Unformatted text preview: with the revenue maximizing output and price. In such cases, revenue maximization is tantamount to profit
maximization! Back to the RMP:
Since and is now a function of ⏟ let’s write revenues as ( )
() , () ( ) with which the RMP becomes:
⏟ , ⏟ The Lagrangian equation is: , [ () , [ ⏟] The FOC and KT conditions are:
, , , ⏟, [ [ ⏟] We know that there will be several possible solutions to the RMP. Before solving for and characterizing the conditions
for each case, let’s use the envelope theorem to interpret the Lagrange multipliers and establish some general results
about revenue maximization.
To apply the envelope theorem we note that after we solve the RMP, the Lagrange multipliers will tell us something
(don’t they always?): notice that if you solved the RMP and substituted ( , , ) into the Lagrangian equation, you will
get the “optimal Lagrangian equation” where some terms will be zero (why?): 22
ECO 204 Chapter 16: Analysis of Firms with Market Power (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. () [⏟ ⏟ ⏟] [ This implies:...
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This document was uploaded on 01/19/2014.
- Fall '14
- The Land