Question

1. A firm can manufacture a product according to the following production function, Q = 4K1/2 L1/2 and the Marginal Product of Labor is MP(L) = 2K1/2 L-1/2. Recall that VMP(L) = w. a. Suppose that capital is fixed at 25 units. If the firm can sell its output at $200 per unit and employs 64 units of labor, how much should it pay its labor to maximize profits? b. Using the information in (a), assume that you pay $5/unit for capital. Can you, given the information at hand, determine total profits?

Answer 1

(a)

A firm maximizes profit when it hires that amount of labor corresponding to which VMP of labor equals wage rate.

VMP = w

MPL * Price of product = w

[2K^1/2/L^1/2] * 200 = w

[(2 * 25^1/2)/64^1/2] * 200 = w

1.25 * 200 = w

w = 250

In order to maximize profit, firm should pay labor $250.

(b)

Calculate the Total output produced -

Q = 4 * K^1/2 * L^1/2 = 4 * (25)^1/2 * (64)^1/2 = 4 * 5 * 8 = 160 units

Calculate the total revenue -

Total revenue = Price * Quantity = $200 * 160 = $32,000

Calculate the total cost -

Total cost = [Units of capital * Price of capital] + [Units of labor * Price of labor]

Total cost = [25 * $5] + [64 * $250] = $125 + $16,000 = $16,125

Calculate the total profits -

Total profits = Total revenue - Total cost = $32,000 - $16,125 = $15,875

The total profits is $15,875