Utility and Choice

1
Chapter 2

• Utility and Choice

2
Theory of Choice

• The interaction of preferences and constraints
  that causes people to make the choices they do
• Choices are conditioned by preferences
• Preferences are constrained by scarcity of e.g.
  time, money, etc.

3
Utility

• The pleasure, satisfaction, or need fulfillment
  that people get from their economic activity.
• To identify all of the factors that affect
  utility would be virtually impossible
• Much economic analysis is based on the ceteris
  paribus assumption.

4
Ceteris Paribus Assumption

• In economic analysis, holding all other factors
  constant so that only the factor being studied is
  allowed to change
• Other factors are held constant so that we may
  choice is a simple setting that isolates the
  economic factors that affect behavior

5
Utility from Consuming Two Goods

• In this chapter we assume that a person receives
  utility from the consumption of two goods X and
  Y which we can show in functional notation by
• The other things that appear after the semicolon
  are assumed to be held constant.

6
Measuring Utility

• Two problems make it difficult to measure utility
  directly.
• Because the real-world is constantly in flux, the
  ceteris paribus assumption is difficult to
  impose.
• There is no unit of utility measurement.
• However, it is possible to do a fairly complete
  job of studying choices without having to measure
  utility.

7
Assumptions about Utility

• Basic Properties of Preferences
• Preferences are complete The assumption that an
  individual is able to state which of any two
  options is preferred.
• Preferences are transitive The property that if
  A is preferred to B, and B is preferred to C,
  then A must be preferred to C.

8
Application 2.1 Can Money Buy Health and
Happiness?

• Can income be a proxy for happiness?
• Income and health
• Top quarter income earners live 7 years longer on
  average
• Heart disease and cancer rates are lower for top
  income earners as well
• Higher incomes
• Allow better health care
• Reduce risk of health-damaging behavior e.g.
  smoking
• Reverse causality does better health increase
  income?
• Healthy individuals are more likely to get a
  well-paying job
• Healthy people save on medical expenses so they
  can invest to increase their incomes

9
Application 2.1 Income and Happiness

• People can rank themselves in terms of how happy
  they are on a numerical scale
• Richard Easterlin annual income of 75000
  averages 2.8 in happiness, 20000lower ranking,
  on a 4-point scale
• Changes on perceived happiness do not appear to
  depend on changes in income
• Aspirations rise together with income

10
More Is Better Defining an Economic Good

• An economic good is one that yields positive
  benefits to people. Thus, more of a good is, by
  definition, better.
• This is shown in Figure 2.1 where all points in
  the darkly shaded area are preferred to the
  amounts of X of good X and Y of good Y.
• Movement into the shaded area is unambiguously
  better since the person gets more of one good
  without the loss of another.

11
FIGURE 2.1 More of a Good Is Preferred to Less
Quantity of Y per week
?
Y
?
Quantity of X per week
X
0
12
Voluntary Trades and Indifference Curves

• The areas marked with question marks in Figure
  2.1 are difficult to compare to X, Y since they
  involve more of one good but less of another.
• Trading one good (such as money) for another good
  (such as a candy bar) is the essence of demand.

13
Indifference Curves

• Definition. A curve that shows all the
  combinations of goods or services that provide
  the same level of utility is called indifference
  curve.
• Definition. A collection of several indifference
  curves is called indifference curves map.

14
Labeling Indifference Curves
Hamburgers per week

• Since utility can not be measured, the labeling
  of indifference curves has no meaning except to
  indicate that utility increases from U1 to U2 and
  then to U3

A
6
H
5
B
G
4
U3

• In any indifference curve map, all we can assume
  is that utility increases as we move to higher
  indifference curves.

C
3
U2
D
2
U1
Soft drinks per week
2
3
4
6
0
5
15
Indifference Curve an Example
Hamburgers per week
The curve U1 includes all combinations of
hamburgers and soft drinks that yield the same
level of utility.
Point A, with 6 hamburgers and 2 soft drinks, has
the same utility as point B, 4 burgers and 3
drinks. Since all points on the curve yield the
same utility, the person has no reason to prefer
one point over another.
A
6
B
4
C
3
D
2
U1
Soft drinks per week
2
3
4
5
6
0
16
More is Better Principle

• Points such as E are above (to the northeast) of
  U1.
• Since E has more of both goods than point C, E is
  preferred to C (more is better)

Hamburgers per week
A
6

• Because of transitivity, E is preferred to any
  point on U1.
• Points above an indifference curve are preferred
  to points on the curve.

B
E
4
C
3
D
2
U1
Soft drinks per week
2
3
4
5
6
0
17
Less is Worse
Hamburgers per week

• Points such as F are below (to the southeast) of
  an indifference curve.
• Point C is preferred to point F since it contains
  more of both goods.

A
6

• Because of transitivity, all points on U1 are
  preferred to point F.
• Points on an indifference curve are preferred to
  points below it.

B
E
4
C
3
D
F
2
U1
Soft drinks per week
2
3
4
5
6
0
18
Slope of Indifference Curve

• The negative slope of an indifference curve shows
  that, if a person must give up some hamburgers,
  the only way he/she can be as happy as before is
  if they get more soft drinks.
• In giving up one hamburger to go from point B to
  point C means that the person receives one soft
  drink to compensate him or her.

Hamburgers per week
A
6
B
4

• The slope of U1 is approximately -2 between
  points A and B since hamburgers decline by two
  units to gain one unit of soft drinks.

C
3
D
2
U1
Soft drinks per week
2
3
4
5
6
0
19
Indifference Curves and the Marginal Rate of
Substitution

• Definition. The rate at which an individual is
  willing to reduce consumption of one good when he
  or she gets one more unit of another good is
  called the marginal rate of substitution.
• Note. The MRS is equal to the negative of the
  slope of the indifference curve at a particular
  point.

20
Diminishing Marginal Rate of Substitution

• On indifference curve U1 the person is willing to
  only give up one hamburger to gain one more soft
  drink between points B and C.
• Between points C and D, the consumer is only
  willing to give up ½ a hamburger to gain one more
  soft drink.

Hamburgers per week

• The MRS between points A and B on U1 is
  (approximately) 2.

6
B
4
C
3
D
2
U1
Soft drinks per week
2
3
4
6
0
21
Balanced Consumption

• The MRS diminishes along an indifference curve
  moving from left to right.
• This reflects the idea that consumers prefer a
  balance in consumption.

Hamburgers per week
A

• Point G reflects a bundle that is between
  points A and D.
• Since it is above U1 point G is preferred to any
  bundle on the indifference curve.

6
B
G
4
C
3
D
2
U1
Soft drinks per week
2
3
4
6
0
22
Product Positioning in Marketing

• Assume consumers have preferences for taste and
  crunchiness in breakfast cereal as represented by
  U1

Taste

• If points X and Y represent competitors,
  positioning, a cereal at point Z would increase
  utility to consumers.
• If competitors have similar costs, this should
  offer good market prospects for the new cereal.

X
Z
U1
Y
Crunchiness
23
Product Positioning in Marketing

• Marriott Hotels
• Small focus groups of consumers rate different
  hotel attributes
• Check-in convenience
• Room service
• Swimming pools
• Construct multi-dimensional indifference curves
• Position new products based on competitors
  location on these indifference maps
• Options Packages
• When to incorporate options, how to price them?
• 1980 Japanese automakers
• Air-conditioning
• Power windows
• Sun-roofs
• Approach was successful to give a luxury feel to
  middle-class models
• Dell and Compaq
• Larger hard drives
• Extra memory
• Powerful modems

24
Particular Preferences
Smoke
Houseflies
grinders
per week
per week
U
U
U
1
2
3
U
1
U
2
U
3
Food per week
0
10
Food per week
0
10
(a) A useless good
(b) An economic bad
Gallons
Right shoes
of Exxon
per week
per week
U
4
4
U
3
3
U
2
2
U
1
1
U
U
U
1
2
3
Gallons of Mobil
0
Left shoes
0
1
2
3
4
per week
per week
(c) Perfect substitute
(d) Perfect complements
25
Utility Maximization An Initial Survey

• Economists assume that when a person is faced
  with a choice among several possible options, he
  or she will choose the one that yields the
  highest utility
• The process of looking for this choice is called
  utility maximization.
• Economists assume that people know their own
  minds and make choices consistent with their
  preferences.
• People are constrained in their choices by the
  size of their incomes.
• Of the choices the individual can afford, the
  person will choose the one that yields the most
  utility.

26
A Simple Case

• When choosing to allocate income between two
  goods (e.g. hamburgers and soft drinks) the
  consumer will
• spend his or her entire income on the two goods
• Since both goods (and only these goods) provide
  more utility with increased consumption the
  consumer will spend his or her entire income on
  the goods.
• The only other alternative is to throw the income
  away which does not increase utility.
• choose a combination of goods for which the
  marginal rate of substitution between the two
  goods is equal to the ratio of their prices.

27
Equality of MRS with the Ratio or Prices

• Suppose the individual is currently consuming
  where MRS 1.
• Assume the price of hamburgers is 1 and the
  price of soft drinks is .50.
• This yields a price ratio (PS/PH) of (.50/1)
  ½.

28
Equality of MRS with the Ratio or Prices

• The person could give up one hamburger (freeing
  1) and purchase one soft drink using .50.
• Since his or her MRS 1, the person would be just
  as happy as before but would now have an
  additional .50 to spend which would enable him
  or her to increase utility.
• The only way utility can not be increased further
  is when MRS price ratio.

29
Budget Constraint

• Definition. An individuals budget constraint is
  the limit that income places on the combinations
  of goods and services that a person can buy.

30
Individuals Budget Constraint for Two Goods
Quantity of Y per week

• If all income is spent on X, Xmax can be
  purchased.
• If all income is spent on Y, Ymax can be
  purchased.

Ymax
Income
Not affordable

• The line joining Xmax and Ymax represents the
  various mixed bundles of good X and Y that can be
  purchased using all income.

Affordable
Quantity of X per week
Xmax
0
31
Downward Slope of the Budget Constraint
Quantity of Y per week

• The downward slope of the budget line reflects
  the fact that more X can be purchased only if
  less Y is purchased.
• If Y is expensive relative to X the line will be
  relatively flat.
• If Y is relatively inexpensive compared to X the
  line will be relatively steep.

Ymax
Quantity of X per week
Xmax
0
32
Budget Constraint Algebra

• Assume an individual has I dollars of income to
  spend on goods X and Y.
• Suppose the price of X is Px and the price of Y
  is PY.
• The total amount spent on X and Y are PxX and
  PYY respectively.

33
Budget Constraint Algebra

• Since all income must be spent on either X or Y
  we have
• Amount spent on X Amount spent on Y I
• or

34
Budget Constraint Algebra

• Solving for Y, so that it is expressed in the
  standard form for a linear equation, we have

• If all income is spent on Y, (i.e. if X0), the
  consumer can buy units.
• Similarly, if only X is bought, an income of I
  would afford units.

35
Slope of the Budget Constraint

• The slope of the budget constraints is equal to
  the opportunity cost of one good in terms of the
  other.

36
Graphic Demonstration of Utility Maximization
Hamburgers per week

• An individual can afford all bundles of X and Y
  that fall within the budget constraint
  represented by the shaded area
• Point A is affordable but not all of the
  consumers income would be spent.

B
Income

• Point B is affordable but is not on the highest
  indifference curve that can be reached by the
  consumer.

A
U1
0
Soft drinks per week
37
Graphic Demonstration of Utility Maximization
Hamburgers per week

• Point D is on a higher indifference curve than B,
  but is not affordable given the budget
  constraint.

B
D
Income
U3
A
U1
0
Soft drinks per week
38
FIGURE 2.7 Graphic Demonstration of Utility
Maximization
Hamburgers per week

• Point C, where the consumer chooses X, Y is the
  point that is affordable that lies on the highest
  indifference curve, so it represents utility
  maximization.

B
D
Income
U3
Y
C
U2
A
U1
0
Soft drinks per week
X
39
Utility Maximization

• At point C all income is spent.
• At point C indifference curve U2 is tangent to
  the budget line so that the
• or when utility is maximized, a consumer chooses
  a combination of X and Y such that

40
APPLICATION 2.3 Ticket Scalping

• Scalping is the practice of re-selling tickets at
  higher prices, which becomes possible due to
  rationing
• Rationing is the practice of keeping prices for
  highly desirable items at reasonable levels
• First-come-first-served basis
• Limiting the number of tickets each buyer can
  purchase

41
Rationing of Tickets Leads to Scalping
Other goods

• Since Super Bowl tickets are rationed at one per
  consumer, the individual maximizes utility at
  point B, but would be happier if he or she could
  be at point A purchasing 4 tickets.

• Buying two tickets to move to point C is
  preferable in terms of utility
• CD is the amount of other goods this consumer is
  willing to sacrifice for the ability to move to C.

B
C
Income
D
A
U2
U1
Super Bowl tickets
1
2
3
4
5
42
Scalping a Legal Perspective

• Governments view scalping negatively
• unfair profits (however, whats fair??)
• Regulate prices
• Outlaw scalping
• Economic point of view
• Scalping is a voluntary transaction between
  buyers with low willingness to pay for the ticket
  and those who are willing to pay a lot
• Scalpers are trade facilitators, and trade is
  beneficial

43
Differences in Preferences Result in Differing
Choices
Hamburgers per week
Hamburgers per week
Hamburgers per week
U2
U2
U1
U0
U1
U0
U2
U1
Income
Income
8
Income
U0
2
Soft drinks per week
Soft drinks per week
Soft drinks per week
0
4
20
16
(a) Hungry Joe
(b) Thirsty Teresa
(c) Extra-thirsty Ed
44
FIGURE 2.9 Utility-Maximizing Choices for
Special Types of Goods
Smoke
Houseflies
grinders
per week
per week
U
U
U
1
2
3
U
1
Income
U
2
Income
U
3
E
E
Food per week
0
10
Food per week
0
10
(a) A useless good
(b) An economic bad
Right shoes
Gallons
per week
of Exxon
per week
E
Income
U
3
E
U
2
2
U
1
Income
U
U
U
1
2
3
Gallons of Mobil
0
Left shoes
0
2
per week
per week
(c) Perfect substitute
(d) Perfect complements
45
APPLICATION 2.4 The Sad Tale of Willie and His
Uncle

• Hamer vs. Sidway, New York nephew Willie sued
  his uncle for not paying 5000 if he didnt
  smoke, drink, or gamble until he reached the age
  of 21
• The promise was documented well enough
• The problem was is the uncles promise a
  contract enforceable in court?

46
Composite Goods

• A composite good is obtained by combining
  expenditures on several different goods whose
  relative prices do not change into a single good
  for convenience in analysis.
• Food
• Housing
• This is a common graphing procedure that is used
  when many goods are involved but you want to
  study one good.
• How do we measure a composite good?
• Use dollar prices, but what if relative prices
  change?
• Physical composition of the composite good in
  terms of units what proportions to choose?

47
Willies Utility and His Uncles Promises
Other Goods

• Willie prefers point A if no promise is made
• Uncle offers point B no sin, but higher utility
  due to more consumption of other goods and
  services
• Uncle promised to give the money to Willie once
  he was capable of using it wisely, but he died
  before paying

Budget constraint
B
C

• Willie ends up at C with a lower utility compared
  to A

A

• Willie got paid in the end

U3
U2
U1

Sin
48
FIGURE 1 Kinked Budget Constraint Resulting from
a Quantity Discount

• When consumers receive quantity discounts or have
  to pay excessive use fees, the budget line is no
  longer straight.
• The consumer pays regular price for good X up to
  XD but receive a quantity discount beyond that as
  shown by the flatter budget line after consuming
  XD.

Quantity of Y per period

• All major airlines use quantity discounts
• Filling up empty seats
• Tying consumers to a particular airline

• Since the consumer is indifferent between points
  A and B, a slightly larger discount would cause
  the consumer to reach a higher indifference curve
  by using the discount.

A
B
U1
0
Quantity of X per period
X0