ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

# Eco 204 s ajaz hussain do not distribute noting

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Unformatted text preview: ) ⏟ () () Simplifying: () () ⏟ () () 13 ECO 204 Chapter 12: Practice Problems &amp; Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. () () () ⏟ () Noting that () () () ( ) and ( ) we get: () Since the company has constant returns, follows: () ( ) is a constant. Therefore, we can rewrite the first order condition as () The Kuhn-Tucker conditions are: [ Notice there are 4 possible cases that must be checked: q=0 λ2 = 0 (Check when λ2 ≥ 0) (Check when q ≥ 0) q=c λ1 = 0 q=c λ1 = 0 (Check when λ1 ≥ 0 ) (Check when q ≤ c) (Check when λ1 ≥ 0 ) (Check when q ≤ c) Case A Case B Case C Case D Case A Need to check if This requires that and &gt; 0. Thus case A is impossible. Case B Need to check if Since the KT condition is automatically satisfied. Thus we need to check if Start with the FOC: 14 ECO 204 Chapter 12: Practice Problems &amp; Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. () () Substitute and : () () Thus, for we need: () () () Case B is the solution when with . Intuitively, the incremental revenue of further production is less than (or equal) to the incremental cost, so that the company loses money by producing another unit. () Case B when () Case C Need to check if Since the KT condition is automatically satisfied. Thus we need to check if () () Substitute and : () () Thus, for we need: () () 15 ECO 204 Chapter 12: Practice Problems &amp; Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Case C will be the solution if () : intuitively, if the marginal revenue at capacity exceeds marginal cost, then with decreasing or constant returns, marginal revenue exceeds marginal capacit...
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## This document was uploaded on 01/19/2014.

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