4 Indifference Curve 1
Transcript of 4 Indifference Curve 1
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.