Law of equimarginal utility

Introduction 

 This law was given by Gossen. It is also known as :- Proportionality  Rule, Law of substitution, Law of maximum satisfaction, Law of Indifference, Gossens second law.

This law tells us how a consumer maximises his total utility.
Marshall defined it as "If a person has a thing which he can put to several uses,  he will distribute it among these uses in such a way that it has the same marginal utility in all."

Explanation 

 Every consumer has unlimited wants but his money income is limited. So he will allocate his given income in such a way that he gets maximum satisfaction from every purchase. For this he will compare the marginal utilities of different commodities he wants to buy and also the marginal utility of each commodity to its price. Since each commodity has a price of its own,  the consumer will so allocate his budget on food,  clothing,  recreation and medical care,  etc, that each good will give him same marginal utility.

This law sets the condition of consumers equilibrium in the case of two commodities as:-
MUa/Pa=MUb/Pb
Where,
MU is the marginal utility of a and b respectively
P is the price of a and b.

It can be reststed as:
MUa/MUb=Pa/Pb

 Diagrammatic and Tabular explanation

 This law can be explained with the help of the table and diagram below:-

Draw the table.....

Suppose the consumer has Rs. 12 to spend.  The price of commodity A(suppose it is an apple) is Rs. 2 and that of commodity B ( suppose it as banana)  is Rs. 1 respectively.

For consumer equilibrium 3 conditions need to be fulfilled.  They are; -

1) MUa/Pa= MUb/Pb
If we apply this formula to each unit of commodities we observe that at work then unit this condiction is fulfilled.
Let's illustrate it-
In the 1St unit:- MUa=100 , MUb= 80 , Pa= 2 and Pb= 1
 So,  MUa/Pa= 100/2=50 and
         MUb/Pb= 80/1 = 80
Which means the above condition is not fulfilled.  So 1ST unit is not the consumer equilibrium point.


****explain this formula for every uinto.

In the given the unit; - MUa=40 , MUb= 20 , Pa= 2 and Pb= 1
 So,  MUa/Pa= 40/2=20 and
         MUb/Pb= 20/1 = 20
Which means the above condition is fulfilled.  So 4TH unit is the consumer equilibrium point.

2) MUa/MUB=Pa/Pb
Since the first condition has been fulfilled in the 4TH unit so we will be testing the 2ND condition also in the 4TH unit only.

In the 4TH unit; - MUa=40, MUb=20, Pa=2 and Pb=1
So,  MUa/MUb=40/20=2
        Pa/Pb=2/1=2
Therefore,  the 2ND condition is also fulfilled by the 4TH unit.

3) the consumer must spend his entire income on the purchase of these two commodities only. Algebraically,
           Y=Pa*A+Pb*B
Again considering the 4TH unit we have:- Y=12, Pa=2, A=4,Pb=1 and B=4
 So.,  12=2*4+1*4=12
Hence the 3rd condition is also fulfilled.

Thus it can be concluded that the consumer will get his maximum satisfaction or equilibrium in the 4TH unit of consumption.

****draw the diagram
This consumer equilibrium has been explained with the help of above diagram where on the vertical axis MUa/Pa and MUb/Pb is measured.  The units of apple and banana are measured on horizontal axis. For equilibrium the consumer will be buying OA units of apple and OB units of banana.

Limitations:-

1) Imperfect Knowledge:- It is assumed that the consumer has perfect knowledge of the alternative choices open to him. But this is not so. Most of the time the consumers are unaware of the other useful alternatives which they can get in order to maximise their satisfaction.

2) Goods Indivisible:- It is assumed that utilities, goods, income etc. are fully divisible. This is again an unrealistic assumption. Though money and utility can be divided according to the consumer's convenience, but goods cant be divided and are hence indivisible.


3) Choices Uncertain:- The choices of consumer are assumed to be certain. But this is again incorrect. Consumer choice is very uncertain. A consumer is never sure about what he will buy with a given money income.

4) Consumer Irrational:- The law assumes that the consumer is rational and of calculating mind. But in actuality no consumer calculates before going to the market or buying commodities. Most of them are driven by their tastes, habits etc. A consumer can never be rational in spending his income.


5) No Fixed Accounting Period:- Another limitation lies in the fact that there is no limit or time period set for a consumer to spend or consume. A consumer can spend anytime and can maximise his satisfaction at any time period according to his convenience.

6) Utility not measurable:- The most important criticism lies in the fact that utility is immeasurable. This law of maximum satisfaction is also based on the assumption of cardinal utility which was discarded by many economists. 



 APPLICATIONS

CONCLUSION




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