UNIT 2: UTILITY ANALYSIS

Contents
2.0 Aims and Objectives
2.1 Introduction
2.2 Approaches to Utility Analysis
2.3 The Cardinal Utility Theory
2.4 The Law of Diminishing Marginal Utility
2.5 The Law of Equi-Marginal Utility
2.6 Consumer Surplus
2.7 Summary
2.8 Answers to Check Your Progress
2.9 Model Examination Questions
2.10 References

2.0 AIMS AND OBJECTIVES

The unit discusses the approaches to utility analysis and presents the meaning and Law of
diminishing marginal utility. The unit also presents the meaning of Consumer surplus.

After reading this unit, you will be able to:

 distinguish between cardinal and ordinal approaches to utility analysis;
 explain the law of diminishing marginal utility and its limitations;
 understand consumer surplus.

2.1 INTRODUCTION

Consumers satisfy their through the consumption of goods and services. Goods are
defined as things that have the ability to satisfy a need. Economists call the want
satisfying property of goods as ‘utility’.
‘utility’. In fact, when a consumer buys goods it is not the
goods that are desired but the utility that he derives from the goods. Goods are demanded
by consumers for their ability to satisfy wants. However, the want-satisfying power or
utility is not inherent in goods. Goods posses’ utility because it is imputes to them by the

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consumers. For example, diamonds are like pebbles. But as we attach importance to the
possession of this scarce good, they have a very high value in capitalist societies. But
water, which is essential to life and, therefore, to be considered of very great utility,
commands only a very low and often no more than zero price. For the reason a particular
type of goods will have more utility for some people than it will have for others. Further
more, for a given individual, a particular type of good will have differing amounts of
utility, depending upon the amount consumed. For example when an individual is
hungry, he will be inclined to consume food, which has a high utility for him at the time.
But when he is asked to consume again, he may not be consuming the same quantity and
the utility will be also low. Thus, utility of particular good will vary as the quantity
consumed varies. Therefore, in a technical sense, each unit of a particular good will be
distinct from each other unit.

The consumer is assumed to be rational. Given his income and the market prices of
various commodities, he plans the spending of his income so as attain the highest
possible satisfaction or utility to him. This is the axiom of utility maximization. In the
theory of consumption, it is assumed that the consumer has full knowledge of all the
information relevant to his decision that is he has complete knowledge of all the available
commodities, their prices and his income.

2.2 APPROACHES TO UTILITY ANALYSIS

There are two basic approaches to the problem of comparison of utilities. They are ; (1)
Cardinalist approach, and (2) Ordinalist approach.

The cardinalist approach assumes that utility can be measured. Some economists
suggested that utility can be measured in monetary units, i.e., by the amount of money the
consumer is willing to sacrifice for another unit of a commodity. Others suggested that
utility can be measured in subjective units called ‘Utils’.
‘Utils’. This approach is advocated by
Gossen (1854), Jevons (1871) and Walras (1874) and Aifred Marshall (1890).

On the other hand the ordinal school maintained that utility is not measurable but it is
only comparable. The consumer need not know in specific units the utility of various
baskets of goods according to the satisfaction each basket gives him. The consumer

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would be able to determine his order of preference among the different baskets of goods.
Hicks and R.J.D. Allen are the main supporters of the ordinal school. The main ordinal
theories are the indifference curve approach and the revealed preference approach.

Check Your Progress –1

1. What is meant by cardinal approach to utility?

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2.3 THE CARDINAL UTILITY THEORY

Assumptions
The following are the assumptions behind the cardinal utility approach.

a) Rationality: The consumer is rational. It means he aims at the maximization of his

utility subject to the constraint imposed by his income.
b) Utility is Measurable: The utility of each commodity is measurable. The most
convenient measure is money. The utility is measured by the monetary
units that the consumer is prepared to pay for another unit of the
commodity.
c) Constant Marginal Utility of Money: This assumption is essential if the monetary
unity is used as the measure of utility. The essential feature of a standard
unit of measurement is that it must be constant.
d) Diminishing Marginal Utility: The utility gained from successive unit of a
commodity goes on diminishing as the consumer acquires larger
quantities of it.
e) The total utility of “a basket of goods” depends on the quantities of the individual
commodities. If there are ‘n’ commodities in the bundle with quantities x 1,x2,…….., xn,
the total utility is

U = f (x1, x2…,xn)

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Equilibrium of the Consumer
Let us take a single commodity X. The consumer can either buy ‘X’ or retain his money
income ‘Y’. Under these conditions, the consumer is in equilibrium when the marginal
utility of “X” is equated to its market Price (Px). Symbolically we have

Mux = Px
If the marginal utility of ‘X’ is grater than its price, the consumer can increase his welfare
by purchasing more units of ‘X’. Similarly, if the marginal utility of ‘X’ is less than its
price the consumer can increase his total satisfaction by cutting down the quantity of ‘X’
and keeping more of his income unspent. Hence, he attains the maximization of his utility
when MUx = Px.
If there are more than one commodity, the condition for the equilibrium of the consumer
is the equality of the ratios of the marginal utilities of the individual commodities to their
prices. Symbolically,

MUx = MUx = … … … … … … … = MUn

Px Px Pn

The utility from spending an additional unit to money must be the same for all
commodities. If the consumer derives greater utility on any one commodity, he increases
his welfare by spending more on that commodity and less on the other commodities, until
the above equilibrium condition is fulfilled.

2.4 LAW OF DIMINISHING MARGINAL UTILITY

This is one of the important laws in consumption theory. According to this law, as a
person purchases more and more units of a commodity, its marginal utility declines. In
other words, the more we have of a commodity the less we want to have some more of it.
It is the practical experience of every consumer that as he goes on consuming a particular
commodity, each successive unit gives less and less utility. The law points out that the
marginal utility of a commodity depends upon its quantity but is not proportional to its
quantity. The marginal utility of the commodity to the consumer depends upon the
volume of the stock purchased or possessed already by him. The larger the volume

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possessed or bought by him, the smaller is the utility derived from an additional unit of
the commodity.

Alfred Marshall defined diminishing (marginal) utility as “the additional benefit which a
person derives from a given increase of his stock of a thing, diminishes with every
increase in the stock that he already has. “The above law can be explained with the help
of a simple example. The following table relating to imaginary consumer consuming
bananas illustrates the law clearly.

Table-2.1: Total and Marginal Utilities (in units)

Number of Total Marginal

Bananas Utility Utility
1 15 15
2 25 10
3 30 5
4 30 0
5 25 -5
6 15 -10

From table 2.1 it is clear that as the consumer goes on eating bananas, the additional of
marginal utility goes on decreasing. The 4 th banana gives no additional utility and the 5 th
and 6th bananas have a negative utility. Their consumption instead of giving satisfaction
causes dissatisfaction. If we look at column 2, we will find that the total utility goes on
increasing up to a point. It also seems reasonable that the utility of two bananas should be
more than that of one and so on. But if we look at that more carefully we will notice that
although the total utility does increase, it increases only at a diminishing rate. In the
above table, when the consumer eats the second banana, the increase in utility is 10 units
and when he eats the third the total utility increases by 5 only. This can be explained with
the help of the following diagram.

Diagrammatic Representation

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In diagram 2.1 ‘OX’ axis represents the units of the commodity, i.e.. Bananas and
along’OY’ axis is measured the total and marginal utilities. The total utility curve ‘UT’,
indicates that total utility increases as the consumption of bananas increases. But the
increase is at a decreasing rate. So the marginal utility decreases. At a certain level,
increasing consumption of bananas may not push the total utility up. In the diagram at
point ‘N’ the total utility is the highest where the marginal utility is zero. After that the
total utility also decreases, and then marginal utility becomes negative. In the diagram,
the marginal utility is represented by ‘UM’. The straight lines represent the utility of the
various units of the commodity. The ‘AU’ straight line represents the largest area because
the utility of the first unit is the maximum. But the successive straight lines ‘BD’, ;CE’
are smaller in accordance with the operation of the law. At the 4 th banana (point F) there
is no addition to the total utility, i.e., the marginal utility is zero. And afterwards the
marginal utility is negative which is represented below the ‘OX’ axis. The marginal
utility curve ‘UM’ is sloping downwards to the right because with every increase in the
quantity of the commodity consumed, the marginal utility declines.

Assumptions
The law of diminishing marginal utility is based on three important assumptions. They
are:

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 1. The tastes and preferences of the consumer do not change during the period of
consumption.
2. The units of the commodity are homogeneous i.e., they are same in size and
quality, and
3. There is no time gap between the consumption of the two units of the commodity.
In other words, the process of consumption should be continuous without any
interval.

Limitations or Exceptions

1. The law does not apply in the case of rare collections like stamps paintings
and coins etc. In the case of rare collections, the larger the number the
collects, the greater will be the pleasure. Hence, the law does not apply.
2. When we discuss the law, we are applying it only to normal persons. But
there are some abnormal persons too e.g., misers, drunkards etc. The more
the money a miser has, the greater is the utility that he derives. The more
the drunkard gets pleasure the more he drinks.

Importance
The law of diminishing marginal utility expresses us a basic principle of man’s
behaviour. It is of great practical value to human beings in every walk of life.

1. The law is applied in the sphere of taxation. A rich man is taxed more, fro the
utility of money to a rich man is less than to a poor man. The principle of
progressive taxation is based on this only.
2. The law can also be applied in determining the prices of goods in the market.
An increase in the stock of a commodity brings a person less satisfaction and
therefore he can be induced to buy more only if the price is lowered. Hence,
the greater the supply, the lower should be the price to clear it and vice-versa.
3. The law regulates our daily expenditure pattern. We know that as we go on
buying more of a commodity, its marginal utility falls. Having only a limited
amount of money at our disposal, we do not want to waste it unnecessarily on
the purchase of the same commodity in large quantity. We, therefore, stop

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 purchasing it at a point where the utility of money spent is equal to the last
unit of the good purchased. We spend the rest of our money on other goods.
4. The marginal utility analysis of pricing and the diminishing marginal utility
can quickly dispose of the diamond-water paradox with the aid of this analysis
we can now explain that the relative scarcity of diamonds results in high price,
while the relative abundance of water means that its marginal utility and
consequently its price will be low despite its high total utility.

2.5 THE LAW OF EQUI-MARGINAL UTILITY

It is another important law in consumption theory. This is also known as the Law of
substitution or the equi-marginal principle. It is also called as the Second Law of Gossen
(the law of diminishing marginal utility being Gossen’s First Law), an Austrian
economist who found it. As human wants are unlimited and the resources to satisfy them
are limited, every prudent consumer, therefore, will try to make the best use of the money
at his disposal and derive the maximum satisfaction. In the words of Alfred Marshall if a
person has a thing, which can be put to several uses, he will distributed it among these
uses in such a way that it has the same marginal utility, for if it had a greater marginal
utility in one use than in another, he would gain by taking away some of it from the
second use and applying it to the first.

For getting maximum satisfaction out of the money at our disposal. We carefully go on
weighing the satisfaction obtained from each birr that we spend. If we find that a birr
spent on one commodity had greater utility than in another, we shall go on spending birrs
on the former commodities till the utilities derived from the last birr spend in the two
cases are equal. It means, we substitute some units of a commodity of greater utility for
some units of lesser utility. As a result of this substitution the marginal utility of the
former will fall and that of the latter will rise till the two marginal utilities are equalized.
Hence, this is called the law of Substitution. The following imaginary schedule will
provide us the marginal utilities of two commodities i.e., ‘X’ and ‘Y’.

Table 22: Marginal Utilities of Commodities ‘X’ and ‘Y’

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 Marginal Utility Marginal Utility
Money Units of ‘X’ of ‘Y’
1st Birr 10 8
2nd Birr 8 6
3rd Birr 6 4
4th Birr 4 2
5th Birr 2 0
6th Birr 0 -2
7th Birr -2 -4

In the above table, we are assuming that the consumer has birr 7 at his disposal to spend
on two commodities ‘X’ and ‘Y’. The two utility schedules indicate that the consumer’s
preference for commodity ‘X’ is more marked since he seems to receive more utility
form his consumption of “X’ than from ‘Y’. If he spends his whole income of birr on
commodity ‘X’ alone, he will secure a total satisfaction equivalent to 28 units while if he
spends his entire income on ‘Y’ alone, he will secure only 14 units of utility. But the
consumer will not, however, spend his entire money income on one commodity alone.
The normal consumer behaviour pattern shows that people do not specialize in
consumption. On the basic assumption that he wants to get maximum satisfaction, the
consumer will continue to distribute his limited income on both goods till the marginal
utilities, a birr worth of purchase of the two goods, are equal. From the above utility
schedules we can say that the maximum satisfaction will be attained if the consumer
spends birr 4 on ‘X’ and birr 3 on ‘Y’. The maximum satisfaction will be about 46. In no
there case does this utility amount to this. Now the marginal utility of both commodities
‘X’ and ‘Y’ is same i.e., 4. Thus, we can come to the conclusion that we can attain
maximum satisfaction when we equalize marginal utilities by substituting the more useful
for the less useful commodity.

Diagrammatic Representation
In the two figures given below, we take money units on ‘OX’ axis and marginal utilities
of two goods on ‘OY’ axis. Suppose a consumer has birr 7 to spend on ‘X’ and ‘Y’
whose diminishing marginal utilities are shown by the two curves ‘AP’, and ‘OR’,

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Respectively. The consumer will gain maximum satisfaction if he spends ‘OM’ money
on Y and ‘OM’ on X (4 birr) because in this way the marginal utilities of the two are
equal (PM = PM’). Any other arrangement will give less than total satisfaction. Let the
purchaser spend MN money (one birr more on X and the same amount of money N’M’
(=MN) less on Y. The diagram 22 shows a loss of utility represented by the shaded area
LN’M’P’ and a gain of PMNE utility. As MN = M’M and PM = P’M’ it is proved that
the

Marginal utilities
Marginal utilities

Y Y
AP OR

P P1
E

GAIN OF LOSS
UTILITY UTILITY
0 0
M N X N1 M1 X
Money Money
Fig. 2.2 Equi-Marginal Utility
Figure LN M P (loss of utility from reduced consumption of oranges) is bigger than
1 1 1

PMNE (gain of utility form increased consumption of apples). Hence, the total utility of
this combination will give maximum satisfaction.

Limitations
1. The law is based upon the assumption that a man acts in a perfectly rational
manner when he spends his money-income on a number of different commodities.
If the consumer is ignorant or blindly allows custom or fashion, he will make a
wrong use of money. On account of his ignorance he may not know where utility
is greater and where less.
2. An incompetent entrepreneur will fall to achieve the best result form the units of
land, labor and capital that he employs. This is so because he will not be able to
divert expenditure from less profitable channels to more profitable channels.

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 3. The law does not apply in cases where the resources are unlimited as for example
is the case with the free gifts of nature. In these cases, there is no need of
diverting expenditure from one direction to another.

We had been employing all through our analysis a monetary measure of marginal utility
to make our comparison between the price of a commodity and its marginal utility. The
marginal utility of X in money terms was defined as the maximum amount of money,
which the consumer is willing to pay for an additional unit of X. But the marginal utility
theorists were generally dissatisfied with such a measure. For when money becomes
scarcer, they maintained, its subjective marginal value will increase, like that of any
commodity. Marginal utility must, according to this view, be measured in its own
subjective units. We may call them utile. The view can be referred to as the neo-classical
cardinal utility position. One index that had been developed in this direction is called N-
M index is cardinal and it is intended to be used for making predictions. It is employed to
predict which of two risky alternatives a person will prefer. For example if he has to
choose between two lottery tickets, we are given this individual’s ranking of the
alternative prizes offered by the lottery tickets and the odds on each prize. From this we
wish to be able to infer by numerical calculation, and without actually asking the person,
which lottery ticket he will choose. Even though, by a numerical N-M utility index we
can compute numerical marginal utilities and some of the other measures encounter in
neo-classical utility theory, it is surely not cardinal measurement in the neo-classical
sense.

2.5 THE CONSUMER’S SURPLUS

The concept of consumers’ surplus was introduced in economics by Alfred Marshall,

who maintained that it can be measured in monetary units. In our everyday life, we often
find that the price we pay for a commodity is usually less than the satisfaction we derive
from its consumption. Some times we will be prepared to pay much more for a
commodity than we actually pay. Consumers’ surplus is “equal to difference between the
amount of money that a consumer actually pays to by a certain quantity of a commodity
‘X’ and the amount that he would be willing to pay for this quantity rather than do

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without it”. In some of the items of our daily expenditure, the idea of consumers’ surplus
is quite obvious e.g., a packet of salt, a post-card, a newspaper, a matchbox etc. They are
very useful commodities but at the same time, they are also very cheep. We are,
therefore, prepared to pay much more for them, if need by, than we actually have to pay.
For their purchase, therefore, we derive a good deal of surplus or extra satisfaction over
and above the price that we pay for them this is consumer surplus.
Consumers’ surplus = Total utility – Total amount spent

The following table illustrates the concept of the consumers’ Surplus

Units (Apples Marginal Price Consumers’

In Dozen) Utility (in Birr) Surplus
1 2 3 4
1 20 5 15
2 18 5 13
3 15 5 10
4 11 5 6
5 5 5 0
Total Units Total Total Money
Purchased 5 utility 69 Spent 25 44

In the above table, it is assumed that the price of apples in the market is Br. 5 per dozen.
The consumer wills purchases, as many apples as will make his marginal utility equal to
the price. Thus, he will purchases 5 dozens apples and pay for each dozer Br. 5. Totally,
he spends Br. 25 But his total utility from 5 dozens apples is equal to Br. 69. He, thus,
gets a consumers’ surplus equal to Br. 69 – 2.5 = Br. 44.

The consumers’ surplus can be found out form the fourth column of the table. From the
first dozen of apples, the consumer gets utility equal to Br. 20. Therefore, he consumer
would be ready to pay Br. 20 for it rather than to go without it. But he pays for the first
dozen only Br. 5 because the price of orange in the market is only Br. 5. Therefore, from
the first dozen, he gets consumers’ surplus equal to 20 – 5 = 15. Similarly, he gets Br. 13,
Br. 10 and Br. 6 consumers’ surpluses on the second, third and fourth units. From the
fifth unit the consumer derives utility equal to 5 and he also pays Br. 5 for it. Thus, there

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is no consumers’ surplus on the fifth unit. The total consumers’ surplus is equal Br. 44.
We can also represent consumers’ Surplus with the help of a diagram.

Diagrammatic Representation
In the following diagram, the units of the commodity are measured along ‘OX’ axis and
marginal utility in terms of money is measured along ‘OY’ axis.
Graphically, the consumers’ surplus is
Y
found by this demand curve for

U commodity X and the current market

price, which the consumer cannot
1
P affect by his purchase. In the diagram,
A1
the consumer cannot affect by his
P
A purchase. In the diagram, the
P11
consumers’ demand curves for ‘X’ is a

O straight line UU1 and the market price

M1 M U
1

is ‘A’.
Fig. 2.3 Goods
At this price, the consumer buys ‘M’ units of X and pays an amount AXM for it.
However, he would be willing to pay P1 for M1, P2 for M2 and for P3 for M3 and so on.
The fact that the price in the market is lower than the price he would be willing to pay for
the initial units of ‘X’ implies that his actual expenditure is less than he would be willing
to spend to acquire the quantity ‘M’. This difference is called the consumer’s surplus and
it is represented by the area of the ‘PUA’.

Check Your Progress –2

1. What is consumer surplus?

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2.7 SUMMARY

This unit covered one of the approaches of utility analysis cardinalist approach. In this
the consumer gets the equilibrium when price of a commodity is equal to the additional

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benefit i.e. marginal utility, he derives from consuming that commodity. This condition is
applied even if there are more than one commodity. The law of diminishing marginal
utility states that if you consume more of a commodity without time gap, the marginal
utility you get from that commodity goes on decreasing. Another theory presented is
equi-marginal utility.

2.8 ANSWERS TO CHECK YOUR PROGRESS

1. Cardinal approach assumes that utility can be measured in terms of monetary

units.
2. The utility can be measured in subjective units called ‘utils’
3. The consumer surplus may be defined as the difference between what we are
prepared to pay minus what we have exactly paid.

2.9 MODEL EXAMINATION QUESTIONS

1. Explain the law of diminishing marginal utility with the help of diagram
2. What is equi-marginal utility?
3. What do you mean by consumer surplus?
4. Explain consumer surplus diagrammatically.
5. How do you derive consumer equilibrium is the cardinal utility approach

2.10 REFERENCES

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