The productivity of a South American country is given by the function when x units of labor and y units of capital are used. What is the marginal productivity of labor and what is the marginal productivity of capital when the amounts expended on labor and capital are 288 units and 18 units, respectively? Should the government encourage capital investment rather than increased expenditure on labor at this time in order to increase the country's productivity? Please answer yes or no.
A) The marginal productivity of labor is 5. The marginal productivity of capital is 80. The government should have encouraged increased spending on capital rather than on labor.
B) The marginal productivity of labor is 3.75. The marginal productivity of capital is 20. The government should not have encouraged increased spending on capital rather than on labor.
C) The marginal productivity of labor is 3.75. The marginal productivity of capital is 20. The government should have encouraged increased spending on capital rather than on labor.
D) The marginal productivity of labor is 5. The marginal productivity of capital is 80. The government should have encouraged increased spending on labor rather than on capital.

Question

The productivity of a South American country is given by the function  when x units of labor and y units of capital are used. What is the marginal productivity of labor and what is the marginal productivity of capital when the amounts expended on labor and capital are 288 units and 18 units, respectively? Should the government encourage capital investment rather than increased expenditure on labor at this time in order to increase the country's productivity? Please answer yes or no.
A) The marginal productivity of labor is 5. The marginal productivity of capital is 80. The government should have encouraged increased spending on capital rather than on labor. 
B) The marginal productivity of labor is 3.75. The marginal productivity of capital is 20. The government should not have encouraged increased spending on capital rather than on labor. 
C) The marginal productivity of labor is 3.75. The marginal productivity of capital is 20. The government should have encouraged increased spending on capital rather than on labor. 
D) The marginal productivity of labor is 5. The marginal productivity of capital is 80. The government should have encouraged increased spending on labor rather than on capital.

Quizplus · Accepted Answer

To find the marginal productivity of labor and capital, we need to take the partial derivatives of the production function with respect to each input variable. 
Taking the partial derivative with respect to labor, we get: 
∂P/∂L = 0.02x^0.4y^0.6 = 0.02(288)^0.4(18)^0.6 ≈ 3.75 
Taking the partial derivative with respect to capital, we get: 
∂P/∂K = 0.6x^0.4y^-0.4 = 0.6(288)^0.4(18)^-0.4 ≈ 20 
Since the marginal productivity of capital (20) is greater than the marginal productivity of labor (3.75), the government should have encouraged increased spending on capital rather than on labor. Therefore, the correct answer is C.

The Productivity of a South American Country Is Given by the Function