Suppose the economy's production function is Y = AK0.3N0.7. Suppose K = 200, N = 2000, and A = 1. Calculate the marginal products of labor and capital.
What will be an ideal response?
Using calculus, the marginal product of capital is dY/dK = 0.3A(N/K)0.7 and dY/dN = 0.7A(K/N)0.3.
Plugging in the values for N and K gives: MPK = 0.3 (2000/200)0.7 = 1.5; MPN = 0.7 (200/2000)0.3 = 0.35. If you do not use calculus, you can arrive at the same answer (rounded) by plugging the values of for A, N and K into the production function to find Y = 1002.37. Increase K by 1 and recalculate Y; it is now 1003.88. The difference is the MPK = 1003.88 - 1002.37 = 1.51. Increase N by 1 and recalculate Y; it is 1002.73. The difference is the MPN = 1002.73 - 1002.37 = 0.36.
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What will be an ideal response?
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