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2010_lecture_12_ho

# 2010_lecture_12_ho - Economics 101Lecture 12 The Basic...

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Economics 101—Lecture 12 The Basic Model of the Profit Maximizing Firm I George J. Mailath February 24, 2011

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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 > 0 , d 2 f ( x ) dx 2 i < 0 .
Isoquants f ( k ( ) , ) = q , = f k k + f = 0 = MRTS k = k = f / f / k . MRTS=marginal rate of substitution

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Cobb-Douglas production function q = k α β MRTS k = f / f / k = β k α β 1 α k α 1 β = β k α . Returns to scale: ( λ k ) α ( λ ) β = λ α + β k α β . So, if α + β = 1, Cobb-Douglas has constant returns to scale ; if α + β > 1, Cobb-Douglas has increasing returns to scale ; and if α + β < 1, Cobb-Douglas has decreasing returns to scale .
Other production functions 1 Linear : q = α k + β . Inputs are perfect substitutes . 2 Fixed proportions (or Leontief ): q = min { α k , β } . Inputs are perfect complements . 3 CES ( constant elasticity of substitution ): q = [ k ρ + ρ ] γ / ρ for ρ 1 , ρ = 0 , γ > 0.

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Profit maximization Firms maximize profits, given by π = pq
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