1. Let me introduce our distinguished ____________（guest) today.

(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.

Task 3 Directions: Please match the famous figures with their statements of love. Bertrand Russell 1) Bertrand Russell A. Where does the family start? It starts with a young man falling in love with a girl — no superior alternative has yet been found. 2) Mother Teresa B. The course of true love never did run smooth. 3) Sir Winston Churchill C. It is not how much we do, but how much love we put in the doing. It is not how much we give, but how much love we put in the giving. 4) William Shakespeare D. To fear love is to fear life, and those who fear life are already three parts dead.

A、

B、

C、

D、

A. T+0

B. T+1

C. T+4

D. T+5

A、tε(t)

B、tε(t-2)

C、(t-2)ε(t)

D、(t-2)ε(t-2)

此题为判断题(对，错)。

,其中D_t={(x,y)|0≤y≤t-x,0≤x≤t}(0≤1≤1)。求f(x)的表达式。