Unit 7

A Level Economics
The price system and the micro economy
Background to Demand

Marginal Utility Theory

INDIFFERENCE CURVE ANALYSIS
 INDIFFERENCE CURVE ANALYSIS

The major weakness of marginal utility theory is the fact that utility cannot be
measured.
An alternative approach is INDIFFERENCE CURVE ANALYSIS which involves the ranking
of combinations of goods.
The aim of Indifference Analysis is to analyse [without having to measure utility] how a
rational person chooses between two goods.
Indifference Analysis can be used to show the effect of:
1. A change in the price of one or both goods,
2. A change in a person’s income, on purchases of two goods.
 Indifference curve analysis( ordinal approach)
• Indifference curve is the locus of different combinations of two
goods X and Y, from which the consumer yields equal
satisfaction.
• The consumer will be indifferent among all the combinations of
goods which is represented by the curve.
• so the curve is also called iso-utility curve or equal satisfaction
curve.
• Marginal rate of substitution:
• The rate at which a consumer is willing to substitute one good
for another and stay at the same level of satisfaction.
 Marginal rate of substitution
combination Units of X Units of Y MRSxy/ MRS=dY/dX –
this is X for Y

A 1 20 -

B 2 15 5:1

C 3 11 4:1

D 4 8 3:1

E 5 6 2:1

F 6 5 1:1
• The above table shows the various combinations of two
commodities which are equally acceptable to the consumer or
which give equal level of satisfaction.
• Indifference schedule is a list of combinations of two
commodities, the list is being arranged in such a way that a
consumer is indifferent to all the combinations.
• It is shown in the diagram below:
 Assumptions of ICA
• Non-satiety- the consumer is not yet fully satisfied. It means more of the
goods is preferable to less of the goods.
Suppose a consumer is provided with two
bundles A and B. In bundle A 2X and 2Y is
available and in bundle B 3X and 2Y is
available.
Then as per the non-satiety assumption the consumer will prefer bundle B to
bundle A.
• Consistency- if the consumer is faced with the same situation in future he
will always prefer B to A. Thus his preferences are stable and consistent.
 Assumptions of ICA
• Transitivity- if in any period A is greater than B and B is greater
than C then A will be always greater than C. Here A, B and C
represent bundles of goods containing various units of goods X
and Y.
• Diminishing Marginal Rate of Substitution of goods X and Y- it
means that as the consumer substitutes one good for the
another, the rate of substitution diminishes.
 Assumptions of ICA
The Marginal Rate of Substitution diminishes because of the
variations of marginal utilities of two goods.
It is a common observation that if we have more quantity of
one good and less quantity of the other, then the marginal
utility of the last unit of the good which is larger in quantity is
very low in comparison the marginal utility of the last unit of
the good which is lower in quantity.
The following table illustrates it:
 Marginal Rate of Substitution
Combinations Good X Good Y MRS=dY/dX – this is X for Y

A 1 15 -

B 2 10 5/1 = 5

C 3 6 4/1 = 4

D 4 3 3/1 = 3

E 5 1 2/1 = 2
 MRS of X for Y or Y for X
• MRS of Good X for Good Y is: dY/dX.
• MRS of Good Y for Good X is: dX/dY.
• MRS diminishes because goods are imperfect substitutes of
each other and because of variations in their marginal utilities
when different units of goods are consumed.
• In case of perfect substitutes MRS remains constant.
 Constructing an Indifference Curve

Pears Oranges Point

The consumer is indifferent among the 30 6 a
combinations of goods represented by it 24 7 b
because it would not matter to his 20 8 c
14 10 d
which combination is given. They are 10 13 e
equally preferable to her. 8 15 f
All these combinations can be shown in 6 20 g

a table [an indifference set / schedule].

Combinations of pears and oranges that Shivam prefers equally
as
10 pears and 13 oranges or 6 pears and 20 oranges or any
other.
 30 a
28
26 Pears Oranges Point
24 30 6 a
24 7 b
22
20 8 c
20 14 10 d
18 10 13 e
Pears

8 15 f
16
6 20 g
14
12
10
8
6
4
2
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Oranges
 Properties of IC curve
• Property I. Indifference curves slope downward to the right:
This property implies that an indifference curve has a negative
slope.

• Downward sloping IC means that when the amount of one

good in the combination is increased, the amount of the other
good is reduced. This must be so if the level of satisfaction is to
remain the same on an indifference curve.
 Property II: Indifference curves are convex to the origin:

• Another important property of indifference curves is that they

are usually convex to the origin. This property of indifference
curves follows the marginal rate of substitution of X for Y
(MRSxy) diminishes as more and more of X is substituted for Y.
• Only a convex indifference curve can mean a diminishing
marginal rate of substitution. If indifference curve was concave
to the origin it would imply that the marginal rate of substitution
of X for y increased as more and more of X was substituted, for Y.
 Property III: They must not touch either of the axis.
• They must not touch either of the axis and are not parallel to
each other. They are not parallel to each other because the
MRS of good X for good Y varies on each indifference curve.
An indifference curve cannot touch
either axis. If it touches X-axis, the
consumer will be having only quantity
of good X and none of Y.
Similarly, if an in difference curve
touches the У-axis , consumer will
have only of Y good and no amount of
X.
Such curves are in contradiction to the
assumption that the consumer buys
two goods in combinations.
 Perfect complements IC is L shaped.
• In case of perfect complements IC is L shaped.
• Let us consider this example-Left shoe’ and ‘Right shoe’ can be
considered as perfect complimentary goods. This is because
the utility of Left shoe would be zero without a Right shoe and
vice versa.

• So, we have the following combinations of Left shoe and Right

shoe and every combination would give us the same utility.
 Perfectly substitute IC
• In case of perfect substitutes IC is linear :
• If two goods X and Y are perfect substitutes, the indifference
curve is a straight line with negative slope, as shown in Figure
41 because the MRSXY is constant. The value of this slope is
throughout minus 1, and MRSXY = 1.
In the figure, ab of Y = bc of X, and cd of Y = de of
X. In this case, the consumer does not distinguish
between these two goods and regards them as
the same commodity, such as two brands of tea.
 Property IV: A higher indifference curve represents a higher level of satisfaction than a
lower indifference curve:

The another property of indifference curve

is that a higher indifference curve will represent
a higher level of satisfaction than a lower indifference curve.
In other words, the combinations which
lie on a higher indifference curve
will be preferred to the combinations
which lie on a lower indifference curve.
 Property V: Indifference curves cannot intersect each other:

• Next important property of indifference curves is that they

cannot intersect each other. It is because higher IC provides
higher level of satisfaction to the consumer.
A consumer cannot be indifferent between F and
both B and S
 Classroom task
• Define a budget line. When can it shift to the
right?
 INDIFFERENCE ANALYSIS

Relationship between MRS and MU

Looking at the following figure, consumption at point [a] yields the same satisfaction
as consumption at point [b].
The utility gained by consuming one more X must be equal to the utility lost by
consuming six less Y . The MU of one unit of X must be six times as great as that of Y.
Therefore MUY/MUx = 6 which is the same as the MRS when X is measured on the
horizontal axis and Y on the vertical axis.
So MRS =- MUx/MUy = slope of indifference curve

Therefore, MRS = slope of indifference curve

https://www.youtube.com/watch?v=0KFWqw4sNlM
 Deriving the marginal rate of substitution (MRS)
30 a
DY = 6 MRS = 6
24 b
Units of good Y DX = 1 MRS = Y/X
20

MRS = 1
c
10
DY = 1 d
9
DX = 1

0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
67 13 14
Units of good X
 An Indifference Map

An Indifference Map:
As discussed in the earlier sections indifference curves show combinations
of the two goods which yield higher utility or satisfaction.
It is possible to draw an infinite number of indifference curves in a two
dimensional diagram.
A series of curves or a finite set of indifference curves drawn on a two
dimensional diagram creates an INDIFFERENCE MAP.
The indifference map shows a scale of preferences of the consumer.
 The Indifference Map
The actual amount of utility corresponding to each curve is not
specified, but Indifference curves further out to the right
combinations of two goods that yield a higher utility.
Thus the consumer would prefer or be willing to reach the
highest possible indifference curve.
So the indifference map shows the WILLINGNESS of the
consumer.
Whether the consumer reaches the IC as preferred by them will
depend on the ABILITY of them.
The following diagram shows the Indifference Map.
 An indifference map

The further out the curve, the

Units of good Y higher the level of utility

30

An indifference curve shows all

20
combinations of X and Y that
give a particular level of utility.

10
I5
I4
I3
I2
0
I1
0 10 20

Units of good X
 BUDGET LINE

The budget line shows what combination of two goods a person is able to
buy. In other words it shows various combinations of two goods a consumer
can buy, given the income and the prices of the two goods.
For a given income the person can choose a combination of goods on the line
but not beyond it. The assumption made here is that the consumer has to
spend full amount in buying the goods.
The total expenditure function may be represented as:
TE = Px . Qx + Py . Qy.
From this function the equation of a straight line may be derived as:
Qy = TE/Py – Px/Py . Qx
Qy= -Px/Py .Qx + TE/Py Y=(MX+C)
Thus the slope of the budget line is given by: Slope = - Px/Py
 30 a
A budget line
Units of Units of Point on
good X good Y budget line

0 30 a
b
Units of good Y

20 5 20 b
10 10 c
15 0 d

c Assumptions
10

PX = £2
PY = £1
Budget = £30

d
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Units of good X
 Budget Line
As shown in the previous slide, the budget line remains
the same as long as prices of two goods and income of
the consumer do not change.
But if income or prices of two goods changed then the
budget line will change.
 Effect of an increase
40 Assumptions

PX = £2
PY = £1
Budget = £40
Units of good Y
30

n
20

16
m

10 Budget
= £40
Budget
0 = £30
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

7
Units of good X
 Budget Line

•Change in Price
The relative prices of the two goods are given by the slope of the budget line. The
slope of the budget line = -PX/PY
If the price of one good falls or rises then the slope of the line changes.
A decrease in price of good x keeping the other factors constant leads to a rotation of
the budget line outwards to the right whereas an increase leads to an inward
rotation.
The effect of a decrease in price of good x is shown in the next slide.
 Equilibrium Position
The willingness and ability of the consumer is separately
depicted in the form of the Indifference Map and the Budget
Line in the earlier sections. We need to put them together.
THE OPTIMUM CONSUMPTION POINT

Bringing together the indifference map and budget line we are

able to establish how a rational consumer will allocate his/her
budget.
The consumer would like to consume on the highest IC, so the
optimum point is where the budget line touches [is tangential
to] the highest possible IC.
Where the IC is tangential to the budget line they will have the
same slope……..
 Optimum Point

THE OPTIMUM CONSUMPTION POINT:

Where the IC is tangential to the budget line they will have the same
slope……..
The slope of the budget line = -PX/PY
The slope of the IC = MRS = -MUX/MUY
Therefore, at the optimum consumption point:
-PX/PY = -MUX/MUY
It is the optimum consumption point because no amount of reallocation of
the budget into the purchases of two goods would lead to a higher level of
utility or satisfaction from the current position.
The following slides show the process through which the optimum point is
derived.
 Finding the optimum consumption

Units of good Y

I5
I4
I3
I2
I1
O
Units of good X
 Finding the optimum consumption

Units of good Y

Budget line

I5
I4
I3
I2
I1
O
Units of good X
 Finding the optimum consumption
Points r, s, u and v
give a lower level of
r utility than point t.

Units of good Y s

Point t gives
the maximum
level of utility
Y1 t

u I5
I4
v I3
I2
I1
O X1
Units of good X
 Optimum Point

• As shown in the previous slide, all points except point “t”

gives the lower levels of utility or satisfaction to the
consumer.
• Thus point “t” only is the optimum point given the prices of
two goods and income of the consumer.
• Thus the consumer buys OX1 units of good X and OY1 units
of good Y.
• However, in the long run, with the changes in prices of two
goods and income of the consumer, the optimum position
changes.
 Classroom task
• Explain any two properties of indifference curve with the help
of diagrams.
 Effect on Optimum Position
• THE EFFECT OF CHANGE IN INCOME
An increase in income will lead to a new optimum consumption
point on a higher IC.
The following slides show a sequence of optimum consumption
points with the changes in income. Here both the goods are
shown as normal goods. Normal goods are those goods which
have POSITIVE INCOME EFFECT.
The line joining these optimum points relating to different levels
of income is known as the INCOME-CONSUMPTION CURVE.
An upward sloping ICC indicates that more of both the goods are
bought at higher levels of income. ICC traces the income effect.
 Effect on consumption of a change in income

Units of good Y

B1 I1
O
Units of good X
 Effect on consumption of a change in income

Units of good Y

I2
B1 B2 I1
O
Units of good X
 Effect on consumption of a change in income

Units of good Y

I4
I3
I2
B1 B2 B3 B4 I1
O
Units of good X
 Effect on consumption of a change in income

Units of good Y

Income-consumption curve

I4
I3
I2
B1 B2 B3 B4 I1
O
Units of good X
 Effect on Optimum Position

• THE EFFECT OF CHANGES IN PRICE

If either good X or good Y changes in price, the budget line
will ‘pivot’.
In the following case there is a reduction in the price of X
and it swings the budget line outwards.
This produces a new optimum consumption point when new
budget line becomes tangent to a different indifference
curve. Further reductions in price will produce the similar
effects.
If we join up these optimum points we create the PRICE-
CONSUMPTION CURVE. The PCC traces the price effect.
 Effect of a fall in the price of good X
a
30 The price–consumption curve shows how
consumption is affected by a change in the
price of one of the two goods

20
Price-consumption curve
Units of good Y

k
j
10

I2
0
0 5 10 15 20 25 30

B1 I1 B2

Units of good X
 Definitions
• Price Effect: It measures the effect on the purchases of two
goods with the changes in price of a good keeping the money
income and price of the other good constant.
• Income Effect: It measures the effect on the purchases of a
goods as a result of changes in income keeping the relative
prices constant. The income effect will vary depending upon
the nature of goods; Normal, Inferior and Giffen goods.
•
 Definition
• Substitution Effect: It measures the effect on the purchases of
the goods made as a result of changes in relative prices of the
goods keeping the real income constant.
For example, when good X becomes relatively cheaper in
comparison to good Y the consumer substitutes good X for
good Y. The increase in the purchases of good X and reduction
in purchases of good Y is also known as substitution effect.
 Price Effect = Income effect + Substitution Effect

THE INCOME AND SUBSTITUTION EFFECTS OF A PRICE CHANGE:

When the price of a good rises consumers will purchase less of it for
two reasons:
1.The INCOME EFFECT, and
2.The SUBSTITUTION EFFECT
Indifference curve analysis allows us to show these two effects of the
price change.
However effects are different for different types of goods.
 Effects

• In case of normal goods IE and SE support each other and

therefore a large change in quantity demanded of the good
takes place with the change in price. Demand curve is normal
and relatively elastic.
• In case of inferior goods, demand curve is normal but relatively
inelastic.
 Income and substitution effects: NORMAL good

Units of good Y

f
I1

I2

I3
I4
I5
B1 I6
QX 1
Units of Good X
 Income and substitution effects: NORMAL good

Rise in the price

of good X
Units of good Y

f
I1

I2

I3
I4
I5
B2 B1 I6
QX 3 QX 1
Units of Good X
 Income and substitution effects: NORMAL good

Substitution effect
of the price rise
Units of good Y

g
h

f
I1

I2

I3
I4
I5
B2 B1a B1 I6
QX 3 QX 2 QX 1
Substitution Units of Good X
effect
 Income and substitution effects: NORMAL good

Income effect of
the price rise
Units of good Y

g
h

f
I1

I2

I3
I4
I5
B2 B1a B1 I6
QX 3 QX 2 QX 1
Income Substitution Units of Good X
effect effect
 INDIFFERENCE ANALYSIS

THE INCOME & SUBSTITUTION EFFECTS FOR INFERIOR GOODS

In the following slides we see the substitution effect and income

effect of a rise in price of an INFERIOR [NON GIFFEN] GOOD.
 Income and substitution effects: Inferior good

Units of good Y

I1

I2 B1

QX 1
Units of Good X
 Income and substitution effects: Inferior good

Rise in the price

of good X
Units of good Y

f
h

I1

I2 B1
B2
QX 3 QX 1
Units of Good X
 Income and substitution effects: Inferior good

Substitution effect
of the price rise
g
Units of good Y

f
h

I1

I2 B1
B2 B1a
QX 2 QX 1
Substitution effect Units of Good X
 Income and substitution effects: Inferior good

Income effect of
the price rise
g
Units of good Y

f
h

I1

I2 B1
B2 B1a
QX 2 QX 3 QX 1
Substitution effect Units of Good X
Income effect
THE INCOME & SUBSTITUTION EFFECTS FOR GIFFEN
GOODS

In the following slides we see that the substitution

effect is lower than the income effect of a rise in price
of the good.

We see that the consumption of a Giffen good

increases as price rises.
 Income and substitution effects: Giffen good

Units of good Y

I1

I2 B1
QX 1
Units of Good X
 Income and substitution effects: Giffen good

Rise in the price

of good X
Units of good Y

I1

B2 I2 B1
QX1QX3
Units of Good X
 Income and substitution effects: Giffen good

Substitution effect
g of the price rise
Units of good Y

I1

B1a
B2 I2 B1
QX2 QX1QX3
Substitution effect Units of Good X
 Income and substitution effects: Giffen good

Income effect of
g the price rise
Units of good Y

I1

B1a
B2 I2 B1
QX2 QX1QX3
Substitution effect Units of Good X
Income effect
Derivation of the Consumer's Demand Curve: Normal Goods
With the help of diagrams, use marginal utility
theory and indifference curve analysis to explain
what is meant by consumer equilibrium and how it
is related to a consumer’s demand curve. [20]