Consumer Choice:
Indifference Theory
Chapter 5
LIPSEY & CHRYSTAL
ECONOMICS 12e
Introduction
• In this chapter we look more closely at the
determinants of consumer demand. In
particular, we discuss the concept of utility
and use it to gain insights into how
consumers allocate their spending.
• We show how indifference curves can be
used to describe consumers’ tastes and then
introduce a budget line to describe the
consumption possibilities open to a consumer
who has a given income.
Learning Outcomes
• In particular, you will learn that:
• Consumers will maximize their overall satisfaction when
the marginal utility per pound spent is equal for all
products purchased.
• A theory of demand can be built by focusing on bundles
of goods between which the consumer is indifferent.
• Indifference curves show combinations of goods that give
the same level of satisfaction.
• A budget constraint shows what the consumer could buy
with a given income.
• A consumer optimizes by moving to the highest
indifference curve that is available with a given budget
constraint.
Learning Outcomes
• In particular, you will learn that (cont’d):
• The response to a price change can be decomposed into
an income and a substitution effect.
• For a good to have a negatively sloped demand curve it
is necessary (but not sufficient) that it be an inferior good.
• The basic assumption here is that consumers
are motivated to make themselves as well off
as they can, or as economists like to put it: to
maximize their satisfaction, or utility.
• All units of the same product are identical but
the satisfaction that a consumer gets from
each unit of a product in not the same.
• This suggests that the satisfaction that people
get from consuming a unit of any product
varies according to how many of this product
they have already.
• Economists and philosophers thinking about
consumer choice and satisfaction in the
nineteenth century developed the concept of
utility and were hence sometimes called
utilitarians.
• But the big breakthrough for economics came
in the 1870s with what is known as the
marginal revolution, which gave birth to
neoclassical economics.
Marginal and total utility
• The satisfaction a consumer receives from
consuming that product is called utility.
• Total utility refers to the total satisfaction
derived from all the units of that product
consumed.
• Marginal utility refers to the change in
satisfaction resulting from consuming one
unit more or one unit less of that product.
Diminishing marginal utility
• A basic assumption of utility theory, which is
sometimes called the law of diminishing
marginal utility, is as follows:
The marginal utility generated by additional
units of any product diminishes as an
individual consumes more of it, holding
constant the consumption of all other
products.
Maximizing utility
• We can now ask: what does diminishing
marginal utility imply for the way a consumer
who has a given income will allocate
spending in order to maximize total utility?
• How should a consumer allocate his or her
income in order to get the greatest possible
satisfaction, or total utility, from that
spending?
• If all products had the same price, the answer
would be easy.
• A consumer should simply allocate spending
so that the marginal utility of all products was
the same.
• If the marginal utility of all products were not
equal then total utility could be increased by a
different spending pattern.
For example!
• If one product had a higher marginal utility
than the others, then expenditure should be
reallocated so as to buy more of this product,
and less of all others that have lower
marginal utilities.
• By buying more, its marginal utility would fall.
This continues until the consumer's utility
equates to his/her expenditure and utility is
maximized.
• How does this work if products have different
prices?
• Again, the same principles apply but now the
best a consumer can do is to rearrange
spending until the last unit of satisfaction per
pound spent on each product is the same.
Note!
To maximize utility consumers allocate
spending between products so that equal
utility is derived from the last unit of
money spent on each.
Conditions for maximising utility
• The conditions for maximizing utility can be
stated more generally.
• Denote the marginal utility of the last unit of
product X by MUX and its price by pX.
• Let MUY and pY refer, respectively, to the
marginal utility of a second product, Y, and its
price.
• The marginal utility per pound spent on X will
be MUX/pX.
• The condition required for any consumer to
maximize utility is that the following
relationship should hold, for all pairs of
products:
Note!
• This is the fundamental equation of utility
theory.
• Each consumer demands each good up to
the point at which the marginal utility per
pound spent on it is the same as the marginal
utility of a pound spent on each other good.
• When this condition is met, the consumer
cannot shift a pound of spending from one
product to another and increase total utility.
Consumers choose quantities not
prices
• If we rearrange the terms in previous
equation we can gain additional insight into
consumer behaviour:
• The right-hand side of this equation states the
relative price of the two goods.
• It is determined by the market and is beyond
the control of individual consumers, who react
to these market prices but are powerless to
change them.
• The left-hand side of the equation states the
relative contribution of the two goods to add
to satisfaction if a little more or a little less of
either of them were consumed, a choice that
is available.
Note!
• If the two sides of eqn (5.2) are not equal, the
consumer can increase total satisfaction by
changing the spending pattern.
• Assume, for example, that the price of a unit
of X is twice the price of a unit of Y (pX/pY =
2), while the marginal utility of a unit of X is
three times that of a unit of Y (MUX/MUY = 3).
• Reducing purchases of Y by two units frees
enough purchasing power to buy a unit of X.
• Since one extra unit of X bought yields 1.5
times the satisfaction of two units of Y
forgone, the switch is worth making.
• What about a further switch of X for Y?
• As the consumer buys more X and less Y, the
marginal utility of X falls and the marginal
utility of Y rises.
• In this example the consumer will go on
rearranging purchases—reducing Y
consumption and increasing X
consumption—until the marginal utility of X is
only twice that of Y.
• At this point, total satisfaction cannot be
further increased by rearranging purchases
between the two products.
Note!
• It shows that an equilibrium position reached
when decision-takers have made the best
adjustment they can to the external forces
that constrain their choices.
• When they enter the market, all consumers
face the same set of market prices.
• When they are fully adjusted to these prices,
each one of them will have identical ratios of
their marginal utilities for each pair of goods.
• A rich consumer may consume more of each
product than a poor consumer and get more
total utility from them.
• However, the rich and the poor consumer
(and every other consumer who is
maximizing utility) will adjust their relative
purchases of each product so that the relative
marginal utilities are the same for all.
• Thus, if the price of X is twice the price of Y,
each consumer will purchase X and Y to the
point at which his or her marginal utility of X is
twice the marginal utility of Y.
• Consumers with different tastes will, however,
derive different marginal utilities from their
consumption of the various commodities.
• So they will consume differing relative
quantities of products
Note!
• But all will have declining marginal utilities for
each commodity and hence, when they have
maximized their utility, the ratios of their
marginal utilities will be the same for all of
them.
Total and Marginal Utility Schedules
Number of films
attended per month
Total utility
Marginal utility
0
0.00
1
15.00
15.00
2
25.00
10.00
3
31.00
6.00
4
35.00
4.00
5
37.50
2.50
6
39.00
1.5
7
40.25
1.25
8
41.30
1.05
9
42.20
0.90
10
43.00
0.80
Total and Marginal Utility Schedules
 As consumption increases, total utility rises but
marginal utility falls.
 The marginal utilities are the changes in utility when
consumption is altered by one unit.
 For example, the marginal utility of 10m, shown in
the entry in the last column, arises because with
attendances at the second film total utility increase
from 15 to 25 a difference of 10.
 The data in this table are plotted in the following
figure.
Total and Marginal Utility Curves
50
20
40
30
15
20
10
10
5
0
2
4
6
8
10
0
2
4
6
8
Quantity of films [attendance per month]
[i]. Increasing total utility
[ii]. Diminishing marginal utility
10
Consumer’s Surplus for an Individual
3.00
2.00
1.00
Market price
0.30
1
2
3
4
5
6
7
8
Glasses of milk consumed per week
9
10
Consumer’s Surplus for an Individual
 Consumer’s surplus is the sum of the extra valuations placed
on each unit above the market price paid for each.
 This figure is based on the data in the table.Ms.
 Green pays the red area for the 8 glasses of milk she
consumes per week when the market price is £0.30 a glass.
 The total value she places on these 8 glasses of milk is the
entire shaded area (red and green).
 Hence her consumer’s surplus is the green area.
Consumers’ Surplus for the Market
D
0
Quantity
Consumers’ Surplus for the Market
Market price
p0
D
0
Quantity
q0
Consumers’ Surplus for the Market
 The area under the demand curve shows the total valuation
that consumers place on all units consumed.
 For example, the total value that consumers place on q0 units
is the entire area shaded red and green under the demand
curve up to q0.
 At a market price of p0 the amount paid for q0 units is the red
area.
 Hence consumers surplus is the green area under the
demand curve and above p0.
MARGINAL UTILITY
The Utility Theory of Demand
• Marginal utility theory distinguishes between the total
utility that each consumer gets from the consumption of all
units of some product and the marginal utility each
consumer obtains from the consumption of one more unit
of the product.
– The basic assumption in utility theory is that the utility the
consumer derives from the consumption of successive units of a
product diminishes as the consumption of that product increases.
– Each consumer reaches a utility-maximizing equilibrium when the
utility he or she derives from the last £1 spent on each product is
equal.
MARGINAL UTILITY
• Another way of putting this is that the marginal utilities
derived from the last unit of each product consumed
will be proportional to their prices.
• Demand curves have negative slopes because when
the price of product X falls, each consumer restores
equilibrium by increasing his or her purchases of X.
• The increase must be enough to lower the marginal
utility of X until its ratio to the new lower price of X is
the same as it was before the price fell.
• This restores the equality of the ratio to what it is for
all other products.
MARGINAL UTILITY
Consumers’ Surplus
• Consumers’ surplus is the difference between [1] the
value consumers place on their total consumption of
some product and [2] the actual amount paid for it.
• The first value is measured by the maximum they
would pay for the amount consumed rather than go
without it completely.
• The second is measured by market price times
quantity.
MARGINAL UTILITY
• It is important to distinguish between total and marginal
values because choices concerning a bit more and a
bit less can not be predicted from knowledge of total
values.
• The paradox of value involves confusion between total
and marginal values.
• Elasticity of demand is related to the marginal value
that consumers place on having a bit more or a bit less
of some product; it bears no necessary relationship to
the total value that consumers place on all of the units
consumed of that product.
Bundles Conferring Equal Satisfaction
Bundle
Clothing
Food
A
30
5
B
18
10
C
13
15
D
10
20
E
8
25
F
7
30
Bundles Conferring Equal Satisfaction
35
a
30
25
g
20
b
15
c
d
10
h
10
f
T
5
5
e
15
20
Quantity of food
25
30
35
Bundles Conferring Equal Satisfaction
 None of the bundles in the table are obviously superior to any of
the others in the sense of having more of both commodities.
 Since each of the bundles shown in the table give the consumer
equal satisfaction, he is indifferent between them.
 The data in this table are plotted in the corresponding figure.
An Indifference Map
I5
I4
I3
I1
0
Quantity of food per week
I2
An Indifference Map
 A set of indifference curves is called an indifference map.
 The further the curve from the origin, the higher the level of
satisfaction it represents.
 Moving along the arrow is moving to ever-higher utility levels.
Shapes of Indifference Curves
Perfect Substitutes
A good that gives zero
utility
Perfect Complements
I2
I2
I2
I1
I1
I1
0
0
[i]. Packs of green pins
[ii]. Right hand gloves
0
[iii]. Meat
Shapes of Indifference Curves
A good that confers a negative utility
after some level of consumption
An absolute necessity
I1
a
All other goods
I2
A good that is
not consumed
I2
I2
I1 0
0
w
f0
[iv]. Water
[v]. Food
0
b
I1
[vi]. Good X
The Equilibrium of a Consumer
Quantity of clothing per week
35
30
25
20
15
10
5
5
10
15
20
Quantity of food per week
25
30
35
Quantity of clothing per week
The Equilibrium of a Consumer
30
a
b
25
c
20
E
15
10
I5
d
I4
5
e
I3
I2
I1
f
5
10
15
20
Quantity of food per week
25
30
35
The Equilibrium of a Consumer
 Paul has an income of £150 a week and faces prices of £5 a
unit for clothing and £6 a unit for food.
 A bundle of clothing and food indicated by point a is attainable.
 But by moving along the budget line to points such as b and c,
higher indifference curves can be reached.
 At E, where the indifference curve I4 is tangent to the budget
line, Paul cannot reach a higher curve by moving along the
budget line.
 If he did alter his consumption bundle by moving, for example,
from E to d, he would move to the lower indifference curve I3
and thus to a lower level of satisfaction.
An Income-consumption Line
Quantity of clothing per week
Income-consumption line
E3
E2
E1
I3
I2
I1
0
Quantity of food per week
An Income-consumption Line
 This line shows how a consumer’s purchases react to changes
in income with relative prices held constant.
 Increases in income shift the budget line out parallel to itself,
moving the equilibrium from E1 to E2 to E3.
 The blue income-consumption line joins all these points of
equilibrium.
The Price-consumption Line
Quantity of clothing per week
a
Price-consumption
line
E1
E2
E3
I3
I2
I1
b
c
Quantity of food per week
d
The Price-consumption Line
 This line shows how a consumer’s purchases react to a
change in one price, with money income and other prices held
constant.
 Decreases in the price of food (with money income and the
price of clothing constant) pivot the budget line from ab to ac
to ad.
 The equilibrium position moves from E1, to E2 to E3.
 The blue price-consumption line joins all such equilibrium
points.
Derivation of an Individual’s Demand Curve
E1
Price-consumption line
E2
E0
I0
0
60 120 220 267
I1
I2
400
800
[i] Petrol [litres per month]
x
0.75
y
0.50
z
0.25
0
Demand curve
60
120 220
Derivation of an Individual’s Demand Curve
 The points on a price-consumption line provide the
information needed to draw a demand curve.
 In part (i) Phillip has an income of £200 per month and
alternatively faces prices of £0.75, £0.50, and, £0.25 per litre
of petrol, choosing positions E0, E1, and E2.
 The information for the number of litres he demands at each
price is then plotted in part (ii) to yield his demand curve.
 The three points x, y, and z in (ii) correspond to the three
equilibrium positions E0, E1 and E2 in part (i).
The Income and Substitution Effects
Value of all other goods [£ per week]
a
a1
E0
E1
Substi
tution
effect
0
q0
I1
q1
b q
2
j1
Quantity of petrol [litres per week]