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Unformatted text preview: UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Producer Input Demand and Output Supply Example Problem Suppose a firm is producing a single product, Q, using two inputs, L and K. The firms engineers tell you that the production technology for product Q is given by c b K L a Q = , where a=2, b=1/2 and c=1/4. The firm operates in perfectly competitive markets; therefore, the firm takes prices as given. Find the firms input demand curves for L and K and the firm's supply curve for Q. Suppose that the given, per unit prices of Q, L and K are, respectively, P Q =100, P L =2 and P K =3. Find the firms profit-maximizing levels of L, K and Q. Example Solution TC TR ofit Pr max Q , K , L- = c b K L a Q : to subject = Replace TR and TC with their definitions . . . ( 29 K P L P Q P ofit Pr K L Q Q , K , L max + - = c b K L a Q : to subject = Substitute the production function constraint into the objective function to eliminate Q . . .Substitute the production function constraint into the objective function to eliminate Q ....
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