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Subject ECONOMICS
Paper No and Title 3: Fundamentals of Microeconomic theory
Module No and Title 4: Indifference curve theory
Module Tag ECO_P3_M4
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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TABLE OF CONTENTS
1. Learning Outcomes
2. Introduction
3. Assumptions of ordinal utility theory
4. Indifference curve
5. Concept of Marginal rate of substitution
6. Properties of indifference curve
7. Different shapes of indifference curve
8. Concept of budget line
9. Consumer equilibrium: ordinal approach
10.The effect of change in income on the consumer equilibrium: ICC
11.The effect of change in price of a good on the consumer
equilibrium: PCC
12.Summary
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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1. Learning Outcomes
After studying this module, you shall be able to
Know the concept of ordinal utility, budget line and indifference curve.
Learn how to measure the utility by giving preference.
Identify the consumer equilibrium where the consumer finds optimum
combinations of two goods which give him maximum utility given his income.
Evaluate the changes in consumer equilibrium when the prices or income
changes.
Derive the demand curve from ICC and PCC.
2. Introduction
The theory of consumer behavior based on the ordinal approach was propounded by J.R.
Hicks and R.G.D. Allen in 1934. According to this approach, utility cannot be measured
in any quantifiable number. It could only be measured by giving order, ranks or
preferences. Hence the ordinal utility means consumers preferences or choice for one
commodity or for a basket of goods over the other. Here, the preferences could be
expressed in terms of ‘more’ or ‘less’ preferable. Moreover, since the consumers have a
limited income which they can spend on their consumption, therefore, in this approach, a
consumer will prefer a basket of goods over the other given the prices of the goods and
the income of the consumer. This would be explained with the help of budget line and
indifference curve later in this chapter.
But before moving ahead let’s talk about the assumptions of this theory.
3. Assumptions of Ordinal utility theory
Rationality: A consumer is always rational i.e. he always prefers more of goods
and services to derive maximum utility. Thus he always buys the commodity
which gives him maximum utility first and then he buys the least utility giving
commodity at the end.
Finite money income: The consumers have limited money income which they
spend on the purchase of all the goods and services for their living. Thus they
allocate this income as their consumption expenditure on all goods and services.
Ordinal utility: The utility derived from the consumption of each good or a basket
of goods could be measured ordinally by giving preferences for each good over
the other.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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Transitivity and consistency of choice: Consumer’s preferences are always
transitive i.e., if a consumer prefers good X over good Y and the same consumer
prefers good Y over good Z then according to this assumption of transitivity, he
must prefer good X over good Z also.
If, X>Y
If, Y>Z
Therefore, X>Z.
Whereas as per consistency of choice, if a consumer prefers good X to good Y in
one period then he must not prefer good Y to good X in another period or must
not treat both the goods as equal. Symbolically,
If, X>Y in one period
Then, Y > X or Y ≠ X in other period.
Non Satiety: According to this, a consumer always prefers more of a good or
larger quantity of all the goods because he has not reached the saturation level nor
he is oversupplied with all the goods.
Diminishing marginal rate of substitution: Marginal rate of substitution refers to
the rate at which a consumer substitute one good X for the other good Y so that
the level of utility/ satisfaction obtained from it remains the same to him.
Symbolically, MRS = ∆X/∆Y or ∆Y/∆X.
According to this assumption, as a consumer continues to substitute X for Y or Y
for X, his MRS diminishes/decreases. This would be explained in the later
sections in more detail.
4. Indifference Curve
Indifference curve is defined as the locus of the points of the different combinations
of different goods which gives an equal level of satisfaction to the consumer.
Therefore a consumer is indifferent between any of the combination which lies on the
same indifference curve. This happens because the consumer has a power to
substitute among various goods, given their prices and his income level.
For simplicity let’s take the example of two goods x and y. Now given the income of
the consumer and the prices of x and y, the consumer can choose different
combinations of x and y to be consumed in order to maximize his satisfaction. All
those combinations of x and y which gives an equal utility to the consumer forms an
indifference curve (as in the following fig). Moreover the consumer can substitute
between x and y and thus can either consume more of x or more of y but the main
point is that the level of satisfaction arising from the different combination of x and y
remains the same to him.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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As has been depicted in the above figure, that at point ‘a’ the consumer consumes y3
and x1 combination of goods, whereas at point ‘b’ he substitute y with x and the
combination at point ‘b’ becomes x2 and y2, similarly at point ‘c’ the consumer
consumes x3 and y1 combination of both the goods, given his income and Px and Py.
However all the points, a,b and c, gives the consumer equal level of satisfaction.
Hence, he is indifferent among a,b and c. Therefore, the curve joining a, b and c is
known as indifference curve, where the consumer is indifferent of the different choice
which he has as they all gives him equal level of satisfaction. Here only the
combinations of x and y are different at each point but the level of satisfaction which
the consumer obtained from them is the same.
Now if the consumer either consumes more of a good or of both the goods then he
would be able to increase his level of satisfaction and thus a new IC would be drawn
above this IC which represents the different combinations of x and y (higher than the
previous combinations) which gives him the same level of satisfaction (higher than
the previous level of satisfaction).
Similarly a lower IC would represent the combinations of x and y (lesser than the
previous combinations) which gives him equal satisfaction (lesser than the previous
level of satisfaction).
Hence the higher an IC, the higher is the level of satisfaction and the lower the IC, the
lesser is the level of satisfaction obtained by the consumer.
Representation of the different combinations of goods and different levels of
satisfaction on a graph is known as an Indifference map.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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5. Concept of Marginal rate of substitution
Marginal rate of substitution is defined as the rate at which a consumer
substitutes one good for the other obtaining the same level of satisfaction. In this
case, it is the rate at which a consumer substitute good y with good x in order to
get the same level of satisfaction.
Symbolically, MRSyx = ∆y/∆x or MRSxy = ∆x/∆y
MRS is also known as the slope of the IC.
As we can see from the diagram below, that as the consumer consumes more of
x, he reduces the quantity of y from y3 to y2 in order to get the same level of
satisfaction. Similarly, he further substitute y from y2 to y1 with good x in order
to get more of x and the same level of satisfaction. This rate of change in y due to
the increase in the quantity of x by one unit is known as Marginal rate of
substitution (MRS).
As we can see, an IC has a diminishing MRS, means that the consumer substitute
x for y at a diminishing rate. In other words, as the consumer increases the
consumption of x by one unit, their consumption of y reduces at a decreasing
rate. Hence we can say that an IC has a diminishing slope.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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As we can see that ∆x1 = ∆x2 = ∆x3 = ∆x4 but ∆y0< ∆y1 < ∆y2 < ∆y3.
This MRS falls because of the following reasons:
Diminishing MU
The decline in the ability of the consumer to sacrifice a commodity whose
quantity goes on declining.
6. Properties of Indifference curve
IC’s have a negative slope because of the diminishing MRS.
IC’s never intersect with each other else they will break the assumption of
transitivity.
IC is convex to origin for the imperfect substitute goods.
A higher IC represents higher level of satisfaction.
7. Different shapes of Indifference curves
Substitute goods: Substitute goods are those goods which give the same
utility to the consumers i.e. they can be substituted in place of their related good
as they posses almost same characteristics like their related good. In other words,
two goods are considered as substitute goods for one another when the utility
derived from both of them is same. For instance wheat and rice, coke and pepsi
etc. Therefore the MRS between substitute goods is constant as ∆y=∆x, so MRS =
∆y/∆x. in this case we can write MRS = ∆x/∆x (because ∆y=∆x), therefore, MRS
= 1. Graphically:
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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Complimentary goods: Complimentary goods are those goods which are
consumed in fixed proportions like pen and refill, left socks and right socks, car
and petrol etc. In such a case if we even increase the quantity of one good the
quantity of other good does not increase, hence, MRS = 0.
Symbolically, MRS = ∆y=∆x
But in such a case ∆y = 0, ∆x = 1
Thus, MRS = 0/1 = 0.
Graphically,
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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One good is necessary: In case of one good is a necessary good without
which we cannot survive like water, then in such a case the shape of the IC would
be like follows:
In case of a BAD good: A bad good is defined as a good whose excess is
bad for the consumption i.e. if the consumer will consume more of it then his
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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utility would decrease, for instance cigarette ( for a mediocre or non smoker). In
such a case the shape of the IC is as follows:
Hint: in order to draw an IC always find out the worst point of both the goods and
then bend the IC towards that common worst point. As in, in this case, the worst
of y is 0 however the worst of BAD is the excess, therefore the IC bend away
from 0 towards x axis.
In case of a neutral good: Neutral goods are those goods which neither yield
utility nor disutility to its consumers. Thus a consumer is indifferent to its
consumption. In such a case the IC will be a straight line as shown below.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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A good turning bad after some point: If a good is a normal good till some
point and then after that point it becomes bad for its consumer i.e. it provides
utility to its consumer till some point but after that point if the consumer still
consumes it then it starts providing disutility to him then in such a case the IC will
be like :
8. Concept of budget line
We have seen that IC is tool through which a consumer can measure his utility of
consuming goods. But in real life, a consumer is always constrained with two things in
order to maximize his utility. One is his limited money income and the other is the price
of the commodities. Both limited money income and prices of the goods act as a
constraint to the utility maximizing behavior of the consumer. This is known as
budgetary constraint. Symbolically:
Px*X + Py*Y ≤ M …………………….. (a)
This equation is known as budget line of a consumer, where Px and Py are the price of
the two goods X and Y, X and Y are the respective quantities of X and Y which a
consumer consumes given his money income M and prices of these goods.
Hence according to this budget line a consumer always decide about how much quantity
of goods to be consumed based on his money income and the prices of the consumer.
Then from this set of goods he tries to choose which combination would give him the
maximum utility.
Now if we just adjust the above budget line equation for X then we get:
X = M/Px – Y*Py/PX
Here this –Py/Px is also known as the slope of the budget line.
Now if X=0, then Y= M/Py and if Y=0, then X= M/Px
Plotting these points on a graph we get the following curve as the budget line:
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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Hence as per the budget line all the points which come inside or on the budget line
represents a feasible area as given the income of the consumer and prices of the goods the
consumer can consume any combination. But if the combination costs more than his
given income then that will fall outside the budget line, which is represented by infeasible
area in the above graph.
Thus, the budget line is drawn based on the money income of the consumer and the
prices of the goods, therefore, if any of these factors changes then the budget line will
also change.
If the money income of the consumer changes then the budget line will shift either
outside or inside as follows:
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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As it can be clearly seen from the above diagram, if the money income of the consumer
changes from M to M’, the budget line moves upward as now with more of his income he
can consume more of both the goods and vice a versa.
Now if the prices of the goods changes then it will pivot the budget line as follows:
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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As it can be clearly seen from the above graph that if the price of X increases from Px to
Px’, then given his money income M, he will reduce the consumption of X as now X has
become expensive. However he will continue consuming the same quantity of Y. Hence
the budget line will pivot inward to B2.
Similarly, if the price of X reduces from Px to Px’’ then he can increase his consumption
of X as now given his money income M, X has become relatively cheaper. Hence the
budget line will pivot outward to BL1.
9. Consumer equilibrium: ordinal approach
A consumer attains equilibrium at a point where he maximizes his utility from the
consumption of goods, given his money income and the prices of the goods. According to
the ordinal utility analysis two sets of conditions must be fulfilled for a consumer to
attain equilibrium. These two conditions are as follows:
Necessary condition: as per this MRS must be equal to Px/Py, i.e. the slope of
budget line must be equal to the slope of the IC.
Sufficient condition: The necessary condition must prevail on the highest IC.
Hence, consumer equilibrium is attained where the above mentioned two conditions
prevails. This is illustrated as follows:
As represented in the above diagram, ‘E’ is the equilibrium point where the slope of the
budget line and that of the IC is the same. Thus, the consumer will consume Qx and Qy
quantity of X and Y in order to maximize his utility, given his money income M and the
prices of X and Y as Px and Py.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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As we can see that the equilibrium takes place on IC’, it does not take place at IC nor on
IC”. The reason for this is that IC comes in the feasible area under the budget line but the
consumer does not maximize his utility on IC because he has a higher income and thus
using that income he can increase his consumption of both the goods and can move to
IC’. So on IC’ both the necessary as well as sufficient conditions apply. However, if he
further moves from IC’ to IC” then all those combinations lying on IC” are not feasible
because his money income is less. All the points on IC” would definitely give the
consumer a higher utility as compare to the combinations lying on IC’ but the
combinations on IC” are not attainable. Hence the consumer equilibrium cannot take
place on IC” too.
10.The effect of change in income on consumer equilibrium : ICC
As we have seen in the above section that consumer equilibrium happens at the point
where the IC is tangent on the budget line. But when the income of the consumer changes
then the budget line also changes and correspondingly the IC also changes. For instance,
if the income of the consumer increases then the budget line will shift upward. This
represents that now the consumer can afford more of both the goods hence his IC will
also shift and the tangency of the new IC with this new budget line gives new consumer
equilibrium. Similarly if the process will go on then the equilibrium points will keep on
changing. If we connect all these equilibrium point with a line, then this line joining all
the equilibrium points is known as income consumption curve, which shows the changes
in the consumer equilibrium due to a change in the income of the consumer. This is
represented in the following diagram.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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The above is the case of the normal goods. Here normal goods are the goods which show
a positive relationship between the demand of the good and the income of the consumer,
i.e. if the income of the consumer increases, his demand for normal good also increases
and vice versa.
However, in case of inferior goods, the ICC would not be upward sloping because
inferior goods shows an inverse relationship between the demand of the inferior good and
the income of the consumer, i.e. if the income of the consumer increases, his demand for
the inferior good reduces. In such a case the ICC would be downward sloping, as given
below:
As has been represented in the above diagram, as the income of the consumer increases
his demand for the inferior good reduces and that of normal good increases. Hence based
on this his budget line is shifting and IC is also increasing but the combination which he
chooses for each increased income comprises of less of inferior good and more of normal
good in order to maximize his utility.
ICC is also known as Engel curve. We can further derive the demand curve for a good
based on his ICC.
Note that here we are only showing how to derive the demand curve of the normal good.
You can derive the demand curve of the inferior good in the same way.
Let us now derive the demand curve from the ICC of a normal good:
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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Clearly, for a given price of a good, if the income of the consumer increases, he
demands more of good X. This gives point E, E’ and E” and three different demand
curves emerges with ICC for good X.
Note that here we can see that the demand curve is downward sloping, representing an
inverse relationship between the price and quantity of the good.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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11. The effect of change in Prices of the goods on consumer equilibrium
: PCC
If the price of any of the good changes, then, this leads to a change in the consumer
equilibrium too. For instance, if the price of X falls, then this will make X relatively
cheaper and the consumer will demand more of X and same quantity of Y and thus this
will pivot his budget line outward. But when budget line pivots then consumer will
change his combination of goods which will maximize his consumption. Now his new
basket of goods will comprise of more of X and less or same quantity of Y, hence his IC
will shift upward too. The tangency of the new IC with the new budget line gives the new
equilibrium point of the consumer. Joining all such points, gives the price consumption
curve (PCC). This is depicted in the following diagram:
The above is the case of the normal good, where normal goods shows the inverse
relationship between the price of the good and the quantity of the good, i.e. if the price of
the consumer falls it’s quantity consumed or demanded increases.
However if there exists a positive relationship between the price of the good and the
quantity of the good then that type of good is known as Giffen good. In such a case if the
price of the Giffen good falls its quantity also falls. This is depicted in the following
diagram:
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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In the above diagram we can see that if the price of the Giffen good falls the budget line
pivots outward but the quantity demanded of the Giffen good reduces. And hence the
points joining the consumer equilibrium i.e. e, e’, e” gives a downward sloping PCC.
We can also derive the demand curve with the help of PCC in the following way.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
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The above graph clearly shows that as the price of X reduces, budget line pivots outside
and then the quantity of x increases, when these points drawn below then they form
demand curve for X.
12. Summary
The entire chapter has explained how the utility can be measured in terms of indifference
curve. This has also explained how the consumer attains his equilibrium with the help of
budget line and indifference curve. Then we have seen how the changes either in the
price or in the income of the consumer affect the changes in his equilibrium and then we
have derived ICC and PCC and then the demand curve.
ECONOMICS Paper 3: Fundamentals of Microeconomic theory
Module 4: Indifference curve theory
