ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP -...

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
1
ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013)
Department of Economics (STG), ECO 204, Sayed Ajaz Hussain
_________________________________________________________________________________________________
P
RACTICE
P
ROBLEMS
W
ITH
S
OLUTIONS TO
:
C
HAPTER
12 : The Long Run Cost Minimization Problem
Updated: 3/7/2013
(12.1) Write down ● the Lagrangian objective function ● the first order conditions ● and (any) Kuhn-Tucker conditions
for the following profit maximization problem (do NOT solve the problem):
( ) ( )
What are the possible “signs” of the Lagrange multipliers (i.e. positive, zero, negative)?
(12.2) Write down ● the Lagrangian objective function ● the first order conditions ● and (any) Kuhn-Tucker conditions
for the following profit maximization problem (do NOT solve the problem):
( ) ( )
What are the possible “signs" of the Lagrange multipliers (i.e. positive, zero, negative)?
(12.3) Consider the following profit maximization problem:
( ) ( )
What can be said about the firm’s capacity if at the optimal solution ? Give a brief explanation and use graphs
to illustrate your answer. Do NOT solve the Profit Maximization Problem.
(12.4) Consider a company that has purchased (not leased) capital to produce a target output . Assume straight
line depreciation, zero salvage value, and constant opportunity cost rate of return. What are: ● the lowest and highest
values of owned capital ● the lowest and highest prices of owned capital? Give a brief explanation and show all
necessary calculations.
(12.5)-[PART A] A company with market power has constant returns. Setup, solve, and derive the conditions for the
various Kuhn-Tucker cases of the following general Profit Maximization Problem given that the company can charge a
uniform price or 1
st
degree price discrimination prices:
( ) ( ) ⏟

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
2
ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013)
You must express all first order conditions and the conditions for the Kuhn-Tucker various cases in terms of marginal
revenue and marginal cost only. State all assumptions and show all calculations.
(12.5)-[PART B] In the paper “Econometric Analysis of Collusive Behavior in a Soft - Drink Market” published in the
Journal of Economics and Management Strategy (Summer 1992), Gamsi, Laffont and Vuong (GLV) estimated the
following demand functions for Coke and Pepsi concentrate syrup based on quarterly data 1968 – 1986:
The subscript is for Coke and is for Pepsi where:
= quarterly quantity of syrup sold
= price of syrup (1986 dollars)
= square root of quarterly advertising expenses (1986 dollars)
{
= real income (1986 dollars)
The average values of the variables in the data set (except season) were:
●
̅̅̅̅
●
̅̅̅̅
●
̅̅̅
●
̅̅̅
●
̅̅̅̅
●
̅̅̅̅
●
̅
GLV also estimated Coke and Pepsi’s average variable cost to be (these are constant across seasons):
● ●