24January2017

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## Law of Equi-Marginal Utility

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### 0.1. Statement

Ali is in equilibrium when he spends his money income on different goods in such a way, that MU of the last unit of money spent on each good is equal.

### 0.2. Explanation

This can be explained with the help of the following schedule.

Here it is assumed that the prices of goods and income of the consumer are given, i-e Rs 5. It has to be spend on two goods X and Y. So the MU of these are given as:

 Units of money MU of X MU of Y 1 16 utilities 14 utilities 2 12 utilities 10 utilities 3 10 utilities 8 utilities 4 9 utilities 7 utilities 5 8.5 utilities 6.5 utilities

In this schedule the 1st column shows units of money income to be spent, while the 2nd and the 3rd columns show the marginal utilities the consumer derives from the goods X and Y respectively. (When a consumer uses the units of good X, its MU decreases). The consumer spends the first unit of money on the good X which gives him more utility and gives 16 utilities. Now the 2nd unit of the money is also spent on the above rule and it is spent on Y first utilities and reaches 14 units. Again the third unit is spent on X and takes 12 utilities. The 4th unit of money is spent on Y and it gives 10 utilities. The 5th unit of money is spent on Y and it gives 10 utilities. According to the law, the consumer is in an equilibrium when he spends three units of money on X and two units of money on Y and here the MU of both are equilized and the total utility of the consumer is maximum.

• When the consumer spends Rs 3 on X. It gives 38 utilities, while he spends Rs 2 on Y and takes 24 utilities. So he takes total of 62 utilities.
• Now let he spends Rs 4 on X then its UU is 46 utilities with MY of the 4th units of 8. Again he uses 5th rupee on Y and its UU (MU) is 14. The TU, consumer takes is 60 and it is less than the first distribution. Here MUX and MUY are also not equilized as:

MUX=9 ≠MUY=14

In the same manner any other distribution of the money income on both X and Y does not give the maximum utility.

Now law of EMU will be explained with the help of Diagram:

In this diagram the right horizontal measures the units of money spend on X good and the left horizontal axis shows the units of money on Y good. The vertical axis shows the MU derived from both goods X and Y.

Now when the combination of Rs 3 spents on X and Rs 2 spent on Y, then MU of both goods X and Y are equal. (MUX=MUY) and total utility is maximum, i-e total utility=utility from good X, i-e 16+12+10=38 and utility from good Y= 14+10=24. So, TI=38+16=54. Contrary if we have other distribution Rs 4 on X and Rs 1 on Y is taken then we have MUX=8 while MUY=14. We see that the gain to the total uu is less than loss to TU due to substituting (Rs 1 from Y to X) so the total utitlity is maximized when MUX=MUY, i-e when a consumer spends his money income on the goods in such a way that their M utilities are equalized.

# Consumer's Equilibrium with multiple goods

We have seen that the consumer is maximizing his T.U when he distributes his money income on the goods in such a way that M utilities derived from the goods are equalized.

According to the classical economists the consumer purchases a good until its MU and the price is equal as MU=P.

This was a single commodity case. We can state this rule for two goods case and then can generalize it from any numbers of goods. For two goods or more it is stated as, A consumer having a fixed income and the prices are also given will attain equilibrium when he spends his income on the goods in such a way that the ratio of MU of the last units of the goods purchased and their prices are equal. It is given as

Xpx+ypy+zpz+…..I(i)

And that

Mux/Px=MUy/Py=MUz/Pz…..=I(i)

Here x , y and z are goods, Px, PY, and Pz are their prices, i=income. Mux, MUy and MUz are their marginal utilities.

It can be explained with the help of the following schedule where we have two goods X and Y their prices are Px=2, Py=1 and income=10.

 Units of X Mux Units of Y MUy 1 20 1 8 2 15 2 7 3 10 3 6 4 5 4 5 5 0 5 4

The consumer will use the units of X and Y in such a way that the ratio Mux/Px is equal to MUy/Py according to the rule. In this way its total income will also be spent. We have the distribution of 3x and 4y units where ratios are equal and income is last out.

Here MU of 3rd x=10

P of X=2

Mux/px=10/2=5

Now

MU of 4th y=5

Y=1

MUy/Py=5/1=5

Mux/Px MUy/Py=5

Now we see that income is also last out. We have

I=xpx+ypy

I=3(2)+4(1_=6+4=10

Now we see that the consumer has spent all his income. Any other combination does lead consumers to maximize his utility and be in equilibrium.

From the ratio we can get a ratio of marginal utilities and from prices of the two goods too as

Mux/Px=MUy/Py

Mux.py=MUy.PX

Mux/MUy=Px/Py

It shows that the consumer will be in equilibrium when the ratio of marginal utilities and the ratio of prices are equalized. From this we note, this rule can be generalized for as many as goods are available. Again the ratio of marginal utilities shows the distribution of goods which a consumer wants to make and the ratio of price shows the substitution of goods which a consumer can make actually in the market.

## 1. Limitations of Equi Marginal utility

The law of E.M.U is not applicable in the following cases:

### 1.1. When income, prices and tastes are changing

The law will not hold good result if these are fixed the law will not be applicable.

### 1.2. Indivisible goods

if goods are not divisible then the consumer cannot substitute one good for another, i-e car, cow etc. Then the law will not be applicable.

### 1.3. Custom and fashion

Sometimes people purchases a good as a fashion or custom. There they do not care to equalized M.U so law will not be applicable.

### 1.4. Time problem

Some goods last for short period of time, while some for long period. So, it is difficult to compare the MU of a chair with chicken which is used in no time.

### 1.5. UU is not measureable

In real world we cannot measure UU in a cardinal number. So it is difficult to compare utilities of different goods to find maximum uu. Further it is possible to add or subtract utility.

## 2. Practical Importance

The law of E.M.U has a great practical importance in every field of eco-life. The importance of this law can be proved with the help of the following facts.

### 2.1. its application in consumption

We have unlimited wants and scares resources. The main objective of the consumer will be to achieve maximum satisfaction. He can achieve maximum satisfaction when M.U of different goods consumes are equal.

### 2.2. its application in production

The main objective of a producer is to earn maximum profit. It will be possible only when the marginal utilities of all factors of production are equal.

### 2.3. its application in exchange

Exchange in nothing, but substituting one thing for another. Hence in this department the L.E.M.U has a great importance. Different goods are exchanged in such a way that a sacrifice made by both persons is equal.

### 2.4. its application in distribution

In distribution shares of different factors of production are determined. These shares are determined according to the principles of marginal productivity.

### 2.5. its application in saving and II

As we know y=c+s. If we feel that rupee save has a greater importance in future than consumption. We shall save more. The substitution of spending for saving will go on till the MU of a rupee spent and rupee saved is the same.

• Budget Line
• GNP | GDP | NNP
• Production Function
• Law Of Diminishing MU | Marginal Utility

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