Consider the following production function: 9 = 9LK + 5L2 (3) L3

Economics Nov 07, 2020

Consider the following production function: 9 = 9LK + 5L2 (3) L3. Given the following expressions for the marginal productivity of each input: MPL = 9K + 10L - L2 and MPK = 9L Assuming capital is plotted on the vertical axis and labor is plotted on the horizointal axis, determine the value of the marginal rate of technical substitution when K = 30 and L = 15. (Round your answer up to two decimal places and include the proper sign.) MRTS =

Expert Solution

MRTS = - MP_L/MP_K

K=30, L=15

MP_L = 9K+10L-L² = 9*30+10*15 - 15² = 270+150-225 = 195

MP_K = 9L = 9*15 = 135

MRTS =-195/135 = -1.44

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