ajaz_eco_204_2012_2013_chapter_16_Market_Power

Ceteris paribus these are to find the change in and

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Unformatted text preview: () That is, the optimal value of the Lagrangian is the optimal (maximal) value of revenues. We can use the envelope theorem to calculate the change in due to a small change in a parameter (without resolving the problem): ❶ Express the Lagrangian equation in terms of parameters. We don’t know the specific functional form of the demand function and so the “parameterized Lagrangian” is: () [ ⏟] [ ❷ Differentiate the Lagrangian equation with respect to the parameter. The only parameters so far are and and to find the change in due to a small change in a parameter (ceteris paribus) we differentiate with respect to the parameter. Ceteris paribus these are: ❸ To find the change in -- and therefore -- due to a small change in a parameter (ceteris paribus) we evaluate the derivative in step ❷ at the optimal solution (which we’ll know after we have solved the RMP): From KT conditions we know that which tells us that a small expansion in the firm’s capacity will never lower revenues. From KT conditions we know that which tells us that a small incre...
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This document was uploaded on 01/19/2014.

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