平狄克微观经济学第六版课后答案

firm will hire labor up until the point where the marginal revenue product (p*MPL) equals the wage rate. Using the first method:

TR TC pq wL

150*8*L 75L

1 600L2 75 0 L

L 64.12

b. Find the profit-maximizing quantity of q.

From part a, the profit maximizing quantity of labor is 64 so substitute this quantity of labor into the production function to find q 8L 8* 64. 12

c.

d. What is the maximum profit? Profit is total revenue minus total cost or 150*64 75*64 4800. Suppose now that the firm is taxed $30 per unit of output and the wage rate is

subsidized at a rate of $15 per hour. Assume the firm is a price taker, so that the price of the product remains at $150. Find the new profit-maximizing levels of L, q, and profit.

After the $30 tax per unit of output is paid, the firm receives 150-30=$120 per unit of output sold. This is the relevant price for the profit maximizing decision. The input cost is now 75-15=$60 per unit labor after the subsidy is received. The profit maximizing values can be found as in parts a-c above:

TR TC pq wL

120*8*L 60L

1 480L2 60 0 L

L 64

q 6412

3840.

e. Now suppose that the firm is required to pay a 20% tax on its profits. Find the

new profit-maximizing levels of L, q, and profit.

The profit maximizing values can be found as in parts a-c above, only here profit is 80% of total revenue minus total cost.

.8(TR TC) .8(pq wL)

.8(150*8*L 75L)

1 480L2 60 0 L

L 64

q 6412

3840.