Exercise 1. Firm Supply in the Short Run
Consider a firm with the following production function:y=L½K½. The cost function is C=w∙L+r∙K.
- In the short-run the input K is given at K=100. What is theshort-run production function y(L)?
- Let w=0.1 and r=1. What is the cost function C(y)? Using theexpression y(L) you found in part a, transform it into L(y) andplug it into the cost function C(L) to get C(y). Was a minimizationnecessary? Why or why not?
- Given C(y) you find in part b, find AC(y) and MC(y). What isthe firm’s short-run supply function S(p)?
- At what level of y is the average cost minimized?
- 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 producersurplus? How many workers does the firm employ? Find L.
- 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 producersurplus? How many workers does the firm emply? Find L.
- 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 producersurplus? How many workers does the firm emply? Find L.
