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Problem #1yKLr wy$py = fA1/41/4ðA1/41/4 rK -wLa

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Problem #1yKLr wy$py = fA1/41/4ðA1/41/4 rK -wLa.  Find the profit maximizing levels of K Lrw p 1.  Consider two firms that produce a single output good, , using two inputs: Capital, , and labor, . the prices of each unit of capital and labor are and , respectively. The output good sells for per unit.Firm A's production function is (K,L) = K L. The profit function is thus:

(K,L) = K L-

and as functions of , , and.

b.  Suppose that r = w = $1 and p = $4. What is the profit maximizing level of output, y ?

 

Problem #2

 

2.  Consider an industry in the U.S. facing aggregate (inverse) demand function:

p(y) = 1050 - 5y

 

The industry is currently in long run equilibrium. The market price is $225 and there are n = 11 firms producing. Each firm's variable cost is:

 

c_v(y) =  y³

 

a.  What is each firm's fixed cost?