For the production function Q(K,L) = K^0.5L^0.5, the marginal product of capital is: A) K^-0.5L^0.5. B) 0.5K^-0.5L^0.5. C) 0.5K^0.5L^-0.5. D) 0.25X^-0.5Y^-0.5.

Question

Quizplus · Accepted Answer

The marginal product of capital (MPK) is found by taking the partial derivative of the production function with respect to capital (K). In this case, the exponent on K is 1, so when we differentiate with respect to K, we bring down the exponent (1) as a coefficient (which doesn't change the expression since multiplying by 1 has no effect), and subtract 1 from the exponent, resulting in an exponent of 0.5. The 0.5 in front of the expression is a result of the differentiation process, indicating that the marginal product of capital is proportional to K raised to the power of 0.5, with all other terms remaining the same.

For the Production Function Q(K,L) = K0

For the Production Function Q(K,L) = K⁰