ajaz_eco_204_2012_2013_chapter_16_Market_Power

# Ceteris paribus these are to find the change in and

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 01/19/2014.

Ask a homework question - tutors are online