Why normally the shape of Indifference curve is convex to the origin? | What is Indifference Map? | What are Monotonic Preferences?
Introduction
In previous session, we learned about the Ordinal Utility
Analysis approach which is used to study the consumer behavior. In that
approach we came across the concept of indifference curve which shows the
several combinations of two or more products may be a good or service or
commodity having or providing equal utility to the consumer and hence making
the consumer indifferent among those combinations. We then discussed Marginal
Rate of Substitution which refers to the rate at which consumer is ready to forego
on good for the other. And after few cycles of exchange, the Marginal Rate of
Substitution starts decreasing. This phenomenon of decreasing Marginal Rate of
Substitution is known as the Law of Diminishing Marginal Rate of Substitution.
In this session, we will discuss the other case of
indifference curve where the goods of which the bundles or combination are
made, that the consumer chooses are perfect substitute making the case unique
and different the normal indifference curve.
Shape of Indifference Curve
Why normally the shape of Indifference curve is convex to
the origin?
In the previous scenario, the indifference curve that we
discussed, in form of its graphical presentation, the shape of the indifference
curve was convex to the origin. The rationale behind the indifference curve
being convex was the Law of Diminishing Marginal Rate of Substitution. The Law
of Diminishing Marginal Rate of Substitution states that the Marginal Rate of
Substitution keeps on diminishing as the consumer keeps on exchanging what they
have with the new one. As the good they already have starts reducing, the
utility they attach to the remaining keeps on increasing. And at the same time,
as the amount of new good keeps on increasing, the utility that they have
attached to the new one, keeps decreasing. Hence automatically the Marginal Rate
of Substitution keeps on diminishing. So the curve which represents the
combination among which the consumer is indifference curve becomes convex to
origin as initially it is steep when Marginal Rate of Substitution is high and
when Marginal Rate of Substitution slowly keeps on diminishing, the curve becomes
less and less stepper and more flatter.
But what will happen if the goods in question are perfect
substitute of each other?
When the goods among which the consumer has to choose are
perfect substitute, the Marginal Rate of Substitution will not diminish or
decrease but will remain constant.
Let us understand this with an example.
|
Combination |
Quantity of 10 Rupee Notes |
Quantity of 10 Rupee Coins |
MRS |
|
A |
1 |
5 |
NA |
|
B |
2 |
4 |
1:1 |
|
C |
3 |
3 |
1:1 |
|
D |
4 |
2 |
1:1 |
Here as can be seen in graphical representation, the
consumer is ready to forego one 5-rupee coin for every one additional 5-rupee
note. These clearly means that the Marginal Rate of Substitution remain equal
as each additional one new note will replace each existing one coin, both
having denomination equal thus giving equal utility to the consumer. And as the
Marginal Rate of Substitution remains equal and does not diminishes, the graphical
representation of the combinations will be linear and the indifference curve
depicting the points will be a straight line. So the commodities which are
perfect substitute form an indifference curve which is a straight line.
Monotonic Preferences
As we have seen the consumer chooses between several bundles
having different combinations of goods or commodities. Now one thing which is important
to take note of is the basic rationale which is at work while studying the
preferences.
If the consumer has two bundles of two same commodities of
different amounts as (a1, a2) and (b1, b2), and if in one of the bundle (here
for the sake of understanding say 2nd bundle [b1, b2]) any one of
the good is more in amount for e.g., b1>a1, other good being of equal
quantity i.e., b2=a2, then the consumer will prefer the 2nd bundle over the 1st.
These type of preferences is known as Monotonic Preferences. Thus a consumer’s
preference would be called monotonic if the consumer prefers between any two
bundles made of same two commodities, a bundle having more of at least one good
and the other good at least being equal i.e., no less than the other.
Indifference Map
There can be several combinations among different bundle of goods. So there will be different bundles among which the consumer will need to choose. And out of several bundles there will be set of bundles which will be giving equal utility to the consumer forming an indifference curve. Like this, there will be several set of bundles forming several indifference curves. These family of indifference curves is known as the Indifference Map of the consumer. Each indifference curve would represent a set of bundles between which consumer would be indifferent to choose from. Now from these indifference curve, as per the concept of Monotonic Preferences, the bundles represented by the indifference curves above will be automatically preferred over the bundles represented by the indifference curves lying below.
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