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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
) 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.
- Fall '14