2010_lecture_13

2010_lecture_13 - Economics 101—Lecture 13 The Basic...

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Unformatted text preview: Economics 101—Lecture 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 firm’s 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 firm’s profit-maximization “problem” means expressing the choice variables (output and inputs) in terms of variables known to the firm—prices and technology parameters (like α and β from Cobb-Douglas). These are the output supply and input demand functions of the firm, such as for Cobb-Douglas (assuming α + β < 1), k ( p , r , w ) = p α 1 − β β β w − β r β − 1 1 1 − α − β ....
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2010_lecture_13 - Economics 101—Lecture 13 The Basic...

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