Question

A firm's production function is given by Q = 40ln (E1 + E2) where E1 and E2 are the number of white workers and black workers employed by the firm, respectively. From this, it can be shown that the marginal product of labor is M = E1 + E2. Suppose the market wage for black workers is $50, the market wage for white workers is $100, and the price of each unit of output is $20. a) How many workers of each race would a nondiscriminating firm hire? How much profit is earned if there are no other costs? b) How many workers of each race would a firm with a discrimination coefficient of 0.6 against black people hire? How much profit is earned if there are no other costs? c) How many workers of each race would a firm with a discrimination coefficient of 1.2 hire? How much profit is earned if there are no other costs?

Answer 1

Employing black workers equally to white workers maximizes profit and benefits both workers and firms.

a) The firm's profit will be $17,500.

b) The firm's profit will be $22,000.

c) The firm's profit will be $18,000.

a) To maximize profit, a firm will hire workers until the marginal product of labor equals the market wage. In this case, the marginal product of labor is M = E1 + E2. The market wage for black workers is $50, and the market wage for white workers is $100. Therefore, the firm will hire workers until E1 + E2 = $50 for black workers and E1 + E2 = $100 for white workers.

Solving these equations, we find that the firm will hire 25 black workers and 50 white workers. The total output of the firm will be Q = 40ln(25 + 50) = 40ln(75) = 1200 units. The firm's profit will be P = (20 * 1200) - (50 * 25) - (100 * 50) = $17,500.

b) A firm with a discrimination coefficient of 0.6 against black people will pay black workers 60% of the market wage for white workers. Therefore, the market wage for black workers is $50 * 0.6 = $30.

To maximize profit, a firm will hire workers until the marginal product of labor equals the market wage. In this case, the marginal product of labor is M = E1 + E2. The market wage for black workers is $30, and the market wage for white workers is $100. Therefore, the firm will hire workers until E1 + E2 = $30 for black workers and E1 + E2 = $100 for white workers.

Solving these equations, we find that the firm will hire 33.33 black workers and 66.67 white workers. The total output of the firm will be Q = 40ln(33.33 + 66.67) = 40ln(100) = 1600 units. The firm's profit will be P = (20 * 1600) - (30 * 33.33) - (100 * 66.67) = $22,000.

c) A firm with a discrimination coefficient of 1.2 against black people will pay black workers 80% of the market wage for white workers. Therefore, the market wage for black workers is $50 * 1.2 = $60.

To maximize profit, a firm will hire workers until the marginal product of labor equals the market wage. In this case, the marginal product of labor is M = E1 + E2. The market wage for black workers is $60, and the market wage for white workers is $100. Therefore, the firm will hire workers until E1 + E2 = $60 for black workers and E1 + E2 = $100 for white workers.

Solving these equations, we find that the firm will hire 16.67 black workers and 83.33 white workers. The total output of the firm will be Q = 40ln(16.67 + 83.33) = 40ln(100) = 1600 units. The firm's profit will be P = (20 * 1600) - (60 * 16.67) - (100 * 83.33) = $18,000.