ajaz_eco_204_2012_2013_chapter_14_PMP_Algebra

# Ifwhen is this says the company should produce the

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Unformatted text preview: ted in the same profits) see the graph below: Unconstrained solution Demand Case C ⏟ If/when is ? If/when is ? This says the company should produce the minimum output (which is assumed to strictly less than capacity). Therefore we know that ⏟ To see when Case C arises we need to see when . Substitute ⏟ and in the FOC: 6 ECO 204 Chapter 14: The Mathematics of the Profit Maximization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ⏟ ⏟ ⏟ (⏟) (⏟) Now: (⏟) (⏟) (⏟) (⏟) This says that if the marginal cost of the minimum quantity (here zero) is greater than or equal to the marginal revenue of the minimum quantity (here zero) then the firm should produce minimum quantity (here zero) and in which case (⏟) ( ⏟ ). This allows us to re-interpret the FOC: from the envelope theorem recall that so that the FOC can be written as: ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ Intuitively, the firm should produce the minimum output when it is greater than or equal to the “unconstrained optimal output” (see example below). If the firm is producing the minimum output then at the optimal solution “marginal revenue = total marginal cost” where the total marginal cost consists of the marginal cost of inputs used to produce an additional unit of output plus the reduced profits due to “excessive production”. is a negative number whenever the minimum required output is greater than the unconstrained solution – see graph below: 7 ECO 204 Chapter 14: The Mathematics of the Profit Maximization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Demand Unconstrained solution On the other hand, is zero whenever the minimum required output is equal to the unconstrained solution – see graph below: Dem...
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## This document was uploaded on 01/19/2014.

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