ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

# Next lets review how to setup and solve a general

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Unformatted text preview: st, marginal cost, etc. Next, let’s review how to setup and solve a general parametric CMP. With by (where ) the long run CMP can be written as: ( ⏟ ) inputs and denoting the target output ⏟ This is a mixed equality and inequality constrained optimization problem. From lecture 1 and chapter 1 recall that the ECO 204 constrained optimization methods work for maximization not minimization problems. To transform the “min CMP” into a “max CMP” we multiply the objective (the total cost of inputs) by ( ⏟ Now the cost of inputs is ∑ )( ∑( )( )( ( ⏟ ⏟ ) so that: ) ( ∑( ) ) ) ( ⏟ ) ⏟ ⏟ Now setup the Lagrangian equation: ∑( 7 )( For example: [ ) ( ) ∑ or 22 ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Since we have a combination of equality and inequality constraints we would solve this problem by a combination of the Lagrangian and Kuhn-Tucker methods. For example, the general 2 inputs CMP will be (here, both inputs have a lower limit of zero): [ The FOCs and...
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## This document was uploaded on 01/19/2014.

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