420worksheet3ans

# 420worksheet3ans - 1 = 1.069 Thus rental price of capital...

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Worksheet 3 1. Suppose that an economy’s production function is Cobb-Douglas with parameter α =0.3, a. Calculate the fraction of income that capital and labor receive? Y=K 0.3 L 0.7 MPK = 0.3K -0.7 L 0.7 Multiplying both sides by K will give MPK * K = 0.3K 0.3 L 0.7 = 0.3 Y A profit maximizing firm will use capital till MPK = (R/P) (R/P)*K = 0.3 Y Thus the share of income to capital is 0.3 Y=K 0.3 L 0.7 MPL = 0.7K 0.3 L -0.3 Multiplying both sides by L will give MPK * L = 0.7K 0.3 L 0.7 = 0.7 Y A profit maximizing firm will use capital till MPL = (W/P) (W/P)*L = 0.7 Y Thus the share of income to labor is 0.7 b. Suppose that immigration raises the labor force by 10 percent. What happens to total output (in percent). The rental price of capital? The real wage? Y 2 =K 0.3 (1.1L) 0.7 Y 1 =K 0.3 L 0.7 Y 2 /Y 1 =K 0.3 (1.1L) 0.7 /K 0.3 L 0.7 = 1.069 Thus output increases by 6.9% SHORT METHOD: Share of real rental price of capital = 0.3 Y (R/P) 1 *K = 0.3 Y 1 (R/P) 2 *K = 0.3 Y 2 (R/P) 2 *K/(R/P) 1 *K = 0.3Y 2 /0.3Y 1 (R/P) 2 /(R/P) 1 = Y 2 /Y

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Unformatted text preview: 1 = 1.069 Thus rental price of capital increases by 6.9% Share of real wage = 0.7 Y (W/P) 1 *L = 0.7 Y 1 (W/P) 2 *1.1L = 0.7 Y 2 (W/P) 2 *1.1L/(W/P) 1 *L = 0.7Y 2 /0.7Y 1 (W/P) 2 1.1/(W/P) 1 = Y 2 /Y 1 = 1.069 (W/P) 2 /(W/P) 1 = 1.069/1.1 = 0.972 Thus real wages decrease by 2.8% LONGER METHOD: MPK 1 = 0.3K-0.7 L 0.7 MPK 2 = 0.3K-0.7 (1.1L) 0.7 Calculate share of Y going to K. MPK 1 *K = 0.3K-0.7 L 0.7 *K = 0.3Y 1 MPK 2 *K = 0.3K-0.7 (1.1L) 0.7 *K = 0.3Y 2 Substitute (R/P) for MPK. (R/P) 2* K /(R/P) 1 K = 0.3Y 2 /0.3Y 1 = 1.069 Real rental price of capital increases by 6.9% MPL 1 = 0.7K 0.3 L-0.3 MPL 2 = 0.7*1.069K 0.3 L-0.3 Calculate share of Y going to L. MPL 1 *L = 0.7K 0.3 L-0.3 *L = 0.7Y 1 MPL 2 *1.1L= 0.7*1.069K 0.3 L-0.3 *L = 0.7*1.069*Y 1 Substitute (W/P) for MPL (W/P) 2 *1.1L /(W/P) 1 *L = 1.069 (W/P) 2 /(W/P) 1 = 1.069/1.1 = 0.972 Real wage decreases by 0.972-1 = 2.8%...
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## This document was uploaded on 10/28/2011 for the course ECON 420 at UNC.

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420worksheet3ans - 1 = 1.069 Thus rental price of capital...

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