Indifference Curve

Introduction

• A geometrical device that has been used to replace the neo-

classical cardinal utility concept.

• The indifference curve analysis measures utility ordinally.

• It explains consumer behaviour in terms of his preference or

rankings for different combinations of two goods.

• In the ordinal sense utility is viewed as the level of

satisfaction rather than amount of satisfaction.

• The level of satisfaction is relatively comparable but not

quantifiable.

Assumptions

• Consumer is rational and tries to maximize satisfaction.

• There are two goods X & Y.

• Consumer possesses complete information about the prices of the goods.

• The price of the two goods is given.

• Consumer’s taste, habits, and income remains same throughout the analysis.

• He prefer more of X to less of Y or more of Y to less of X.

• An indifference curve is negatively inclined sloping downward.

• An indifference curve is always convex to the origin.

Assumptions…• An indifference curve is smooth and continuous meaning

that the the two goods are highly divisible and the level of

satisfaction also changes in a continuous manner.

• The consumer arranges the two goods in a scale of

preference which means he has both preference and

indifference for the goods.

• Both preference and indifference are transitive, meaning if

combination A is preferable to B and B to C than A is

preferable to C.

• Similarly if he is indifferent between combination A & B

and B & C, then he is indifferent between A & C.

Indifference Schedule1

Combination

2

X

3

Y

4

MRS of X&Y

1 1 18 -

2 2 13 5:1

3 3 9 4:1

4 4 6 3:1

5 5 4 2:1

6 6 3 1:1

Indifference Map• Combinations of two goods (Units)

I II III

A B A B A B

1 1 10 2 15 3 20

2 2 6 4 10 5 14

3 3 3 6 6 7 10

4 4 1 8 3 9 7

IC1 IC2 IC3

Properties of Indifference Curve

1. A higher indifference curve to the right of another

represents a higher level of satisfaction and preferable

combination of the two goods.

2. In between the two indifference curve there can be a

number of other indifference curves, one for every point in

the space on the diagram.

3. The number I1, I2, I3, I4 … etc. given to indifference curve

are absolutely arbitrary.

4. The slope of an indifference curve is negative, downward

sloping and from left to right.

Properties…

5. Indifference curve can neither touch nor intersect each other

so that one indifference curve passes through only one

point on an indifference map.

6. Indifference curves are convex to the origin, meaning as the

consumer substitute X for Y, the MRS (marginal rate of

substitution) diminishes.

• It means that as the amount X is increased by equal

amounts that of Y diminishes by smaller amounts. The

slope of the curve becomes smaller as we move to the right.

Marginal Rate of Substitution (MRS)

• The MRS is the rate of exchange between some units of

goods X and Y which are equally preferred.

• The MRS of X for Y (MRS)xy is the amount of Y that

will be given up for obtaining each additional unit of X.

MRS…

1

Combination

2

X

3

Y

4

MRS of X&Y

1 1 18 -

2 2 13 5:1

3 3 9 4:1

4 4 6 3:1

5 5 4 2:1

6 6 3 1:1

The Price / Budget Line• Alternative Purchase Possibilities

• Total Income Rs. 50. Price of X Rs 5, Price of Y Rs 10

Units of goods X Units of goods Y

A 5 0

4 2

3 4

2 6

1 8

B 0 10

Consumer’s Equilibrium

• A consumer is in equilibrium when given his taste and

price of the two goods he spends a given money

income on the purchase of two goods in such a way as

to get max. satisfaction.

Assumptions

• The consumer’s indifference map for the two goods X & Y

is based on his scale of preference for them which does not

change at all in this analysis.

• His money income is given and is constant.

• Price of the two goods are also given and are constant.

• The goods are homogeneous and divisible.

• There is no change in the taste and habits.

• There is perfect competition in the market.

• The consumer is rational – maximizes his satisfaction.

The Equilibrium Position• The budget line should be tangent to the indifference Curve.

Expenditure Plan

Combination Units of X

Rs 10

Units of Y

Rs 5

Q 5 0

N 4 2

T 3 4

S 21/2 5

K 11/2 7

R 1 8

P 0 10

First Condition

• Algebraically, I = Px . X + Py . Y

• This budget equation is the equation of the line connecting

the points A & B, where A = I/Px and B = I/Py

• Thus AB is the budget line.

• On this budget line a consumer can have any combination

out of the seven possible combination.

• Combination A&B are out of question.

• He would not take combination a or e on a lower IC I1,

because combination b is also available on IC I2.

• There is another combination c on the highest IC I3.

• Since other combinations lie on lower IC than c this is consumer’s equilibrium.

• The consumer is in equilibrium when his budget line is tangent to an IC. AB is tangent at c at this point he is also satisfying the budget equation –

• I (Rs 50) = ON . Px + OR . Py

= 21/2 units of X . Rs 10 + 5 units of Y . Re 5

= Rs 25+ Rs 25

= Rs 50

Second Condition • At the point of equilibrium the Slope of IC and the Budget

Line should be same.

• At c, the slope of the IC is the marginal rate of substitution of X for Y and on the budget line it is the ratio of the price of X to the price of Y.

• The slope of budget line

• AB = I / Py / I /Px

• = I / Py x Px / I = Px / Py

• And the slope of I3 curve is MRSxy

• Thus, MRSxy = Px / Py at point c.

Third Condition

• IC should be convex to the origin.

• At the point of Equilibrium, the MRSxy must be

falling for equilibrium to be stable.

• For equilibrium to be stable at any point on IC, the

MRS between any two goods must be diminishing

and be equal to their price ratio i.e. MRSxy = Px / Py

Income Effect

• Consumer’s demand for goods changes when his income changes.

• How a consumer will react to the change in his income, in relation to the fixed price of goods and his given preference is described as Income Effect .

• In terms of IC techniques, change in income can be interpreted through shifts in the budget line.

• When income rises the budget line shifts towards its right.

• When the income falls the budget line shifts to its left.

Income Effect…

• At the locus of all such points we may draw a curve

called income–consumption–curve, showing how

equilibrium position and combination changes as income

changes.

• The ICC has an upward slope implying a positive effect

for the two goods.

• The upward movement on ICC places a consumer on a

higher IC and and downward movement implies a lower

IC.

Income Effect…

• Sometimes there may be a negative income effect

• It implies that the consumer will tend to buy less of a commodity when his income increases above a certain level.

• This happens in case of inferior goods. More of which is demanded when the consumer is poor.

• But as his income increases he reduces the consumption of such goods.

• In case of negative income effect, the ICC will have either a backward slope or downward slope.

Substitution Effect

• If there is a change in the relative price of goods, a rational consumer will be induced to substitute a relatively cheaper goods for the dearer one. This is substitution effect.

• The consumer will buy more of a goods whose price has fallen.

• The rearrangement in the purchase made by the consumer, caused by the change in the relative price of goods, while his real income remains constant, so that his level of satisfaction remains as before.

Substitution Effect …

• As a result of a fall in the price of X, there is a rise in

his real income, as he could buy now more than before.

• To eliminate this income effect, his money income must

be altered appropriately so that his real income remains

at the original level.

• Thus, when his surplus income is taken away he will

neither better nor worse off than he was before.

• This is called compensating variation in income.

Substitution Effect …

• It is defined as an appropriate change in the consumers

income which would just compensate for a change in

relative price of goods, so that he is neither better nor

worse off than he was before.

• Graphically, the substitution effect is measured by

movement from one point to another on the same

indifference curve.

Substitution Effect…

1. Income effect is measured along the ICC. The

substitution effect is measured along the IC.

2. To measure pure substitution effect the real income is

kept constant through the method of compensating

variation in income.

• The movement from one point to another on the same IC

measures the substitution effect.

3. The income effect may be positive or negative. The

substitution effect is always positive.

Price Effect

• The consumer’s reaction to a change in the price of a commodity, other things held constant, is described as the price effect.

• In the IC technique the price effect is measured along the price-consumption-curve.

• To draw a PCC we assume a successive fall in the price of X, price of Y being constant.

• Thus, there is a change in the ratio Px / Py.

• The ratio is decreasing as such the slope of price line becomes progressively flatter.

Price Effect…

• Hence, with every fall in the price of X the assumed

price line tends to shift as AB1 to AB2 and AB3…

• The consumer’s equilibrium point will shift P1, P2 and

P3… where each new price line is becoming tangent to a

higher IC.

• By having the locus af all such subsequent points of

equilibrium like P1, P2 and P3 etc. we derive a curve

called PCC.

• The PCC depicts price effect.

Price Effect in Inferior Goods

• Income effect tends to be negative in case of inferior

goods.

• When income of the consumer rises as a result of fall in

the price of a commodity the income effect will induce

him to buy less of this cheaper inferior good as he will

prefer to buy a superior good instead.

• But the price effect is the net effect of income as

substitution effect combined together.

• The substitution effect is always positive, whether the

goods is superior or inferior.

Inferior Goods…

• If the positive substitution effect is more powerful than the negative income effect. Which is weak, the resulting net price effect will be positive as the negative income effect is more than counter balanced by the strong substitution effect.

• In symbolic terms –

• When + ve Se > - ve Ie

• Therefore Pe = Se + (-Ie) = + ve net effect

• In the fig. Ab1 is the initial price line.

• Initial equilibrium point is P, indicating ON1 of X is bought.

Inferior Goods…

• X being inferior good, when its price falls, the real income of the consumer rises, but it carries a negative effect, so the consumer first move from P to R on the IIC, which is backward slopping.

• The P to R movement implies that he would buy less of X by N1 n2 . But there is a stronger substitution effect which forces the consumer to move again from R to Q. this substitution effect causes the consumer to buy N2 N3 of X. thus –

• Net Pe = Ie + Se• N1 N3 = (-N1 N2) + (N2 N3)• N1 N1 is +ve, therefore (+N2N3) > (-N1N2)

Inferior Goods…

• Thus, in case of inferior goods, the net price effect

turns out to be positive when income effect is negative

but weak and substitution effect is positive and strong.

• Graphically, therefore, the ICC curve has a backward

slope while the PCC has a positive slope.

Giffens’ Paradox

• There may be a few goods for which the negative income efect caused by a fall in their prices is stronger and predominant while the substitution effect is positive but weak so that the overall price effect tends to be negative.

• In such cases the consumer tends to buy less of them, after a point, when the prices fall.