Law of Equi-Marginal Utility:
(Equilibrium of the Consumer
Through the Law of Equi-Marginal Utility):
Other Names of this Law:
Law of Substitution
OR Law of Maximum Satisfaction
OR Law of Indifference OR
Proportion Rule OR Gossen's Second Law.
In the
cardinal utility analysis,
the principle of equal marginal utility occupies an important place.
Definition and
Statement of Law of Equi-Marginal Utility:
The law of equi-marginal utility is simply an extension of
law of diminishing marginal
utility to two or more than two commodities. The law of equilibrium utility is
known, by various names. It is named as the Law of Substitution, the Law of
Maximum Satisfaction, the Law of Indifference, the Proportionate Rule and the Gossen’s Second Law.
In cardinal utility analysis, this law is stated by Lipsey in the
following words:
“The household maximizing the utility will so
allocate the expenditure between commodities that the utility of the last penny
spent on each item is equal”.
As we know, every consumer has unlimited wants. However, the income this
disposal at any time is limited. The consumer is, therefore, faced with a choice
among many commodities that he can and would like to pay. He, therefore,
consciously or unconsciously compress the satisfaction which he obtains from the
purchase of the commodity and the price which he pays for it. If he thinks the
utility of the commodity is greater or at-least equal to the loss of utility of
money price, he buys that commodity.
As he buys more and more of that commodity, the utility of the successive units
begins to diminish. He stops further purchase of the commodity at a point where
the marginal utility of the commodity and its price are just equal. If he pushes
the purchase further from his point of equilibrium, then the marginal utility of
the commodity will be less than that of price and the household will be loser. A
consumer will be in equilibrium with a single commodity symbolically:
MUx = Px
A prudent consumer in order to get the maximum satisfaction from his limited
means compares not only the utility of a particular commodity and the price but
also the utility of the other commodities which he can buy with his scarce
resources. If he finds that a particular expenditure in one use is yielding less
utility than that of other, he will tie to transfer a unit of expenditure from
the commodity yielding less marginal utility. The consumer will reach his
equilibrium position when it will not be possible for him to increase the total
utility by uses. The position of equilibrium will be reached when the marginal
utility of each good is in proportion to its price and the ratio of the prices
of all goods is equal to the ratio of their marginal utilities.
The consumer will maximize total utility from his income when the utility from
the last rupee spent on each good is the same. Algebraically, this is:
MUa / Pa = MUb / Pb =
MUc = Pc = MUn = Pn
Here: (a), (b), (c)…. (n) are
various goods consumed.
Assumptions of
Law of Equi-Marginal Utility:
The main assumptions of the law of equi-marginal utility are as under.
(i) Independent utilities. The marginal
utilities of different commodities are independent of each other and
diminish with more and more purchases.
(ii) Constant marginal utility of money. The
marginal utility of money remains constant to the consumer as he spends more
and more of it on the purchase of goods.
(iii) Utility is cardinally measurable.
(iv) Every consumer is rational in the purchase of
goods.
Example and
Explanation of Law of Equi-Marginal Utility:
The doctrine of equi-marginal utility can be explained by taking an example.
Suppose a person has $5 with him whom he wishes to spend on two commodities, tea
and cigarettes. The marginal utility derived from both these commodities is as
under:
Schedule:
|
Units of Money |
MU of Tea |
MU of Cigarettes |
|
1 |
10 |
12 |
|
2 |
8 |
10 |
|
3 |
6 |
8 |
|
4 |
4 |
6 |
|
5 |
2 |
3 |
|
$5 |
Total Utility = 30 |
Total Utility = 30 |
A rational consumer would like to get maximum satisfaction from
$5.00. He can spend money in three ways:
(i) $5 may be spent on tea only.
(ii) $5 may be utilized for the purchase of cigarettes only.
(iii) Some rupees may be spent on the purchase of tea and some on the purchase of
cigarettes.
If the prudent consumer spends $5 on the purchase of tea, he gets 30 utility. If
he spends $5 on the purchase of cigarettes, the total utility derived is 39
which are higher than tea. In order to make the best of the limited resources,
he adjusts his expenditure.
(i) By spending $4 on tea and $1 on cigarettes, he
gets 40 utility (10+8+6+4+12 = 40).
(ii) By spending $3 on tea and $2 on cigarettes, he
derives 46 utility (10+8+6+12+10 = 46).
(iii) By spending $2 on tea and $3 on cigarettes,
he gets 48 utility (10+8+12+10+8 = 48).
(iv) By spending $1 on tea and $4 on cigarettes, he
gets 46 utility (10+12+10+8+6 = 46).
The sensible consumer will spend $2 on tea and $3 on cigarettes and will get
maximum satisfaction. When he spends $2 on tea and $3 on cigarette, the marginal
utilities derived from both these commodities is equal to 8. When the marginal
utilities of the two commodities are equalizes, the total utility is then
maximum, i.e., 48 as is clear from the schedule given above.
Curve/Diagram of
Law of Equi-Marginal Utility:
The law of equi-marginal utility can be explained with the help of diagrams.
In the figure 2.3 MU is the marginal utility curve for tea and KL of cigarettes.
When a consumer spends OP amount ($2) on tea and OC ($3) on cigarettes, the
marginal utility derived from the consumption of both the items (Tea and
Cigarettes) is equal to 8 units (EP = NC). The consumer gets the maximum utility
when he spends $2 on tea and $3 on cigarettes and by no other alternation in the
expenditure.
We now assume that the consumer spends $1 on tea (OC/ amount) and $4
(OQ/) on cigarettes. If CQ/ more amounts are spent
cigarettes, the added utility is equal to the area CQ/ N/N.
On the other hand, the expenditure on tea falls from OP amount ($2) to OC/
amount ($1). There is a toss of utility equal to the area C/PEE. The
loss is utility (tea) is greater than that The loss in utility (tea) is maximum
satisfaction except the combination of expenditure of $2 on tea and $3 on
cigarettes.
This law is known as the Law of maximum
Satisfaction because a consumer tries to get the maximum satisfaction from
his limited resources by so planning his expenditure that the marginal utility
of a rupee spent in one use is the same as the marginal utility of a rupee spent
on another use.
It is known as the Law of Substitution because consumer
continuous substituting one good for another till he gets the maximum
satisfaction.
It is called the Law of Indifference because the maximum
satisfaction has been achieved by equating the marginal utility in all the uses.
The consumer than becomes indifferent to readjust his expenditure unless some
change fakes place in his income or the prices of the commodities, etc.
Limitations/Exceptions of Law
of Equi-Marginal Utility:
(i) Effect on fashions and customs: The law
of equi-marginal utility may become inoperative if people forced by fashions
and customs spend money on the purchase of those commodities which they
clearly knows yield less utility but they cannot transfer the unit of money
from the less advantageous uses to the more advantageous uses because they
are forced by the customs of the country.
(ii) Ignorance or carelessness: Sometimes
people due to their ignorance of price or carelessness to weigh the utility
of the purchased commodity do not obtain the maximum advantage by equating
the marginal utility in all the uses.
(iii) Indivisible units: If the unit of
expenditure is not divisible, then again the law may become inoperative.
(iv) Freedom of choice: If there is no perfect
freedom between various alternatives, the operation of law may be impeded.
Importance of Law
of Equi-Marginal Utility:
The law of equi-marginal utility is of great practical importance. The
application of the principle of substitution extends over almost every field of
economic enquiry. Every consumer consciously trying to get the maximum
satisfaction from his limited resources acts upon this principle of
substitution. Same is the case with the producer. In the field of exchange and
in theory of distribution too, this law plays a vital role. In short, despite
its limitation, the law of maximum satisfaction is meaningful general statement
of how consumers behave.
In addition to its application to consumption, it applies equally to the theory
of production and theory of distribution. In the theory of production, it is
applied on the substitution of various factors of production to the point where
marginal return from all the factors are equal. The government can also use this
analysis for evaluation of its different economic prices.
The equal marginal rule also guides an individual in the spending of his saving
on different types of assets. The law of equal marginal utility also guides an
individual in the allocation of his time between work and leisure. In short,
despite limitations the law of substitution is applied to all problems of
allocation of scarce resources.
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