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BUSINESS
ECONOMICS

PAPER No
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5 : UTILITY

TABLE OF CONTENTS
1
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Introduction
3
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Utility Functions
Concept of Utility Functions
Types of Utility Functions
The Cobb-Douglas utility function
The Quasi-linear Utility Function
Perfect Substitutes utility function
Perfect Complements utility function
5
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Summary

1
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Introduction
We mentioned in the module on Law of Demand that the economic model of consumer behaviour
is very simple and can be summarized in one sentence: people choose the best things they can
afford
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For this, we will introduce the concept of
‘Utility’ and explore what role it plays in consumers’ choices
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The theory of consumer behavior has been
formulated entirely in terms of consumer preferences, and utility is seen only as a way to describe
preferences1
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We have already discussed in detail consumers’ demand and its relation with prices ad
income
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3
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Economists define utility as the benefits consumers
obtain from the goods and services they consume
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Moreover the price we are willing to pay is not always
linked to how useful a good is
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Also there are many questions we need
to answer like - how are we supposed to quantify the “amount” of utility/benefits associated with
different choices? Is one person’s utility/benefit comparable to that of another’s? How do the
benefits derived from consumption of different quantities of the same good differ? To answer
1
2

Varian, Hal - Intermediate Microeconomics (8th Edition)
See Varian (8th Edn), Chapter 2
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Economists have discussed various ways to use the indicator of utility to measure benefit derived
by a person from consumption
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Over time economists have identified that all that matters about utility as far
as consumer’s choice behavior is concerned is whether one consumption bundle has a higher
utility than another consumption bundle
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Total Utility (TU):
Total Utility or TU is the total amount of satisfaction or total benefit derived from consuming a
given good or a specific bundle of goods and services in a particular period of time
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e
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However, utility increases at a diminishing rate as consumers consume
more and more of a good
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In case and if a third unit is consumed, then it results in total
utility increasing to 200 units and so on
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This is the point of ‘satiation’ for the consumer, as
thereafter total utility actually declines if more than 6 units of ice cream are consumed in a day
(e
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, the consumer starts feeling ‘sick’ from having so much ice cream in a day !)
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As more and more of a good
is consumed in a given period we expect that the TU will increase at a decreasing rate (hence the
shape of the curve observed in the top panel of Figure 1)
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The total
utility changes with each unit consumed
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Marginal utility (MU):
Marginal utility (MU) is defined as the change in total utility (TU) that can be attributed to
consumption of an additional unit of a good during a particular period of time
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However as
she consumes the third unit, marginal utility diminishes as the additional utility from the third
unit of ice cream is only 40
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e
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e
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e
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e
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Hence marginal utility can also be written as the
following ratio:
MUx = ΔU/Δx
It implies that to calculate the change in utility associated with a small change in consumption of
good x, we can just multiply the change in consumption of x by the marginal utility of x and get:
ΔU = MUx*Δx

Diminishing Marginal Utility
We see the marginal utility is derived from total utility clearly from the example in Table 2
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e
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This is because as we consume more, the good becomes less
desirable with subsequent units giving lesser satisfaction at the margin than the previous unit
consumed
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In the above example, we see that as the consumer moves from 1 st unit to 2nd unit, the additional
utility derived from 2 nd unit (40) is less than what is derived from the 1st unit (100) and it is
consistently declining (MU = 40 for the third unit and so on)
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Another very basic example is water
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The first glass of water you drink gives you immense satisfaction as it
quenches your thirst
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Subsequently the third and fourth glasses of water give even less
satisfaction or utility as your thirst is already quenched
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The above phenomenon is called the Law of Diminishing Marginal Utility3
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additional unit of the good consumed”

An Application: The diamond/water paradox
The paradox in Adam Smith’s 4 words “The things which have the greatest value in use have
frequently little or no value in exchange; and, on the contrary, those which have the greatest value
in exchange have frequently little or no value in use
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A diamond, on the
contrary, has scarce any value in use; but a very great quantity of other goods may frequently be
had in exchange for it
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The maximum
amount a consumer is willing to pay for a given unit of a good depends on the marginal utility he
derives from it; i
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, from the example in Table 2 above, the consumer will be willing to pay the
most for the 1st unit of ice cream consumed and he’d be willing to pay less for additional units
consumed thereafter
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Also willingness to pay depends, ceteris paribus, on the level of
consumption, since the greater the amount consumed, lower is marginal utility
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Whereas diamonds (d) are scarce in
relation to demand and because we use them in small quantities (as compared to water) the utility
derived from the last unit and its price are very high
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However, demand
depends on marginal utility and not on total utility
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Since we consume few diamonds, the MU is high, and consumers are willing to pay a high
price
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The magnitude of marginal utility depends on the magnitude of utility
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This means that marginal utility itself has no behavioral
substance and we can’t calculate marginal utility from a consumer’s choice behavior
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4
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In simple words, utility function (Uf) is a method of assigning a numeric value to each and every
consumption bundle in a way that more preferred consumption bundle gets a higher value than a
less preferred bundle
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It there are two
goods, x and y, then the utility function would be:
Uf = Uf (x,y)
In general, individuals consume many goods and individuals’ preferences are assumed to be
represented by a utility function of the form
Uf (x, y, z,………, l, m)
where x, y, z,…, l, m are the quantities of each of n goods, (X,Y,Z,…
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For simplification, we stick to two commodities X and Y
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i
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If (x1,y1) ≻ (x2,y2), then Uf (x1,y1) > Uf (x2,y2)
There are different types of utility functions
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1
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The Cobb-Douglas utility function

Uf (x; y) = xαyβ
where α > 0 and β > 0 and describe the preferences of the consumer
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The Quasi-linear Utility Function
A Quasi-linear utility function has the following functional form:
Uf(x, y) = F(x) + y
where F(x) is some non linear function of x
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In these functions, the utility function is linear in one good, but (possibly) nonlinear in another;
hence the name quasilinear utility, which means “partly linear” utility
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Perfect Substitutes utility function
If x and y are perfect substitutes, this means the consumer is interested in the total number of
units of x and y he is consuming as both x and y fulfill exactly the same purpose
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Thus it is natural to measure utility by
the total number of x and y
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For example: Green pencils and blue pencils
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Hence they
perfectly substitute each other if available at the same price
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Perfect Complements utility function
A situation directly opposite to the case of perfect substitutes is perfect complements
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they are used in a certain combination by a consumer and may be one without the other will
have no use for the consumer
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This can be expressed in the mathematical form of the following utility function:
Uf (x, y) = Min(αx, βy)
Here α and β are positive parameters, and the term “min” means that utility is given by the
smaller of the two goods in the parentheses
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Now, even if we increase the number of slices but do not
increase the quantity of jam, the utility attained remains the same at two units
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If only both are
doubled (or increased proportionally), then only utility would increase
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5
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One method gives importance to the numerical value of
the utility, which is called cardinal utility; while the other method utilizes the numeric value to
just rank the consumption bundles; it is called ordinal utility theory
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These are
known as cardinal utility theories
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This concept was given by Alfred Marshall, where he mentioned that utility can be
measured in terms of some unit
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If we want to compare the utility
derived from one cup of tea with that of utility derived from one cup of coffee, we use a utility
function to get the value of utility for both
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The numeric value by assigning a higher utility, besides telling the more
preferred good, will also exactly tell us the intensity of preference
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For this, we require a standard unit of measurement in which utility of all goods can be measured
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But the value we place on a good depends on the value
of the measurement unit i
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money
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This means a rupee means same to you whether you are
rich or poor
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It should not be the case that as you get richer, the value of the
extra rupee diminishes; or as the money left with you gets smaller and smaller, we start valuing it
more so that marginal utility of money keeps on increasing
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a) The utility is cardinal – it can be measured quantitatively; b) The
marginal utility of money is constant
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e
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Knowing how much larger doesn’t add anything to the description of
choice
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Another school of thought gave the
concept of ordinality of utility
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Theory of Ordinal Utility
Ordinal utility just ranks the consumption bundles on the basis of utility attained from each
bundle
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Because of this emphasis on ordering bundles of goods, this kind of utility is
referred to as ordinal utility
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This clearly shows that as tea is assigned a
higher number, it gives more utility than coffee and hence tea is preferred over coffee
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Even if coffee gives utility equal to 19 units, then also
tea is preferred over coffee
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Some important points:
 More is better (MIB) - Monotonicity
It says, if one bundle has more of a good than another, and no less of any other goods, then it’s a
prefered bundle
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This assumption fails if you assume that there is a satiation point (when
MU= 0 & MU < 0, thereafter)
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In technical terms, our notion of utility is defined only up to an orderpreserving (“monotonic”) transformation
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Consequently, it makes no sense to ask “how much more is A
preferred than B?” since that question has no unique answer
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A person’s utility is influenced not only by his or her consumption of physical goods,
but also by psychological attitudes, peer group pressures, personal experiences, and the socioeconomic and cultural environment
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This ceteris paribus (other things being equal) assumption is used throughout the analyses of
utility-maximizing choices so as to make the analysis of choices manageable
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Once we have these three assumptions about preferences,
we can use them to find a way to draw a picture of people’s preferences
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Unlike ordinal utility, cardinal utility concept attaches a numerical value to each basket which
cannot be arbitrarily doubled or tripled without altering the differences between the values of
various consumption bundles
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Moreover, we
also cannot make out whether one person gets twice as much satisfaction as another person by
consuming the same consumption bundle
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But here we require just the comparison between different consumption bundles for a
single consumer
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The entire consumer theory tries to explain the consumer behavior based on a consumer’s
preferences
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This concept will be discussed in great detail in the next module
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Summary
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Utility is the satisfaction derived from consuming given good(s) in a particular period of time
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
The Law of Diminishing Marginal Utility states that each additional unit of a good eventually
gives less and less extra utility
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
There can be different types of utility functions; e
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, Cobb Douglas utility function, Quasilinear utility function etc
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While ordinal utility
theory utilizes the numeric value to just rank the consumption bundles in order of preference

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