This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y zero?
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:
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 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.
We already know that case A and B cannot be the solution. Therfore, the solution must be either case C or case D.
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.
- Fall '14