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Exercise 1. Firm Supply in the Short Run Consider a firm with the following production function: y=L½K½....

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Economics

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.

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

  1. 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?

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

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

  1. 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.

  1. 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.

  1. 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.

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