Question

Suppose that production of a firm's output is described by the following production function Q = K0.25 L0.5

In the short run, the firm's capital is fixed at 10,000. Suppose further that the market price of the output is $37, and that the market wage is $25.

What is the Marginal Revenue Product of Labor (MRPL) for the 147th worker?

Enter your answer rounded to the nearest two decimals.

Answer 1

Marginal revenue Product(MRP) is the additional revenue earned when you hire one additional unit of input.

So MRP of Labor = P*MPL where P = Price of Output = 37 and MPL = Marginal product of Labor

Q = K0.25L0.5 and It is given that K = 10,000 => Q = 10,0000.25L0.5 = 10L0.5

MPL = dQ/dL = 10*0.5/L0.5 = 5/L0.5

Now we have to calculate MRP when L = 147

Thus, MRP = MPL*P = (5/L0.5)*32 = (5/1470.5)*32 = 13.20

Hence, the Marginal Revenue Product of Labor (MRPL) for the 147th worker = 13.20