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Unformatted text preview: Economics 101Lecture 13 The Basic Model of the Profit Maximizing Firm II George J. Mailath March 1, 2011 In our last episode Production function q = f ( x 1 , x 2 , . . . , x n ) , and isoquants. MRTS=marginal rate of technical substitution MRTS k = k = f / f / k . In our last episode Production function q = f ( x 1 , x 2 , . . . , x n ) , and isoquants. MRTS=marginal rate of technical substitution MRTS k = k = f / f / k . A perfectly competitive firm takes prices as given . That is, the prices are, from the firms perspective, parametric or predetermined . (Just as the consumer took prices as parametric.) In our last episode, cont. Profit maximization : max ( q , x 1 , ... , x n ) pq n i = 1 w i x i subject to q = f ( x 1 , . . . , x n ) . In our last episode, cont. Profit maximization : max ( q , x 1 , ... , x n ) pq n i = 1 w i x i subject to q = f ( x 1 , . . . , x n ) . Two approaches. 1 Eliminate q first: max ( x 1 , ... , x n ) pf ( x 1 , . . . , x n ) n i = 1 w i x i . In our last episode, cont. Profit maximization : max ( q , x 1 , ... , x n ) pq n i = 1 w i x i subject to q = f ( x 1 , . . . , x n ) . Two approaches. 1 Eliminate q first: max ( x 1 , ... , x n ) pf ( x 1 , . . . , x n ) n i = 1 w i x i . 2 Do cost minimization first: max q pq C ( q , w ) , where C ( q , w ) = min ( x 1 , ... , x n ) n i = 1 w i x i subject to q = f ( x 1 , . . . , x n ) . Solution vs Characterization The firm knows prices, but must choose level of output and inputs. Solving the firms profitmaximization problem means expressing the choice variables (output and inputs) in terms of variables known to the firmprices and technology parameters (like and from CobbDouglas). These are the output supply and input demand functions of the firm, such as for CobbDouglas (assuming + < 1), k ( p , r , w ) = p 1 w r 1 1 1 ....
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 Spring '08
 DANNICATAMBAY
 Economics, Microeconomics

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