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CHAPTER 5
INCOME AND SUBSTITUTION EFFECTS
Problems in this chapter focus on comparative statics analyses of income and ownprice
changes.
Many of the problems are fairly easy so that students can approach the ideas
involved in shifting budget constraints in simplified settings.
Theoretical material is
confined mainly to the Analytical Problems which stress various elasticity measures
and introduce the Almost Ideal Demand System.
Comments on Problems
5.1
This problem shows the convenient result that budget shares can be computed
from expenditure functions through logarithmic differentiation.
5.2
This problem asks students to pursue the analysis of Example 5.1 to obtain
compensated demand functions.
The analysis essentially duplicates Examples
5.3 and 5.4.
5.3
This is a problem with no substitution effects.
It shows how price elasticities
are determined only by income effects which in turn depend on income shares.
5.4
An exploration of the notion of homothetic functions.
This problem shows that
Giffen's Paradox cannot occur with homothetic functions.
5.5
This is a problem in revealed preference theory.
The bundles here violate the
strong axiom.
5.6
A fixedproportions example.
Illustrates how the goods used in fixed
proportions (peanut butter and jelly) can be treated as a single good looking at
utility maximizing choices.
5.7
Another utility maximization example.
In this case, utility is not separable and
crossprice effects are important.
5.8
An example of perfect substitutes. Solving this is easy with intuition, but
students should not try to use calculus because of the “knifeedge” nature of
demand with perfect substitutes.
Analytical Problems
5.9
Price indifference curves.
This problem introduces a graphical concept that is
sometimes used to illustrate theoretical points.
5.10
Aggregation of elasticities for many goods.
This problem shows how the
aggregation relationships introduced in Chapter 5 for two goods can be
generalized to any number of goods.
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Chapter 5: Income and Substitution Effects
5.11
The almost ideal demand system.
This problem introduces a parametrization
of the expenditure function that is widely used in empirical studies of demand.
The connections between this problem and Problem 5.14 are quite important in
the interpretation of many empirical studies.
5.12
More on elasticities.
Shows how the elasticity of substitution affects the sizes
of price elasticities.
5.13
Quasilinear utility (revisited).
This extends Problem 3.12 to consider the
special form of the Slutsky Equation for the Quasilinear function.
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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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