10.6 Aggregation - Lecture 14

# 10.6 Aggregation - Lecture 14 - Producer Theory(Part 2...

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Unformatted text preview: Producer Theory (Part 2) Producer Theory Producer Theory (Part 2) October 5, 2011 Producer Theory (Part 2) Producer Theory From Last Time L commodities Firms can produce any input-output vector y 2 Y & R L y l < 0 for inputs y l > 0 for outputs [Picture 5.B.1] Transformation Function Y = f y : F ( y ) ¡ g F ( y ) = 0 is Transformation Frontier Usually we assume F is di/erentiable Producer Theory (Part 2) Producer Theory Pro&t Maximization Problem π ( p ) = max y 2 Y p & y This can be rewritten... π ( p ) = max y 2 R L p & y such that F ( y ) ¡ y ( p ) = arg max y 2 R L p & y such that F ( y ) ¡ No nonegativity constraints May have "problems" if Y is nonconvex There are easy cases where y ( p ) = ∅ and π ( p ) = + ∞ . Why? [PICTURE] Producer Theory (Part 2) Producer Theory Pro&t Maximization Problem This is very similar to the EMP Lagrangian: L = p & y + λ ¡ [ ¢ F ( y )] First Order Conditions: p l = λ ∂ ∂ y l F ( y ) Expressed in terms of the Marginal Rate of Transformation (MRT lk ) p l p k = MRT lk = ∂ F / ∂ y l ∂ F / ∂ y k Producer...
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10.6 Aggregation - Lecture 14 - Producer Theory(Part 2...

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