1.10. A firm uses a single input, labor, to produce output q according to the production function . The commodity sells for $150 per unit and the wage rate is $75 per hour.

a. Find the profit-maximizing quantity of L.

b. Find the profit-maximizing quantity of q.

c. What is the maximum profit?

d. Suppose now that the firm is taxed $30 per unit of output and that the wage rate is subsidized at a rate of $15 per hour. Assume that the firm is a price taker, so the price of the product remains at $150. Find the new profit-maximizing levels of L, q, and profit.

e. Now suppose that the firm is required to pay a 20 percent tax on its profits. Find the new profit-maximizing levels of L, q, and profit.