MicroEconomics 5e by besanko braeutigam chapter 03

Chapter 3

Copyright (c)2014 John Wiley & Sons, Inc.

Consumer Preferences and the Concept of Utility

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Chapter Three Overview

1. Motivation
1. Motivation
2. Consumer Preferences and the Concept of Utility
2. Consumer Preferences and the Concept of Utility
3. The Utility Function
3. The Utility Function

••

Marginal Utility and Diminishing Marginal Utility
Marginal Utility and Diminishing Marginal Utility

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4. Indifference Curves
4. Indifference Curves
5. The Marginal Rate of Substitution
5. The Marginal Rate of Substitution

6.6. Some

Special Functional Forms
Some Special Functional Forms

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Motivation
• 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
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goods and services

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Consumer 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.

available for consumption at a particular time, place and under particular physical circumstances.

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These allotments of goods are referred to as baskets or bundles. These baskets are assumed to be


Consumer Preferences
Assumptions

Complete and Transitive
Preferences are complete if the consumer can rank any two baskets of goods (A preferred to

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

A  B; B  C = > A  C
A  B; B  C = > A  C

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B; B preferred to A; or indifferent between A and B)


Consumer Preferences
Assumptions

Monotonic / Free Disposal

Preferences are monotonic if a basket with more of at
least one good and no less of any good is preferred to the
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original basket.

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Types of Ranking

Example:

Students take an exam. After the exam, the students are ranked according to their performance. An ordinal
ranking lists the students in order of their performance (i.e., Harry did best, Joe did second best, Betty did
third best, and so on). A cardinal ranking gives the mark of the exam, based on an absolute marking standard
(i.e., Harry got 80, Joe got 75, Betty got 74 and so on). Alternatively, if the exam were graded on a curve, the
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marks would be an ordinal ranking.

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The Utility Function

The three assumptions about preferences allow us to represent preferences with a utility function.

Utility function

– a function that measures the level of satisfaction a consumer receives from any basket of goods and
services.

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– assigns a number to each basket so that more preferred baskets get a higher number than less preferred
baskets.

– U = u(y)

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The Utility Function
Implications:

•

An ordinal concept: the precise magnitude of the number that the function assigns has no significance.

•

Utility not comparable across individuals.

•

Any transformation of a utility function that preserves the original ranking of bundles is an equally good

y

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representation of preferences. e.g. U = vs. U = + 2 represent the same preferences.

y

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Marginal Utility
Marginal
MarginalUtility
Utilityofofaagood
goodyy

•• additional
additionalutility
utilitythat
thatthe
theconsumer
consumergets
getsfrom
fromconsuming
consumingaalittle
littlemore
moreofofyy
•• i.e.i.e.the
therate
rateatatwhich
whichtotal
totalutility
utilitychanges
changesasasthe
thelevel

levelofofconsumption
consumptionofofgood
goodyyrises
rises
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•• MU
MUyy==∆U/∆y
∆U/∆y
•• slope
slopeofofthe
theutility
utilityfunction
functionwith
withrespect
respecttotoyy

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Diminishing Marginal Utility

The
Theprinciple
principleof
ofdiminishing
diminishingmarginal
marginalutility

utilitystates
statesthat
thatthe
themarginal
marginalutility
utilityfalls
fallsas
as

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the
theconsumer
consumerconsumes
consumesmore
moreof
ofaagood.
good.

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Diminishing Marginal

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Utility

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Marginal Utility

The
The marginal
marginal utility
utility ofof aa good,
good, x,x, isis the
the additional
additional utility
utility that
that the
the consumer
consumer gets
gets from
from
consuming
consumingaalittle
littlemore
moreofofxxwhen
whenthe
theconsumption
consumptionofofall
allthe
theother
othergoods

goodsininthe
theconsumer’s
consumer’s
basket
basketremain
remainconstant.
constant.

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•• U(x,
U(x,y)y)==xx++yy
•• ∆U/∆x
∆U/∆x(y(yheld
heldconstant)
constant)==MU
MUxx
•• ∆U/∆y
∆U/∆y(x(xheld
heldconstant)
constant)==MU
MUyy

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Marginal Utility
Example

ExampleofofU(H)
U(H)and
andMU
MUHH
22
U(H)
=
10H
–
H
U(H) = 10H – H

MUH

2

4

16

6

4

16

24

2

6

36

24

-2

8

64

16

-6

10

100

0

-10

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H

MU
MUHH==10
10––2H
2H
2
H
U(H)

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Marginal Utility

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2
U(H) = 10H – H

MU = 10 – 2H
H

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Marginal Utility
Example
Exampleof
ofU(H)

U(H)and
andMU
MUHH

•

The point at which he should stop consuming hotdogs is the point at which
MUH = 0
This gives H = 5.
That is the point where Total Utility is flat.
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•
•
•

You can see that the utility is diminishing.

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Marginal Utility – multiple goods
22
UU==xy
xy
22
MU
=

y
MUxx = y
MU
MUyy==2xy
2xy
More is better? More y more and more x indicates more U so yes it is monotonic
Diminishing marginal utility?

•

MU of x is not dependent of x. So the marginal utility of x (movies) does not decrease as the
number of movies increases.

•

MU of y increases with increase in number of operas (y) so neither exhibits diminishing returns.

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•
•


Indifference Curves
An Indifference Curve or Indifference Set: is the set of all baskets for which the consumer is
indifferent

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An Indifference Map : Illustrates a set of indifference curves for a consumer

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Indifference Curves

Key Properties
1)1) Monotonicity
Monotonicity=>
=>indifference
indifferencecurves
curveshave
havenegative
negativeslope
slope––and
andindifference
indifferencecurves
curvesare
arenot
not
“thick”
“thick”

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2)2) Transitivity
Transitivity=>
=>indifference
indifferencecurves
curvesdo
donot
notcross
cross

3)3)Completeness
Completeness=>
=>each
eachbasket
basketlies
lieson
ononly
onlyone
oneindifference
indifferencecurve
curve

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Indifference Curves

Copyright (c)2014 John Wiley & Sons, Inc.

Monotonicity

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Indifference Curves
Cannot Cross

Suppose that B preferred to A.
Suppose that B preferred to A.
but..by definition of IC,
but..by definition of IC,
B indifferent to C
B indifferent to C
A indifferent to C => B indifferent
A indifferent to C => B indifferent

And thus a contradiction.
And thus a contradiction.

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to C by transitivity.

to C by transitivity.


Indifference Curves
Example

U = xy

2

Check that underlying preferences are complete, transitive, and monotonic.

MU y = 2 xy

for U = 144
x

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y

xy^2

8

4.24

143.8

4

6

144

3

6.93

144.07

1

12

144

22

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MU x = y

2


Indifference Curves

Example:
Example:Utility

Utilityand
andthe
thesingle
single

Indifference Curve for U = xy2

indifference
indifferencecurve.
curve.

14
12
U = 144

10
8
6
4

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y

2
0

0

1

2

3

4

5

6

7

8

9

X

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Marginal Rate of Substitution
The marginal rate of substitution: is the maximum rate at which the consumer would be willing to substitute a little more of good x
for a little less of good y;

It is the increase in good x that the consumer would require in exchange for a small decrease in good y in order to leave the
consumer just indifferent between consuming the old basket or the new basket;

It is the rate of exchange between goods x and y that does not affect the consumer’s welfare;

MRS

x,y

=

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It is the negative of the slope of the indifference curve:

-∆y/∆x
(for a constant level of preference)

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Marginal Rate of Substitution

The Diminishing Marginal
Rate of Substitution

Copyright (c)2014 John Wiley & Sons, Inc.

If the more of good x you have, the more you are willing to
If the more of good x you have, the more you are willing to

give up to get a little of good y or the indifference curves get
give up to get a little of good y or the indifference curves get
flatter as we move out along the horizontal axis and steeper
flatter as we move out along the horizontal axis and steeper
as we move up along the vertical axis
as we move up along the vertical axis

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