CONSUMER’S
EQUILIBRIUM–UTILITY MAXIMIZATION
The theory of demand starts with the
examination of the behaviour of the consumers. In our everyday life we behave
in different ways while buying and consuming a good or service. The simple
calculations and human reasoning we undertake while doing any transactions have
been transformed into principles which guide us to attain satisfaction or
equilibrium in economic sense. When we go for shopping, we decide beforehand,
what good to buy and how much to spend. It makes sense as we try to get most of
what we are spending. In other words, we always want more of anything and for
that purpose we negotiate and come to an agreed price which we are ready to pay
happily. It is therefore, necessary to be first acquainted with the consumer
behaviour, which forms the basis of the demand theory.
It is assumed that consumers are
rational. Given his money income and the prices of commodities, a consumer
always tries to maximize his satisfaction. That is, to get the maximum welfare
(state of well-being) by spending the given money on various commodities. It is
assumed that the satisfaction a consumer gets by consuming a good is measurable
(measured in terms of money), though in real life it is not possible to measure
satisfaction because it is psychological entity. We only feel the level of
satisfaction and express the same in different ways. We show our satisfaction
by our behaviour like laughing, jumping in excitement or in any other way.
Thus, we cannot measure satisfaction in quantitative terms as we are capable of
measuring time in seconds, weight in kilograms or length in meters. Further,
each consumer is also assumed to be known of what he wants. Moreover, he has
all information regarding market—the goods available, the prices of the goods
at a particular point of time and so on. Every consumer uses this information
in such a way as to maximize his total satisfaction.
To explain consumer’s equilibrium
i.e., how a consumer attains maximum satisfaction by spending his money income
on certain units of commodities, it is worthwhile to be familiar with certain
important terms used in explaining various concepts and theories of demand.
These are explained as under:
Utility
Utility is defined as the power of a
commodity or service to satisfy a human want. Economists have leveled the term
satisfaction as utility. It is subjective concept and therefore varies from person
to person. As already stated, it resides in one’s mind and therefore cannot be
measured in quantitative terms. Though utility and satisfaction are used
synonymously, we should note that utility is the expected satisfaction whereas
satisfaction implies ‘realized satisfaction’.
Total Utility
It is the amount of utility (satisfaction);
a consumer gets by consuming all the units of a commodity. If there are n units of the commodity then the total
utility is the sum of the utilities of all n
units of the commodity. Thus, if there are four units of a commodity, then
total utility is,
U = U1(n1)
+ U2(n2) + U3(n3) + U4(n4)
Where U = total utility; U1…….U4
are the utilities of n1…..n4 units of the commodity.
Thus, if by
consuming first apple, a consumer gets 12 utils of satisfaction, 10 utils from
the second apple, 9 utils from the third and 7 utils from the fourth apple;
then his total utility is,
U = 12 + 10 + 9 + 7 = 38
Thus
utilities of various goods are additive. This means that utilities of different
commodities are independent of one another. The utility derived from one
commodity does not affect that of another.
Marginal Utility
Marginal utility is defined as the
change in the total utility due to a unit change in the consumption of a
commodity per unit of time. It can also be defined as the addition made to the
total utility by consuming an additional unit of a commodity. For example, if
total utility of 3 cups of tea is 18 utils and on consuming the 4th
cup it rises to 20; then marginal utility 20-18 = 2 utils. Thus, by consuming
one more cup of tea, the additional utility, a consumer gets is 2 utils.
Marginal utility can be expressed as,
∆TU
MU =
∆
Q
Where
MU = marginal utility; ∆ΤU = change in total utility; ∆Q
= change in the quantity consumed. ‘Utils’ is the term used by Marshall as a
measuring unit of utility. The following expression can also be used to find
marginal utility:
MU = TUn – TUn-1
Where, TUn
is the total utility of nth unit of
the commodity and TUn-1
utility from the n-1th commodity.
Thus, if TU from the second unit (nth
unit) of apple is 13 and TU from the previous unit (n-1) is 7, then MU is 13 – 7 = 6.
The concept of total utility and
marginal utility is shown in the utility schedule below:
|
Units of apples
|
Total utility
|
Marginal Utility
|
|
1
|
7
|
7 – 0 = 7
|
|
2
|
13
|
13
– 7 = 6
|
|
3
|
18
|
18 – 13 = 5
|
|
4
|
22
|
22
– 18 = 4
|
|
5
|
25
|
25 – 22 = 3
|
|
6
|
27
|
27
– 25 = 2
|
|
7
|
28
|
28 – 27 = 1
|
|
8
|
28
|
28
– 28 = 0
|
When the consumer takes 1st
apple, his total utility is 7 and from the 2nd apple he gets 13 and
so on. The third column shows marginal utility, which diminishes as the
consumer increases units of apples. It is seen that when total utility is
maximum, marginal utility is zero at 8th unit of apple. It is also
seen that total utility is the sum of the marginal utilities of the 1st,
2nd, 3rd, and so on. Thus, at 8th unit of
apple,
TU = MU1 + MU2
+ MU3 + MU4 +…..…+ MUn(8)
i.e. 28 = 7 + 6 + 5 + 4 +…..…+ 0
LAW OF
DIMINISHING MARGINAL UTILITY
One of the very important laws in
regard to the satisfaction of human wants is known as law of diminishing
marginal utility. The law explains common feeling of every consumer. Suppose a
person starts consuming apples one after another. The first apple gives him the
maximum satisfaction as he might be in mood of taking some food at that time
for meeting his appetite. As he takes the second apple, he gets less
satisfaction because by this time he has already met some level of appetite.
The third and more apples yield him lesser satisfaction or utility. It means
that every time the consumer increases his consumption, he gets less and less
satisfaction. The satisfaction also tends to be zero when the consumer feels
totally disgusted to take any more apples. If he takes more, his satisfaction turns
negative or utility now becomes disutility.
Thus law of diminishing marginal
utility states that additional satisfaction a person derives by consuming a
commodity goes on declining as he consumes more and more of a that commodity.
According to Marshall, “The additional
benefit which a person derives from a given
increase of his stock of a thing diminishes with every increase in stock that
he already has.”
Two important reasons for
diminishing marginal utility are the following:
(a) Each
particular want is satiable (can be satisfied): Though there are unlimited
wants, a single want can be satisfied. Thus, when a consumer consumes more and
more of a commodity, his want is satisfied and he does not wish to have any
further increase in the commodity. As such his marginal utility falls when
consumption increases.
(b) Goods
are imperfect substitutes for one another i.e., one good cannot be exactly used in place of another: Satisfaction
from any two goods is not same. Different
goods satisfy different wants. If a good could be perfectly substituted for
another, it would have satisfied other wants. Hence, its marginal utility would
not have fallen but increased.
The law can be explained with the help of a table and
diagram-3.1 below:
|
Units (Apples)
|
TU
|
MU
|
|
|
|
|
|
|
|
1
|
10
|
10
|
|
|
2
|
18
|
8
|
|
|
3
|
22
|
4
|
|
|
4
|
24
|
2
|
|
|
5
|
25
|
1
|
|
|
6
|
25
|
0
|
|
|
7
|
32
|
–7
|
|
|
8
|
44
|
–12
|
|
|
|
|
|
As the consumer
goes on consuming more and more units of apples, total utility (TU) increases but
marginal utility (MU) declines continuously and becomes zero at 6th
unit. When consumer consumes further, utility becomes negative. It is to be
noted that when TU is maximum, MU is zero. Let us now derive the MU curve from
the above schedule as under. Marginal utility is measured along Y-axis while
units of apples along X-axis. MU is the marginal curve falling downwards from
left to right. This is diminishing MU curve. It is seen in the Fig. 3.1 below,
that marginal utility is zero when the consumer buys 6th apple. As
he consumes more, marginal utility becomes negative.
The law of diminishing MU has
certain limitations. These are:
1.
If
units of a commodity consumed are not of same size and shape, the law does not hold
good. In the illustration explained above, units of apples are assumed to be of
same shape and size.
2. The law does not hold good when
there is enough time gap between consumption of two units. For instance, if we
take second apple after a long gap of time, we may feel hungry and hence
satisfaction will increase instead of falling.
3. The taste of consumer should not
change for the law to hold good. It means that the person should consume all
units of a good by same desire and pleasure.
4. The law does not apply to money as
it is said that more money a person has, the more he wants.
5. Change in income of the consumer
will falsify the law. If money income of the consumer increases or decreases
during the time of consumption of a particular set of goods, the marginal
utility will not fall as said above.
The law of diminishing marginal
(additional) utility explains consumer’s equilibrium in case of a single
commodity. A consumer will go on purchasing successive units of a commodity till
the marginal utility of the commodity is equal to price. Thus, for a single
commodity x, a consumer is in
equilibrium when the marginal utility of x
is equal to its market price (Px).
Symbolically,
MUx = Px
In case the price goes down, he will
buy more and the marginal utility will come down to the level of price. If
price rises, less will be purchased and the marginal utility rises till it
reaches the new level of price. Thus, equality between marginal utility and
price indicates the position of consumer’s equilibrium when a single commodity
is being purchased and consumed.
