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CHAPTER 3
PREFERENCES AND UTILITY
These problems provide some practice in examining utility functions by looking at
indifference curve maps and at a few functional forms.
The primary focus is on
illustrating the notion of quasiconcavity (a diminishing MRS) in various contexts.
The
concepts of the budget constraint and utility maximization are not used until the next
chapter.
Comments on Problems
3.1
This problem offers some practice in deriving utility functions from indifference
curve specifications.
3.2
This problem focuses on whether some simple utility functions exhibit convex
indifference curves.
3.3
This problem shows how utility functions can be inferred from
MRS
segments. It
is a very simple example of “integrability”.
3.4
This problem shows that diminishing marginal utility is not required to obtain a
diminishing
MRS
. All of the functions are monotonic transformations of one
another, so this problem illustrates that diminishing
MRS
is preserved by
monotonic transformations, but diminishing marginal utility is not.
3.5
In this problem students are asked to provide a formal, utilitybased explanation
for a variety of advertising slogans.
The purpose is to get students to think
mathematically about everyday expressions.
3.6
Introduces the formal definition of quasiconcavity (from Chapter 2) to be
applied to the functions studied graphically in Problem 3.8.
3.7
This problem is an exploration of the fixedproportions utility function.
The
problem also shows how the goods in such problems can be treated as a
composite commodity.
3.8
This problem requires students to graph indifference curves for a variety of
functions, some of which are not quasiconcave.
Analytical Problems
3.9
Independent marginal utilities.
Shows how analysis can be simplified if the
cross partials of the utility function are zero.
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Chapter 3: Preferences and Utility
3.10
Utility functions and preferences.
The problem asks students to think about
how a common phenomenon might be reflected in a mathematical functional
form.
3.11
CobbDouglas utility.
Provides some exercises with the CobbDouglas
function including how to integrate subsistence levels of consumption into the
functional form.
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 Fall '10
 Anam,Mahmudul

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