7 - MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 7....

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MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 7. Theory of the Firm II Profit Maximization Winter 2009 Stanford University Copyright © 2009 T.A. Weber All Rights Reserved -2- MS&E-241-Winter-2009-TAW AGENDA Profit-Maximizing Price-Taking Firm Key Concepts to Remember
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-3- MS&E-241-Winter-2009-TAW First-order necessary optimality conditions for local unconstrained (or “interior”) maximum. 2 ,1 0 n ii ij qq = ⎡⎤ ∂Π ⎢⎥ ∂∂ ⎣⎦ () 0 i Rq Cq q ∂Π =−= M MCq === Second-order necessary optimality condition for local unconstrained maximum: 2 Dq Π qR q C q Π= That is, the Hessian must be a negative semi-definite matrix at the local maximizer. PROFIT MAXIMIZATION -4- MS&E-241-Winter-2009-TAW R qC q = ''( ) 0 Rq Cq −≤ Necessary optimality conditions in the one-dimensional case q ) ( q* MRq PROFIT MAXIMIZATION (Cont’d)
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-5- MS&E-241-Winter-2009-TAW () MRq MCq = ''( ) 0 Rq Cq Necessary optimality conditions for profit-maximization (one-dimensional case) Different Perspectives External Analyst
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7 - MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 7....

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