ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

# Recall that case b happens when case b when the demand

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: y zero? Answer We can use general solution to the PMP that we derived in question (5.1). “Optimal capacity” corresponds to the unconstrained maximum i.e. a solution whereby or when marginal profit due to expanding capacity slightly is zero. From question (5.1), only case B and case D corresponds to . Recall that case B happens when: Case B when () () The demand curve for Pepsi is: In spring/summer: In fall/winter: Therefore, marginal revenue for Pepsi is (using the short cut rule for linear demand curve): In spring/summer: 17 ECO 204 Chapter 12: Practice Problems & 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. ( ) ( ) () In fall/winter: () Note that . Therefore, clearly, both in spring/summer and fall/winter, () Thus case B is not a solution. Case D happens when Case D when () satisfying is () Therefore, optimal capacity can be solved from the equation: () In spring/summer: ( ( ( ) ) ) In fall/winter: ( Therefore, Pepsi’s optimal capacity is ) in spring/summer and in fall/winter. (b) Assume Pepsi’s actual capacity is 75% of the value you calculated in part (a). Use your answers to (PART A) to solve for Pepsi’s optimal uniform price and output in spring/summer and fall/winter. State all assumptions, show all calculations, and derive all figures up to two decimal places. Answer We already know that case A and B cannot be the solution. Therfore, the solution must be either case C or case D. 18 ECO 204 Chapter 12: Practice Problems & 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. For case C to be the solution, we need: () Case C when () In spring/summer, Pepsi’s capacity is: ( ) Marginal revenue is: ( () Note that ( ) )( ) . Therefore, () And as a result, case C is the solution. Therefore, Pepsi’s optimal output in spring/summer is: And, Pepsi’s optimal uniform price in spring/summer is: ( ) In fall/winter, Pepsi’s capacity is: ( ) Margin...
View Full Document

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

Ask a homework question - tutors are online