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# h5_ans - L K K q L q RTS = = = = ∂ ∂ ∂ ∂ =-RTS =...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 HW 5 ans. 1. (a) When K = 10. the production function is q = 2 K + L = 2(10) + L = 20 + L . If q = 100, L = 100 – 20 = 80. (b) When K = 25, the production function is q = 2(25) + L = 50 + L If q = 100, L = 50. (c) 1 ; 2 = = = = L q MP K q MP L K (d) 2 1 - = - = K L MP MP RTS The RTS is constant at ½. The isoquant is downward sloping and linear. It is not convex because of the constant RTS. This implies in this production process both capital and labor are perfect substitutes. 2. (a) 2000 . 20 = = L K q 10 . = L K 100 . = L K The production function corresponding to this isoquant is downward sloping and convex. L K Slope = 1/2

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2 (b) L K . 20 2000 = K ). 101 ( 100 = K 101 000 , 10 = K = 10,000/101 = 99.009 (c) . . 20 L K q = 2 / 1 2 / 1 20 L K q = 2 / 1 2 / 1 2 / 1 ) ( 10 2 1 . 20 L K L K L q MP L = = = - 2 / 1 2 / 1 2 / 1 ) ( 10 2 1 . 20 K L L K K q MP K = = = - ) ( ) ( ) ( ) ( ) ( 10 ) ( 10 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 L K L K L K L
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Unformatted text preview: L K K q L q RTS = = = = ∂ ∂ ∂ ∂ = +-RTS = K/L = 25/400 = 0.0625 3. (a) a a a b a L L K b L bK L bK L q MP ) ( 1 = = = ∂ ∂ =--b b b b a K K L a L aK L aK K q MP ) ( 1 = = = ∂ ∂ =--(b) When L increases the denominator increases in the expression for marginal productivity of capital. This lowers K/L ratio thereby reducing the marginal productivity of labor. Similarly from the marginal productivity expression for capital, when capital increases, it decreases the L/K ratio, thereby reducing marginal product of capital. L K Slope = RTS 3 (c) ) ( ) ( ) ( ) ( ) ( ) ( L K a b L K a b L K a L K b K L a L K b dK q dL q RTS b a b a b a = = = = ∂ ∂ = +-...
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