Question

The production function for laser eye surgery is given by Q = 20K0.570.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. The marginal product of labor for L = 3 is

a) 9.43
b) 28.28
c) 8.99
d) 11.71

Answer 1

The marginal product of labor for L = 3 can be calculated by taking the derivative of the production function with respect to labor, multiplying it by 3. The correct answer is c) 8.99.

Step-by-step explanation:

The marginal product of labor for L = 3 can be calculated by taking the derivative of the production function with respect to labor, multiplying it by 3. The production function is given as Q = 20K0.5L0.5. Taking the derivative with respect to L, we get dQ/dL = 10K0.5L-0.5. Substituting L = 3, we have dQ/dL = 10K0.5/√3.

Let's calculate the marginal product of labor for L = 3:

dQ/dL = 10K0.5/√3

dQ/dL = 10(2)0.5/√3

dQ/dL ≈ 10(1.414)/√3

dQ/dL ≈ 14.14/√3

dQ/dL ≈ 8.165.

Therefore, the marginal product of labor for L = 3 is approximately 8.165. The correct answer is c) 8.99.