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Unformatted text preview: results to glean further insights about the optimal mix of inputs in the long run CMP. Using
) Marginal product of input 1 and
the “envelope theorem” results and noting that (
let’s take a second look at the FOCs with respect to the inputs for
the 2 input long run CMP:
[ [ ( ) ( ) ( ) ( ) ( ) Now, the FOC for input 1 can be written as:
⏟ ⏟( ⏟ ) ⏟ (
⏟ ) ⏟
9 } Note to self: write an appendix on “transfer pricing” based on this discussion.
27 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. The right hand side is the “total marginal cost of using input 1 to produce output”. The easiest way to understand this is
by imagining that the optimal amount of input 1 is greater than the required minimum amount of input 1 (as in the
following graph): Target
Output 0 Since the minimum input constraint doesn’t bind the FOC becomes: ⏟ It is an accounting identity that the price of hiring an additional unit of input 1 must equal its marginal cost of being used
in production. Next, consider...
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- Fall '14