and labor input by z i.e., F(zK,zL) = A(zK) 0.4 (zL) 0.6 = z 0.4+0.6 AK 0.4 L 0.6 = zY Then we get back the total output also scale up by z. This production function is constant return to scale. c) (5 pts) Derive the labor share (total labor income divided by total output) in the equilibrium of this economy. (Hint: the equilibrium real wage rate is equal to marginal product of labor) Labor’s share 0.4 0.4 0.4 0.6 0.6 0.6

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