Consider a firm with a production function given by q=187N, where q is the quantity producedand N is the number of workers hired. The firm sells its product in a competitive market, and themarket price of its good is p=1.

The firm, however, is the only employer in the town where it operates, and hence it does not takethe cost of labour as given. The inverse labour supply function in this town is given by w=45+0.04N².

1.

a) Solve for the profit-maximizing choice of N.

b) What will the wage be in this town?

c) Is the wage equal to, greater than, or less than p MP_N(where p is the price of the good andMP_N is the marginal product of labour)?Explain intuitively why this is the case in this setting.

d)If the government were to intervene in this market by setting a minimum wage, what would be the optimal level at which to set the minimum wage, if the government's objective is to increase employment as much as possible?