Unformatted text preview: cal equation for the lowest cost of producing any output level . This is: To find the optimal cost of producing an arbitrary output level
in terms of to get: we would substitute expressions for optimal and 33
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. ()
⏟ Here () [[ ] [[ ] is a constant. As long as we remember that this is the lowest cost of producing an arbitrary output we will sometimes write the cost function as ( )
from any of the FOC; for example, from the labor FOC we have: [⏟ [ . Finally we can solve for This implies that: () ( ) ( ) From our discussion of the general long run CMP we know that if we want the change in
parameter that we can use the envelope theorem on:
( Denote [ due to a small change in the ) and we get: Since we know the cost function we can easily derive the and from this : 34
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. And since : See how brains is better than brawn ?
We will now do a detailed analysis of the solutions to the Cobb-Douglas long run CMP: What’...
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