Chapter 3
Chapter Three Overview
Consumer Preferences and the Concept of Utility
The Utility Function
Marginal Utility and Diminishing Marginal Utility
Indifference Curves
The Marginal Rate of Substitution
Some Special Functional Forms
Why study consumer choice?
Study of how consumers with limited resources choose goods and
services
Helps derive the demand curve for any good or service
Businesses care about consumer demand curves
Government can use this to determine how to help and whom to help
buy certain goods and services
Model of Consumer Behavior
• Premises of the model:
1. Individual tastes or preferences determine the amount of pleasure people
derive from the goods and services they consume.
2. Consumers face constraints, or limits, on their choices.
3. Consumers maximize their well-being or pleasure from consumption
subject to the budget and other constraints they face.
Preferences
Consumer Preferences tell us how the consumer would rank (that is,
compare the desirability of) any two combinations or allotments of goods,
assuming these allotments were available to the consumer at no cost.
These allotments of goods are referred to as baskets or bundles. These
baskets are assumed to be available for consumption at a particular time,
place and under particular physical circumstances.
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Assumptions
1. Completeness
Preferences are complete if the consumer can rank any two baskets of goods
(A preferred to B (written A B) ; B preferred to A(written A B); or
indifferent between A and B(written A B).
2. Transitivity
Preferences are transitive if a consumer who prefers basket A to basket B,
and basket B to basket C also prefers basket A to basket C
3. Monotonicity
Preferences are monotonic if a basket with more of at least one good and no
less of any good is preferred to the original basket.
In this regard, a “good” is different than a “bad.”
Indifference Curves. An indifference curve represents all combinations of
market baskets that provide the consumer with the same level of
satisfaction.
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Five important properties of indifference curves:
There is an indifference curve through every possible bundle.
Indifference curves slope downward.
Indifference curves cannot cross.
Indifference curves cannot be thick.
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Bundles of goods on indifference curves further from the origin are
preferred to those on indifference curves closer to the origin.
The Shape of Indifference Curves
We know ICs are downward sloping (since more is better).
Another Assumption:
4. Convexity ICs are usually convex (bowed inward) reflecting that MRS
diminishes as the amount of X increases along an IC.
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Utility
• Utility refers to a set of numerical values that reflect the relative
rankings of various bundles of goods.
• A utility function is simply a way of assigning a preference ordering
consumption bundles. It does this by assigning numbers to consumption
bundles so that the bundles that are more preferred get a higher number than
those bundles that are less preferred.
EX: Given a specific utility function, U = q11/2q21/2
Say, bundle a contains 16 q1and 9 q2: then U(a) =
and bundle b contains 13 q1 and 13 q2 : then U(b) =
Thus, b a
• Utility is an ordinal measure rather than a cardinal one.
• Utility tells us the relative ranking of two things but not how
much more one rank is valued than another.
• We don’t really care that U(a) = 12 and U(b) = 13 in the
previous example; we care that b a.
• A utility function representing a preference ordering is not
unique. The only requirement for a particular assignment of
numbers to be classified as ‘a utility function representing a
preference ordering’ is that it must retain the rank order of
consumption bundles in terms of the preference of the
consumer. Thus, any other assignment of numbers that keeps
the ranking of bundles intact will also be a utility
representation.
For example: both the columns in the table below represent the same
preference ordering over bundles B1 B2 and B3
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If we have a utility function representing a preference ordering, we can
derive an infinite number of utility functions representing the same
preference ordering.
In general, we can form a new function V(X, Y) from U(X,Y)by feeding the
utility numbers into another function, f.
V(X, Y) = f(U(X,Y))
If f has the property that the larger the numbers that we feed, the larger the
numbers that come out, then V(X,Y) is also a utility function that represents
those preferences.
Marginal Utility
More is better implies
Marginal Utility and Marginal Rate of Substitution (MRS)
Curvature of Indifference Curves
• Different utility functions generate different indifference curves:
• The shape of the IC describes the willingness to substitute one good
for the other
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Perfect substitutes: Anna likes pop, but is indifferent whether it is coke or
pepsi
Perfect complements: consumer consumes the goods in fixed proportions
left shoe, right shoe or pie and ice cream . Anna doesn’t like ice cream by
itself or pie by itself, but loves apple pie a la mode (one slice of pie with one
scoop of ice cream)
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• Imperfect Substitutes
Between extreme examples of perfect substitutes and perfect complements
are standard-shaped, convex indifference curves (
• Cobb-Douglas utility function
U = Axy
Where A, , positive constants
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• Quasilinear utility function
