4. consumer choice indifference theory

Consumer Choice:
Indifference Theory
Chapter 5

Learning Outcomes
 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
 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 is not the same.
 This suggests that the satisfaction that
people get from consuming a unit of
any product varies according to how
many units 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:

Optimization
 Optimization Rule 1:
When only one good is consumed and is
available for free, consume till
MUx = 0
When only one good is consumed and is
available for a price: Consume till MUx = Pricex
Law of Equi Marginal Utility or Law of
Substitution : The law states that the consumer
will spend his income on different goods in such
a way that marginal utility of each good is
proportional to it’s price ie. when more than one
good is consumed and the goods’ prices are
different:
Consume till MUx/Px = MUy/Py = MUz/Pz

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 is
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
0
1
3
4
2
10
6
7
5
9
8
0.00
15.00
25.00
31.00
35.00
37.50
10.00
4.00
2.50
1.25
0.90
0.80
Marginal utility
39.00
40.25
41.30
42.20
43.00
15.00
6.00
1.05
1.5

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 Schedules

2 4 6 8 10
10
20
30
40
50
Total and Marginal Utility Curves
[i]. Increasing total utility [ii]. Diminishing marginal utility
Quantity of films [attendance per month]
15
10
5
20
0 2 4 6 8 10
0

Consumers Surplus
 A consumer surplus occurs when the consumer is willing to
pay more for a given product than the current market
price.
 Consumers always like to feel like they are getting a good
deal on the goods and services they buy and consumer
surplus is simply an economic measure of this satisfaction.
For example, assume a consumer goes out shopping for
a CD player and he or she is willing to spend $250. When
this individual finds that the player is on sale for
$150, economists would say that this person has a
consumer surplus of $100.

1 2 3 4
1.00
2.00
3.00
Consumer’s Surplus for an Individual
0.30
10
Market price
5
Glasses of milk consumed per week
8 9
7
6

 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.
Consumer’s Surplus for an Individual

Quantity
0
Consumers’ Surplus for the Market
D

Quantity q0
0
p0
D
Market price

 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.

 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.
MARGINAL UTILITY

Indifference Curve
 An indifference curve shows combinations of products that
yield the same satisfaction to the consumer.
 Assumptions:
 If combination A, contains at least as many units of each commodity as
combination B and more than one unit of at least one commodity, A is
preferred to B.
 Consumers can rank different combination of two goods in order of
preference
 Consumers behavior is consistent
 If consumer is indifferent between combination A and B and between B
and C, thus the consumer must be indifferent between A and C.
The amount of Y that the individual would be willing to give
up for X is called the marginal rate of substitution.

Bundle Clothing Food
Bundles Conferring Equal Satisfaction
A
B
C
D
E
F
30
18
13
10
8
7
5
10
15
20
25
30

5 10 15 20 25 30
10
20
30
35
Quantity of food
25
15
35
5
a
b
c
d
e
f
h
T
g

 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.

Indifference Curves
 Properties of Indifference curves:
- Slope downward: Whenever quantity of one good
increases, quantity of the other good decreases –
Assumption of non satiation
- Convex to the origin and are based on the principle
of diminishing marginal rate of substitution. Absolute
value of MRS has to decrease as the consumer moves
away from the origin on the X - axis
- Non intersecting : If two indifference curves
crossed, it would mean that one of them refers to a
higher level of satisfaction than the other at one side
of the intersection and to a lower level of satisfaction
at the other side of the intersection.

I1
Quantity of food per week
An Indifference Map
0
I2
I3
I4
I5

 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.
An Indifference Map

I1
I2
I2
I2
I1
I1
[i]. Packs of green pins [iii]. Meat
[ii]. Right hand gloves
0 0
0
Perfect Substitutes Perfect Complements A good that gives zero
utility
Shapes of Indifference Curves

I2
I2
I1
I1
[v]. Food
[iv]. Water
All
other
goods
w f0 0
0
0
A good that confers a negative utility
after some level of consumption
An absolute necessity
Shapes of Indifference Curves
The marginal rate
of substitution for
an absolute
necessity
approaches infinity
as consumption
falls towards the
amount that is
absolutely
necessary.

Opportunity Set
 Defined by Budget Constraint.
6x + 3y = 60
Given Px = 6 and Py = 3
•If the consumer spends all his income only on X, he can
purchase 10 units of X, while if he spends all his income on
Y, he can purchase 20 units of Y. Combination of income
spent on X and Y gives the Budget Line
•A change in income, with no change in prices, will lead to a
parallel shift in the budget line.
•Slope of the budget line changes only when the relative
prices change other things remaining the same
-Px/Py is the Slope

5
10
15
25
20
30
35
The Equilibrium of a Consumer
Quantity
of
clothing
per
week
5 10 15 20 25 30 35
Budget line

5
10
15
25
20
30
I5
I4
I3
I2
I1
a b
c
E
d
e
Quantity
of
clothing
per
week
f
5 10 15 20 25 30 35

 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.

I2
I3
I1
E2
An Income-consumption Line
Quantity
of
clothing
per
week
E3
E1
Income-consumption line
0

 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.
An Income-consumption Line

I2
I3
I1
E2
The Price-consumption Line
Quantity
of
clothing
per
week
E3
E1
Price-consumption
line
b c d
a

 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.
The Price-consumption Line

Price-consumption line
[i] Petrol [litres per month]
220
120
60 267 400
0
I0
I1
I2
E2
E0
800
E1
60 120 220
0
0.75
0.50
0.25
x
y
z
Demand curve
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).
Derivation of an Individual’s Demand Curve

E0
E1
I1
j1
b q2
q1
q0
a
a1
0
Substi
tution
effect
Quantity of Good X
Good
Y
The Income and Substitution Effects
Income
effect
A fall in the price of
Good X leads to increase
in consumption of Good
X due to the substitution
effect and the income
effect

 The substitution effect is defined by sliding the
budget line around a fixed indifference curve; the
income effect is defined by a parallel shift of the
budget line
 Substitution effect is usually much larger than the
income effect in the real world.
 The reason being that consumers usually spends
only a small proportion of his income on any one
commodity.
 Thus even a large change in the price does not
result in a large income effect.
 On the other hand, the substitution effect can be
very large if the commodity has many good
substitutes.
Income effect and Substitution Effect

The Income and Substitution Effects

4. consumer choice indifference theory

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