1.Input Combination

Using the production function Q = 20K^0.5L0.5, where K is machine-hours per week, L is worker-hours per week, and Q is output per week. Suppose that capital is $10 per machine-hour and labour is $5 per worker-hour. What would be the cost minimizing combination of capital and labour that could be used to produce outputs at the level of 20.

1.Profit Maximization

Suppose a firm uses capital (K) and Labor (L) to produce milk. The production function is

= 0.250.25.

The price of capital is 1 and the price of labor is 4. The market price of milk is 32.

1)In the short run, suppose the capital the firm has is 4, how much milk will the firm product to maximize its profit?

The firm should produce amount of milk.

2)In the long run:

i) How much milk will the firm produce to maximize its profit? What are the corresponding labor and capital inputs?

The firm should produce amount of milk. Capital input is .

Labor input is .