Question

Exercise 1. Firm Supply in the Short Run

Consider a firm with the following production function: y=L^½K^½. The cost function is C=w∙L+r∙K.

1. In the short-run the input K is given at K=100. What is the short-run production function y(L)?

2. Let w=0.1 and r=1. What is the cost function C(y)? Using the expression y(L) you found in part a, transform it into L(y) and plug it into the cost function C(L) to get C(y). Was a minimization necessary? Why or why not?

3. Given C(y) you find in part b, find AC(y) and MC(y). What is the firm’s short-run supply function S(p)?

4. At what level of y is the average cost minimized?

5. When the market price is p=0.2, how much does the firm supply? Find S(0.2). What is the firm’s profit? What is the firm’s producer surplus? How many workers does the firm employ? Find L.

6. When the market price is p=0.1, how much does the firm supply? Find S(0.1). What is the firm’s profit? What is the firm’s producer surplus? How many workers does the firm emply? Find L.

7. When the market price is p=0.3, how much does the firm supply? Find S(0.1). What is the firm’s profit? What is the firm’s producer surplus? How many workers does the firm emply? Find L.

Answer 1