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this implies that is the optimal

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Unformatted text preview: we can use the envelope theorem to interpret the Lagrange multipliers and establish some general results about profit maximization. To apply the envelope theorem we note that after we solve the PMP, the Lagrange multipliers will tell us something (don’t they always?): notice that if you solved the PMP and substituted ( , , ) into the Lagrangian equation, you will get the “optimal Lagrangian equation” where some terms will be zero (why?): 39 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: That is, the optimal value of the Lagrangian is the optimal (maximal) value of profits. We can use the envelope theorem to calculate the change in due to a small change in a parameter (without re-solving the problem): ❶ Express the Lagrangian equation in terms of parameters. We don’t know the specific functional form of the demand and cost functions and so the “parameterized Lagrangian” is: () () [ [ ⏟] ❷ Differ...
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