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CHAPTER 11
PROFIT MAXIMIZATION
Problems in this chapter consist mainly of applications of the P = MC rule for profit
maximization by a pricetaking firm and some examination of the firm’s derived demand
for inputs.
A few of the problems (13.213.5) ask students to derive marginal revenue
related ideas, but this concept is not really used in the monopoly context until Chapter 14.
Comments on Problems
11.1
A very simple application of the
P = MC
rule.
Results in a linear supply curve.
11.2
Easy problem that shows that a tax on profits will not affect the profit
maximization output choice unless it affects the relationship between marginal
revenue and marginal cost.
11.3
Practice with calculating the marginal revenue curve for a variety of demand
curves.
11.4
Uses the
MRMC
condition to illustrate third degree price discrimination.
Instructors might point out the general result here (which is discussed more fully
in Chapter 13) that, assuming marginal costs are the same in the two markets,
marginal revenues should also be equal and that implies price will be higher in the
market in which demand is less elastic.
11.5
An algebraic example of a profit function with one input.
The problem asks the
student to derive the supply and input demand functions from this profit function
using Shephard’s lemma.
11.6
A problem in the theory of supply under uncertainty.
This example shows that
setting expected price equal to marginal cost does indeed maximize expected
revenues, but that, for riskaverse firms, this may not maximize expected utility.
Part (d) asks students to calculate the value of better information.
11.7
A simple use of the profit function with fixed proportions technology.
11.8
This is a conceptual examination of the effect of changes in output price on input
demand.
Analytical problems
11.9
A CES profit function.
A very brief introduction to the
CES
profit function.
Deriving the function involves a lot of algebra, but seeing how the parameters of
the underlying production function enter this profit function is quite instructive.
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Chapter 11: Profit Maximization
11.10
Some envelope results.
This problem describes some additional mathematical
relationships that can be derived from the profit function.
11.11
More on derived demand with two inputs.
This problem shows how an
industry’s demand for an input can be computed and why that demand will
depend on the elasticity of demand for the good being produced.
This is a nice
problem therefore for tying together input and output markets.
11.12
Crossprice effects in input demand.
This is a continuation of Problem 11.11 to
consider crossprice effects.
The problem attempts to clarify how input cost
shares enter into input demand elasticities.
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This note was uploaded on 06/09/2010 for the course AP 4010 taught by Professor Anam,mahmudul during the Fall '10 term at York University.
 Fall '10
 Anam,Mahmudul

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