Answer Problem #16 on page 140 of Williamson. Hint: The total number of workers that the firm hires, Nd , is the sum of the number of production workers it hires, N, plus the number of pollution abatement workers that it is required to hire. According to the question, the latter is x times the former. Thus, N^d = N + xN = (1 + x)N. From this, solve for the number of production workers N (which is what effectively enters the production function) as a function of the total demand for labor, N^d .

In the course of producing its output, a firm causes pollution. the government passes a law that requires the firm to stop polluting, and the firm discovers that it can prevent the pollution by hiring x workers for every worker that is producing output. that is, if the firm hires N workers, then xN workers are required to clean up the pollution caused by the N workers who are actually producing output. determine the effect of the pollution regulation on the firms profit-maximizing choice of labor input and on the firms labor demand curve.