Law of Equi-Marginal Utility ( with the help of Schedule and Diagram)

Law of equal marginal utility (If prices are not given this law is known as classical law of substitution in consumption, cardinal approach, or classical theory of consumer behavior; marshallian-approach to consumer equilibrium. “A consumer is in equilibrium when he spends his money on different goods such that MU of the last units good is equal” MARSHAL).

Now we explain the law with the help of schedule and diagram.

                   If consumer has 5 rupees and he spend on two goods “X” and “Y”

Then MU of different units of goods is as under:

money Units	Mux.	money Units	Muy.
1. 2. 3. 4. 5.	16. 12. 10. 8. 6.	1. 2. 3. 4. 5.	14. 10. 6. 4. 2.

 

Explanation. In this schedule x it is supposed that consumer is rational and xwants to maximize his utility and at the same time xutility is measurable into numbers.

Now consumer has three options.

i.if he spend all his money on “x” good, total satisfaction or MU will be 16+12+10+8+6=52

ii.if he spend all his money on “y” good, total satisfaction or MU will be 14+10+6+4+2=36

iii.if he spend his money according to the law of equal marginal utility his satisfaction will be more both of above option.(if he spend 3 rupees on “x” and 2 rupees on “y”) in such a way the MU of the last good are equal 10=10 this is confirmation of the law.

MU gain from first three rupees 16+14+12=42 and from reaming 2 rupee 10+10=20, grand total is =62 which is > 52 and 62 also > 36 (this is the prove of maximum satisfaction).

It is shown in this diagram, with the help of figure.

The consumer is in equ when he spend Rs .3 on good “x” and Rs .2 on “y” he gets MU = 62 here also Mux=Muy and (10=10).

Now if he alter his spending pattern RS.4 on “x” and Rs.1 on “y” gain is 8 and loss is 10 and his total MU 16+12+10+8+14=60 which is < 62 and c not equal to d (8 not equal to 10).

Consumer Equilibrium multi goods model or (if prices are given)

According to the law here “a consumer who has fixed income and the prices of goods also fixed will attain equilibrium when he spend his money in such a way that MU of the last units of goods and their prices are equal” it is as &

i.)   xpx + Ypy+……..=1 (income)

This is budget constraint equation and helps us in getting equilibrium.

                              ii.) Mux/px= Muy/py….Muz/pz  (utility maximization equation)

here x,y,z……..represents goods*……..* Mux marginal utility of x and so on.

Note  .the fulfillment of both condition are necessary for consumer equilibrium.

Explanation: we assume that (income) I= 10  ,px=2  ,py=1

The marginal utility of goods “x” and “y” are assumed as in the schedule

Units of good x	Mux	Units of good y	Muy
1 2 3 4 5	20 15 10 5 0	1 2 3 4 5	8 7 6 5 4

 

Reference this scheduled if consumer purchases 4 units of “x” and 2 units of “y”, then putting them in the budget constraint equation.

v xpx + ypy  =1  by putting the values 4(2) + 2(1) = 10   and 10=10 now we check whether ii condition fulfilled.

Mux/ px=Muy/py      5/2   = 7/1      so…….2.5=7    this is not equilibrium position.

Again we check the consumer equ according the law.if he got 3 units of “x” and 4 of “y”.

v xpx + ypy  =1  by putting the values 3(2) + 4(1) = 10   and 10=10 now we check it again.

Mux/ px=Muy/py …………. 10/2   = 5/1      so…….5=5

All this show, if consumer purchase 3 units of x and 4 of y then he is in the position of equ, and here both conditions are fulfilled.     

The utility maximization principle can also be written as (Mux) (py) = (Muy) (py)       

Or………………………………………………………..Mux/Muy = px/py.

If these two rates are not equal, there will be reallocation until they become equal.

Limitations of the Law

1. in real world it is difficult to measure utility in figure, becoz no consumer has any type of utilometer which could represent satisfaction in util.

2. the comparison of prices and MU is very difficult.

3. now a days the purchase mostly made on the basis of fashion, tradition.but in the utility approach, we do not find glimpses of the above said factor.

4. in daily life consumer purchases “consumer durable” like TV, car etc, their MU cannot ascertained, then how a comparison could be made between MU and prices.

5. utility of money not remain the same becoz when prices falls, the MU of money will rise.