Question

A firm's production function is given by Q=40ln(E

W
​
+E
g
​
+1) where E
w
​
and E
B
​
are the number of whites and blacks employed by the firm respectively. From this it can be shown that the marginal product of labor is MPE=
E
W
​
+B
B
​
+1
40
​
Suppose the market wage for black workers is $80, the market wage for white workers is $100, and the price of each unit of output is $40. Question 1 Refer to Scenario 1. How many white workers would a non-discriminating firm hire? Question 2 Refer to Scenario 1. How many black workers would a non-discriminating firm hire? Question 3 Refer to Scenario 1. How much profit is eamed by the non-discriminating firm if there are no other costs? (Reminder: profit is revenue minus cost, and revenue is price times quantity. You are given the firmis production quantity through the production function.)

Answer 1

A non-discriminating firm will hire workers until the value of the marginal product equals the market wage. The exact number of white workers ($100 wage) and black workers ($80 wage) can be found by setting the value of marginal product equal to the market wage and solving for the number workers. Profit is the revenue minus the cost, which requires the number of each group of workers hired.

Step-by-step explanation:

To determine how many white and black workers a non-discriminating firm would hire, we look at the firm's marginal product of labor (MPE) and how it equates to the market wage. The firm will hire workers until the marginal revenue product (the additional revenue from one more worker) is equal to the market wage for that worker. Given the market wage for black workers is $80 and for white workers is $100, and the price per unit of output is $40, the firm would hire workers of either type up to the point where:

Value of Marginal Product (VMP) = Marginal Product of Labor (MPE) x Price of Output = Market Wage

For white workers, VMP would be calculated as follows:

40 x (40 / (Ew + Eb + 1)) = $100

For black workers, the calculation would be similar:

40 x (40 / (Ew + Eb + 1)) = $80

The exact number of workers to be hired requires solving these equations which involve the sum of both white and black workers. As these equations may depend on each other, they might need to be solved simultaneously to find the respective number of workers.

For the profit calculation:

Profit = Revenue - Cost

Revenue = Price x Quantity = $40 x Q

Cost = (Number of White Workers x $100) + (Number of Black Workers x $80)

The total profit can only be accurately calculated once the exact number of white and black workers has been determined, using the production function Q provided.