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Unformatted text preview: Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 6: The Neoclassical Firm 1 Perfect Competition - General Example Under perfect competition, the firm takes both the output price p and the input prices w 1 ,w 2 ,... as fixed. 1.1 The Two-Stage Approach The firm’s profit maximization problem can be seen as a combination of two problems: 1) a cost mini- mization problem, and 2) a profit maximization problem with a cost function. Stage 1: the firm’s cost minimization problem: min x 1 ,x 2 w 1 x 1 + w 2 x 2 s.t. f ( x 1 ,x 2 ) = y This can be solved using the Lagrangian: L = w 1 x 1 + w 2 x 2- μ [ f ( x 1 ,x 2 )- y ] The solution to this problem yields the Input Requirement Functions (IRFs), also called Conditional Input Functions (CIFs) or Conditional Factor Demands (CFDs). x 1 = x c 1 ( w 1 ,w 2 ,y ) x 2 = x c 2 ( w 1 ,w 2 ,y ) Plugging these into the objective function yields the cost function: C ( w 1 ,w 2 ,y ) = w 1 x c 1 ( w 1 ,w 2 ,y ) + w 2 x c 2 ( w 1 ,w 2 ,y ) Stage 2: the firm’s profit maximization problem: max y py- C ( w 1 ,w 2 ,y ) FOC: p- C y ( w 1 ,w 2 ,y ) = 0 or p = MC ( w 1 ,w 2 ,y ) SOC:- C yy ( w 1 ,w 2 ,y ) < 0 or MC y ( w 1 ,w 2 ,y ) > (Look back to the first week’s notes: py- C ( w 1 ,w 2 ,y ) is our function and so the second derivative must be < 0 for it to be a maximum.) 1 The solution to the second stage yields the optimal level of output y = y * ( w 1 ,w 2 ,p ). Finally, the op- timal level of output can be substituted back into the conditional input demand functions to yield the unconditional input demand functions: x 1 ( w 1 ,w 2 ,p ) = x c 1 ( w 1 ,w 2 ,y * ( w 1 ,w 2 ,p )) x 2 ( w 1 ,w 2 ,p ) = x c 2 ( w 1 ,w 2 ,y * ( w 1 ,w 2 ,p )) 1.2 Direct Profit Maximization Alternatively, the profit maximization problem can be set up and solved as an unconstrained maximization...
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This note was uploaded on 04/01/2009 for the course ECON 101a taught by Professor Staff during the Fall '08 term at University of California, Berkeley.
- Fall '08
- Perfect Competition