Consider the following production function: q = 7LK + 5L^2 - (1/3) L^3. Given the following expressions for the marginal productivity of each input: MP_L = 7K + 10L - L^2 and MP_K = 7L Assuming capital is plotted on the vertical axis and labor is plotted on the horizontal 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.)

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Business

Nathalie Zavala

20 October, 03:26

Consider the following production function: q = 7LK + 5L^2 - (1/3) L^3. Given the following expressions for the marginal productivity of each input: MP_L = 7K + 10L - L^2 and MP_K = 7L Assuming capital is plotted on the vertical axis and labor is plotted on the horizontal 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.)

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Romeo · Answer 1

The value of the marginal rate of technical substitution when K = 30 and L = 15 is 1.285

Explanation:

MRTS_KL = MP_L/MP_K

= (7K + 10L - L^2) / 7L

= (7*30 + 10*15 - (15) ^2) / 7*15

= 1.285

Therefore, The value of the marginal rate of technical substitution when K = 30 and L = 15 is 1.285