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Hw2ak - Sonoma State University Department of Economics...

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Sonoma State University ECONOMICS 304 Department of Economics Florence Bouvet Assignment 2 – Answer Key 1) Consider the following production function: Y = 40 K 0.2 L 0.8 , where Y represents output, K represent capital, and L represents labor. a) Does this production function exhibit constant, decreasing or increasing returns to scale? Show your work. F(2K,2L) = 40 (2K) 0.2 (2L) 0.8 = 40x (2) 0.2 (2) 0.8 (K) 0.2 (L) 0.8 = 40.2 1 .(K) 0.2 (L) 0.8 = 2. 40(K) 0.2 (L) 0.8 = 2Y This production function exhibits constant returns to scale. b) Compute expressions for the marginal products of labor and of capital. Does the production function exhibit increasing, constant or diminishing returns to labor? Show your work. MPL = Y L = 40*0.8K 0.2 L -0.2 =32(K/L) 0.2 MPK = Y K = 40*0.2K -0.8 L 0.8 =8(L/K) 0.8 As L goes up, MPL falls, so this production function exhibits diminishing returns to labor. c) Do workers or capitalists (owners of capital) end up getting paid the larger share of total output? What fraction of total output gets paid to workers?
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