2010_lecture_12

2010_lecture_12 - Economics 101Lecture 12 The Basic Model...

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Unformatted text preview: Economics 101Lecture 12 The Basic Model of the Profit Maximizing Firm I George J. Mailath February 24, 2011 Production q output x i input i Production function q = f ( x 1 , x 2 , . . . , x n ) , with derivatives marginal (physical) product, df ( x ) dx i > , d 2 f ( x ) dx 2 i < . Isoquants f ( k ( ) , ) = q , = f k k + f = = MRTS k = k = f / f / k . MRTS=marginal rate of substitution Cobb-Douglas production function q = k MRTS k = f / f / k = k 1 k 1 = k . Cobb-Douglas production function q = k MRTS k = f / f / k = k 1 k 1 = k . Returns to scale: ( k ) ( ) = + k . So, if + = 1, Cobb-Douglas has constant returns to scale ; if + > 1, Cobb-Douglas has increasing returns to scale ; and if + < 1, Cobb-Douglas has decreasing returns to scale . Other production functions 1 Linear : q = k + . Inputs are perfect substitutes . 2 Fixed proportions (or Leontief ): q = min { k , } . Inputs are perfect complements . 3 CES ( constant elasticity of substitution ): q = [ k + ] / for 1 , = , > 0. Profit maximization Firms maximize profits, given by = pq n i = 1 w i x i , where p is the price of output and w i is the price of output i . Profit maximization...
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2010_lecture_12 - Economics 101Lecture 12 The Basic Model...

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