一个企业以劳动作为单一投入，产出为q. 生产函数为q=8L^1/2。商品售价是150美元/单位,工资

(1)找出利润最大化时的L数量。

(2)找出利润最大化时的q数量。

(3)最大化利润是多少？

(4)假设现在每单位的产出要征税30美元，而每小时的劳动能得到15美元的补助。并且假设企业是价格接受者，所以产品价格保持150美元不变。找出新的利润最大化的L、q和利润。

(5)假设企业要为利润支付20%的税额。找出新的利润最大化的L、q和利润。

A firm uses a single input, labor, to produce output q according to the production function q =8√L. The commodity sells for S 150 per unit and the wage rule 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 lax on its profit. Find the new profit - maximizing levels of L, q, and profit.