Question

Consider the following production function:

Y = output = AK1/2N1/2, A = productivity, K = capital, N = labor.

a) (3 pts.) Suppose that Y = 1331, K =121, and N = 121. Find A.

b) (4 pts.) Find the marginal product of capital (MPK), measured as the additional output that arises when the capital stock is increased by 1 unit. (Start with the values of A, K and N that you found in part (a).)

c) (4 pts.) Suppose that capital stock increases from 121 to 144. Relative to your answer in part (b), will the MPK increase or decrease? Why? You can assume that the production function has the “standard” properties. Do not redo your calculations.

Answer 1

Ans. Production Function, Y = A*K^0.5 * N^0.5

a) At Y = 1331, K = 121 and N = 121,

=> 1331 = A * 121^0.5 * 121^0.5

=> A = 11

b) Marginal Product of capital, MPK = dY/dK = 0.5A * (N/K)^0.5

At K = 121 , N = 121, Y = 1331 and A = 11, we get,

MPK = 0.5*11 * (121/121)^0.5 = 5.5

c) MPK at K = 144, N = 121 and A = 11,

=> MPK = 0.5*11*(121/144)^0.5

=> MPK = 5.04167

Thus, MPK decrease when capital stock is increased from 121 to 144. This is because at given labour of 121, the additional capital becomes less productive as there is no additional labour to work on them.

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