3. Consumer theory and elasticity by Xavier Duran, course workshop director.

The consumer is one of the most important units of study in Economics. The analysis

of the consumer supports the study of why goods are demanded. One useful starting

point in the study of the consumer is the analysis of the demand function outlined in

Unit 2 in this course on Foundations of Economics. Utility theory constitutes one of

the building blocks upon which the demand curve is constructed. Thus, if one defines

utility as the level of satisfaction or well-being obtained from the consumption of a

particular product, the objective of the consumer must be the optimisation of utility.

In this process of optimising utility, nevertheless, the consumer is constrained by her

income and the prices of the products she wishes to buy. The analysis of the consumer

thus focuses on a problem of utility optimisation subject to a budget constraint. By

analysing the effects on consumption as a result of changes in prices through the use

of utility functions and budget constraints we can subsequently define a demand

curve. The analysis of utility, furthermore, also supports the analysis of a large

number of situations involving trade-offs. These are crucial in Managerial Economics.

In a situation where there is a separation of ownership from control which permits

managers to pursue their own objectives, for example, there could be a trade off

between profits and sales. Utility theory supports the analysis of such situations by

ascribing a utility function to management.

Another important issue concerns the analysis of the response of the demand to

changes in its determinants which is known as elasticity. Its application in decision-

making resides in the analysis managers can make of the likely reactions of

consumers to the implementation of strategy. Thus, for instance, the price elasticity of

demand measures the response of the quantity demanded to changes in prices, the

income elasticity of demand measures the response of consumers to changes in

income and the cross price elasticity of demand measures the response of the quantity

demanded of one good to changes in the price of another good. While there are a large

number of elasticity measures and these are not limited to the response of consumers

to changes in demand constituents but can also include supply, we will focus on the

study of demand measures.

This chapter begins with an analysis of utility theory which includes the definition of

utility and the term marginal utility. These are used to build indifference curves which

are then put together with budget constraints to study the decisions of the consumer.

A number of applications of indifference curves analysis into decision-making are

then outlined. The chapter moves on to study the price elasticity of demand and its

contributions to revenue optimising pricing through the total revenue test. The income

elasticity of demand and the cross price elasticity of demand are also outlined. These

will be used in Study Guide 3 in the Managerial Economics course.

3.1 Indifference curves and budget constraints

The concept of utility is central to the study of the consumer. In Economics, utility is

used to measure the well-being obtained by consumers from the consumption of

output. The measurement of utility, in turn permits us to summarise the preferences of

the consumer. Furthermore, the consumer’s income and the prices of goods are used

to estimate consumption possibilities. Thus, one of the objectives of the current unit is

to construct a framework to support the study of the consumer who not only orders

her preferences in terms of utility, but who is also subject to her budget. In the context

of the issues commented, this section will begin with the study of preferences and the

measure of utility. It will then continue to describe the budget constraint, and it will

conclude by superimposing utility curves on budget constraints to encounter the

optimal consumption of goods and services.

3.1.1 Utility

Utility is defined as a measure of the satisfaction or well-being consumers obtain from

the consumption of goods and services. Thus, if a consumer drinks 3 cups of coffee,

her utility would be measured by the satisfaction she would gain from the 3 cups.

The relationship between the quantity of a good or a service consumed (q) and the

utility obtained (U) is summarised by a positively sloped utility function. The utility

function is expressed below:

)(qfU = (3.1)

The term marginal utility, on the other hand, measures the change in utility resulting

from a one unit increase in the consumption of a good or service. It refers to the

contribution to utility resulting from consuming one extra unit of a product. The

contribution to utility from consuming the third cup of coffee would therefore be the

marginal utility of the third cup.

While we will assume, for simplicity that the higher quantity of a good or service

consumed, the higher the total utility, which determines the positive slope of the

utility function, we will also assume that extra units contribute less to total utility or

diminishing marginal utility. This assumption results from the contention that

consumers tend to grow tired of goods and services as their consumption increases,

and it is known in Economics as the ‘Law of diminishing marginal utility’. Figure 3.1

illustrates the representation of a positively sloped utility function, where utility

increases with quantity consumed, and where marginal utility diminishes with higher

output.

Figure 3.1 Utility curve

U

q

One of the main problems of the concept of utility resides in its difficulty to be

measured. Consumers cannot put a quantitative value to the utility they obtain from

consumption but only order. Thus, consumers are able to qualitatively put an order to

their preferences and state that they prefer one consumption bundle to another but not

by how much. Notwithstanding this limitation, the use of utility functions continues to

constitute the foundation of the theoretical study of consumer behaviour analyses. The

concept of utility is used in a number of applications in Managerial Economics. For

example, in decision making analysis utility functions are used to measure decision

makers’ attitude to risk.

3.1.2 Indifference curves

The analysis of utility could be extended to measure the well being obtained from the

consumption from bundles of two or more goods. This permits economists to analyse

of a trade off between two goods. In this sense, one must define indifference curves as

curves which summarise the bundles of two goods that yield a constant level of

utility. Consumers are thus indifferent to any of the bundles of goods along an

indifference curve since utility is constant. Figure 3.2 illustrates an example of an

indifference curve:

Figure 3.2 Indifference curve

The level of utility is held constant along the indifference curve. Thus, consumers are

indifferent between bundle A or B in Figure 3.2 as they are on the indifference curve

where utility is held unchanged. As consumers move from bundle A to bundle B, they

give up in the consumption of q2 in order to increase in the consumption of good q1

holding utility constant. Consequently, there is a trade off between the consumption of

the two goods.

While an indifference curve allows comparisons between bundles which yield

constant utility, one must illustrate an indifference map if it is wished to analyse

bundles with different utilities. There is an indifference curve for every level of

B

A q0

q1

q0

q2

q1 q1

U

●

●

utility. But because there are infinite levels of utility, there will be infinite

indifference curves. An indifference map plots a whole set of indifference curves.

Figure 3.3 Indifference map

Higher levels of utility are depicted in Figure 3.3 as higher indifference curves. Thus,

consumers are indifferent between bundles A and B located on the same indifference

curve but prefer bundle C to bundles A and B as it is on indifference curve U1

connected to a higher level of utility. In turn, consumers prefer any bundle on U2 to

bundles on U1.

3.1.3 Slope of indifference curve

One key feature of the indifference curves analysed up to this point is that they are

convex to the origin. This implies that their slope changes. As one moves on the

indifference curve downwards, the slope decreases. The reason for the diminishing

slope will be explained in Section 3.1.4.

The slope of the indifference curve is known as the ‘marginal rate of substitution’

(MRS) and it measures the amount of one good that must be given up in consumption

in order to increase the consumption of the other good by one unit holding utility

constant. In other words, it measures the opportunity cost of consuming one extra unit

of a good. Mathematically, the MRS at one point on the indifference curve is

measured by the derivative of the utility function with respect to the quantity

demanded of one good at the particular point and is illustrated as the slope of the

tangent line to the utility function at the point.

Figure 3.4 Decreasing indifference curve slope

U0

U2

●

●

●

q2

q1

U1 A

B

C

q2

q1

U1

●

●

●

Figure 3.4 illustrates the ‘Law of diminishing MRS’. As a consumer decides to

increase her consumption of the good or service measured on the horizontal axis, she

is willing to give up less of the good measured on the vertical axis. The MRS thus

diminishes.

3.1.4. Characteristics of indifference curves

This subsection focuses on three of the main characteristics of indifference curves we

will use for the purposes of the Managerial Economics course. It must be noted that

indifference curves could differ from the ones presented in this unit. Their shape is

not necessarily convex to the origin and in some cases they are not negatively sloped,

however, the most general analysis of indifference curve outlined in this section

suffices for the purposes of our study.

• Negatively sloped

The negative slope of the indifference curve illustrates the fact that in order to

consume higher amounts of one good consumers must give up in the consumption of

the other if they are to hold utility constant. The slope of the indifference curve, thus,

determines a trade off.

• Convex to the origin

While the previous subsection demonstrated that the ‘Law of diminishing MRS’

resulted in a convex indifference curve, we must demonstrate why this law operates.

The ‘Law of diminishing marginal utility’ is the key to the demonstration of the ‘Law

of diminishing MRS’. As consumers consume more of a good or service, it was

contended they would obtain smaller marginal utility. This means consumers value a

product less as they consume additional units. Given decisions between two goods,

thus, consumers will value a good less the more they consume of it which means they

will be willing to give up less of the other good. The MRS thus must diminish.

• Indifference curves cannot intersect

Figure 3.5 Indifference curves do not intersect

q2

q1

U0

U1

● ●

●

A

B

C

Because A and B in Figure 3.5 are bundles on the same indifference curve U0, they

are equally preferred. Likewise, because A and C are in turn bundles on the same

indifferent curve U1, they are equally preferred. Because consumers are indifferent

between A and B and A and C, we can conclude they are indifferent between B and

C. However, a closer look to Figure 3.5 shows that, while including the same amount

of q1, bundle C includes a higher amount of q2 than bundle B, which means

consumers would prefer C to B. This contradicts the previous contention that

consumers were indifferent between bundles B and C. Therefore utility curves cannot

intersect.

3.1.5 The budget constraint

The budget constraint summarises the bundles of two goods a consumer can afford

given her income and the prices of the goods. Indifference curves summarise the

subjective preferences of consumers, but do not illustrate their ability to consume

them. Thus, the superimposition of the budget constraint on the indifference curve

map is necessary if one wishes to analyse the highest utility one consumer could

obtain given her budget.

The budget constraint can be expressed in terms of the income of the consumer (M),

the price of 1q and the price of 2q :

2211 qpqpM += (3.2)

where 11qp represents the expenditure on q1 and 22qp represents the expenditure on

q2.

Figure 3.6 illustrates the budget constraint:

Figure 3.6 The budget constraint

Bundles of goods included in the region below the budget constraint illustrated in

Figure 3.6 can be afforded by consumers who do not spend all their income. The

bundles on the budget constraint can be afforded when consumers spend all their

income. Bundles included in the region above the budget constraint cannot be

afforded even when consumers spend all their income.

q2

q1

Other key points in the analysis of the budget constraint concern its slope and

position. The slope of the budget constraint is determined by the relative prices of the

two goods with a negative sign to indicate the negative slope: 21 pp− . An increase

in p1 relative to p2 results in a steeper budget constraint. On the other hand, a

reduction in p1 relative to p2 results in a flatter budget constraint. The budget constrain

will shift upwards to the right when consumers’ income increases and will shift

downwards to the left when income decreases.

3.1.6 Consumer equilibrium

The Consumer’s objective is to optimise utility subject to a budget constraint. Thus,

consumers try to reach the highest indifference curve given their income and the

prices of the goods.

The highest indifference curve that can be reached is the one that shares a tangency

point with the budget constraint.

Figure 3.7 Consumer equilibrium

Figure 3.7 illustrates that the highest indifference curve consumers can reach is U1 as

it shares a tangency point with the budget constraint. Consumers optimise their utility

when they consume q1* and q2*. At this equilibrium point, the slope of the budget

constraint is equal to the MRS.

3.1.7 Applications of consumer theory

There are a large number of applications of consumer theory. The use of utility

functions in decision-making analysis to describe attitudes to risk was already

outlined. Indifference curve analysis also plays a key role in explaining a large

number of economic phenomena. For example, it constitutes the theoretical basis used

to derive demand curves. In this sense, one could analyse the effects of changing the

price of a good or a service on the budget constraint and in turn on new consumer

equilibria. Similarly, the illustration of the effects of changes in prices on the quantity

demanded results in the demand curve. Indifference curves are also used to analyse

the effects of public policies on the labour market. Increased taxes, for example, could

have an impact on the budget constraint used in the analysis of workers who must

q2

q1

U1

U2

U0

q1*

q2* ●

decide on whether to work more to outweigh their reduced purchasing power or to

work less as their work becomes worse paid. This analysis, in turn would

consequently define the labour supply curve.

But our interest in the analysis of indifference curves and budget constraints is rooted

in their role in explaining management decisions and in the description of the

objective of businesses under the separation of ownership from control. These issues

will be explored in Study Guide 1 in the Managerial Economics course where it is

contended that indifference curves can be ascribed to management behaviour. In this

context, managers may derive utility from both making profits and revenue, but there

may be a trade off between the two of them which can be illustrated with the use of an

indifference curve. In their pursuit to maximise utility, nevertheless, managers are

constrained by a profit function where output acts as a proxy for sales.

Figure 3.8 Managerial indifference curve

Figure 3.8, in this context illustrates Baumol’s contention that due to the separation of

ownership from control in modern corporations, management who have discretion

over the resources of the firm, may be able to increase revenue above the level

consistent with profit maximisation as long as their revenue contributes to their utility.

The tangency point between the profit constraint and management’s indifferent curves

occurs to the right of the profit maximising level of revenue.

Study Guide 1 contends that the use of indifference curves to ascribe management

behaviour can also be used to illustrate other theories built in the context of the

agency relationships resulting from the separation of ownership from control such as

Marris’ theory of growth and Williamson theory on management discretion. These

issues will be explored in detail in Unit 1 and in the workshops in the Managerial

Economics course.

profit

sales

●

U

Qpm Qs

πpm

πs

3.2 Elasticity

One of economists’ and businessmen most useful tools for the purpose of sensitivity

analysis is the use of elasticity. It is not difficult to underline the contribution of the

concept of elasticity to managerial decision-making as it measures the responsiveness

of a number of variables to the implementation of potential strategies. The ex ante

application of the concept of the price elasticity of demand, for example, resides in its

contribution to the understanding of the likely response of customers to price changes.

The ex post application of the price elasticity of demand, in contrast, permits the

evaluation of the effectiveness of price changes concerning customer response which,

coupled with the study of competitors’ reactions, constitutes the foundation for the

analysis of future price changes. While there are a large number of elasticity

measures, our focus is on demand measures of elasticity. This is the reason for the

inclusion of the concept of elasticity in a chapter dedicated to consumer theory.

3.2.1 The concept of elasticity

Elasticity is defined as a measure of the responsiveness of one variable to changes in

another variable. One could measure elasticities for a large number of pairs of

variables. Usually in Economics, measures of elasticity study the response of a

quantity variable to changes in another variable. Thus, for instance, the price elasticity

of demand measures the response of the quantity demanded to changes in prices, the

cross price elasticity of demand measures the response of the quantity demanded of

one good to changes in the price of another good or the price elasticity of supply

measures the response of the quantity supplied to changes in prices. Our focus is on

the price elasticity of demand, the income elasticity of demand and the cross price

elasticity of demand.

3.2.2 The price elasticity of demand

The price elasticity of demand measures the response of the quantity demanded to

changes in prices. This responsiveness is measured in percentage terms. Expression

(3.3) below summarises the computation of the price elasticity of demand ( pε ):

p

qd

p∆

∆=

%

%ε (3.3)

where dq∆% is the percentage change in the quantity demanded and p∆% is the

percentage change in price.

When the price change results in a more than proportionate change in the quantity

demanded, the term dq∆% is larger than p∆% which implies an absolute value of the

price elasticity of demand ( pε ) greater than one. The demand function is considered

to be ‘elastic’. In contrast when the price increase or decrease results in a less than

proportionate change in the quantity demanded, the term dq∆% is smaller than p∆%

which results in an absolute value of the price elasticity of demand pε smaller than

one. The demand function is considered ‘inelastic’. Only when the price change

results in an equally proportional quantity change, the absolute value of the price

elasticity of demand pε is one.

Because we only consider negatively sloped demand curves, the relationship between

the price and the quantity demanded is negative. This results in a negative price

elasticity value. For simplicity, nevertheless, a large number of economists consider

the absolute value of the price elasticity of demand ( pε ). Thus, the formula can take

the values summarised by Table 3.1.

Table 3.1 Price elasticity of demand

pε <1 inelastic

pε =1 unit elastic

pε >1 elastic

In the extreme when any change in the price does not effect the quantity demanded,

the pε =0 and the demand curve is illustrated as a vertical line. In contrast, when the

price change results in an infinite change in the quantity demanded, pε = ∞ , the

demand function is plotted as a horizontal line. The demand functions are ‘perfectly

inelastic’ and ‘perfectly elastic’ respectively.

3.2.3 Computation of the price elasticity of demand

There are two main methods used in the computation of the price elasticity of

demand. The method used depends on the purpose of the study and the data set

available. Thus, given two points on a demand curve, one can only compute the price

elasticity of demand on the ‘arc’ defined between the two points. In contrast, a

demand function, expressed in its mathematical form, permits the computation of the

price elasticity of demand at any one point on the demand curve. While the first is

known as the ‘arc’ measure of the price elasticity of demand, the latter is known as

the ‘point price elasticity of demand’. The usefulness and selection of the measure

depends on the study the analyst wishes to perform on the demand function.

The ‘arc price elasticity of demand’ measures the value of the price elasticity between

two points on a demand function. The formula for the price elasticity of demand is

thus developed to consider the two points.

0

0

%

%

d

dd

pq

p

p

q

p

q⋅

∆

∆=

∆

∆=ε (3.4)

where dq∆ is the change in the quantity demanded from the original to the new point

on the demand curve, p∆ is the change in price, 0p is the original price, and 0

dq is the

original quantity demanded.

Note that while we have based our percentages from the original point with values p0

and q0, one could base the percentage on the middle point or any point as long as the

calculations used were consistent through the analysis.

Figure 3.9 illustrates graphically the calculation of the ‘arc’ price elasticity of

demand.

Figure 3.9 ‘Arc’ price elasticity of demand

Suppose, for example, two points on a demand function are given: p0=9, q0=98, and

p1=39, q1=10. The absolute value of the arc price elasticity of demand would be:

269.098

9

939

9810=⋅

−

−=pε

Because the absolute value is smaller than 1, the demand curve between the two

points is considered to be inelastic.

In contrast to the ‘arc’ measure, the ‘point price elasticity of demand’ measures the

value of the price elasticity of demand at one point on the demand function. This

measure results from reducing the arc existing between two points on a demand

function so much that the difference becomes infinitesimally small. The intuition

explaining this reduction is that the price elasticity of demand is computed at one

point. Mathematically, this can be expressed with the use of the derivative of the

demand function at that particular point:

0

0

%

%

d

dd

pq

p

dp

dq

p

q⋅=

∆

∆=ε (3.5)

where dp

dqd is the derivative of the demand function with respect to the price.

qd

p

D

●

●

q0 q1

p0

p1

∆q

∆p

E0

E1

Suppose a demand function is given as pqd 839 −= , the absolute value of the point

price elasticity of demand at a point where p=3 and q=15 is calculated below

6.115

38 =⋅=pε

Because the absolute value of the point price elasticity of demand is greater than 1,

the demand curve at this point is elastic.

3.2.4 The total revenue test

One of the main applications of the concept of the price elasticity of demand to

managerial decision-making concerns the relation existing between the values of

elasticity along a demand function and the total revenue function. Unit 2 of this

course on Foundations of Economics introduced this issue by showing that linear

demand functions determine the fact that total revenue increases and then reduces as

output increases (See Section 2.2.2). Our analysis in this unit is extended by the

contention that the value of the point price elasticity of demand changes along a linear

demand function. Management can then implement appropriate price strategies in

order to increase total revenue as long as they know the elasticity of the demand faced

by the business.

One useful starting point is the analysis of the formula used to calculate the point

price elasticity of demand. This formula, summarised by expression (3.5) is composed

of two main parts: the derivative of the demand function with respect to price

( dpdqd ) and the price to quantity ratio ( dqp ). Because the geometric

interpretation of the derivative of a function at one point is the slope of the function at

that point, the derivative of the demand function must be constant along the linear

demand function. In contrast, the second term in the formula concerns the ratio price

to quantity demanded which decreases as one moves downwards along the demand

function. The value of the price elasticity of demand thus decreases as the price is

reduced and the quantity demanded increases. This issue is crucial in economics as it

implies that a linear demand function is always split into different price elasticity

ranges: an elastic range for high prices, a point where the demand is unit elastic and

an inelastic range on the bottom of the demand function. The elastic and the inelastic

ranges of the demand function coincide with the sections of the total revenue function

that increase and decrease respectively as the quantity demanded increases. The level

of output where the demand is unit elastic in turn coincides with the revenue

optimising level of output. Figure 3.10 extends the illustration of the relationship

between the demand and revenue functions to include the elasticities consistent with

different sections of the demand function. This relationship is known as ‘the total

revenue test’.

Figure 3.10 The total revenue test

The relationships summarised by Figure 3.10 offer prescriptions for management

optimising revenue. Thus managers should reduce prices when the demand is elastic

and increase prices when the demand is inelastic. Table 3.2 summarises the effects of

increases and decreases in prices on total revenue.

Table 3.2 Total revenue test

Inelastic demand

pε <1

Elastic demand

pε >1

↑p ↑TR ↓TR

↓p ↓TR ↑TR

The usefulness of the total revenue test resides in the prescriptions it offers to revenue

optimising managers. Nonetheless, the test can be criticised since it does not consider

the competitive response of rivals in oligopolistic industries. While consumers

increase the demand for a good when a firm decreases its price on the elastic range of

the demand curve in order to increase revenue, competitors may match a price

decrease so as not to lose market share. Other problems connected to the test are

discussed in much detail in Study Guide 3 in the Managerial Economics course.

3.2.5 Determinants of price elasticity of demand

The price elasticity of demand varies from one product to another. The demand for

some products like petrol is very inelastic, while the demand for other products such

as luxuries is very elastic. This section outlines some of the determinants of the price

elasticity of demand.

• The number and closeness of substitute products. This is one of the most

important determinants of the price elasticity of demand. The possibility of

buying substitute products implies customers’ response to price changes is

●

p

TR q

q

D=AR MR

TR q*

p*

q*

pε >1

pε =1

pε <1

huge compared to situations where there are no substitutes. In this sense, the

smaller the number and the more differentiated products are, the more inelastic

the demand function. In contrast, the higher the number and the closer

substitute products are, the more elastic the demand. Thus, customers decrease

the demand for green beans more than proportionately when their price is

increased since there are many other vegetables they can buy but keep buying

petrol even when its price increases as they cannot use other substitutes. The

demand for vegetables is therefore quite elastic while the demand for petrol is

quite inelastic. Producers could try to differentiate their products from those

produced by their competitors in order to gain sustainable competitive

advantage which can, in turn, result in more inelastic demands and the

possibility, through the total revenue test, to increase prices and profits.

• The time period. The longer the time period under consideration the more

elastic the demand is likely to be. This is due to the fact that consumers are

able to adapt to price changes over time. Thus, for example, while the demand

for petrol is very inelastic in the short run, it tends to be more elastic over time

as consumers find other substitutes. A consumer who uses the car to get to

work every day will still have to buy petrol even if its price doubles in the

short run, however, in the long run, she may decide to use public transport,

buy a smaller car or even change the job. Europe became more efficient over

time in the use of petrol after the 1970s petrol crises by using less energy,

promoting smaller engines than their American counterparts and by

encouraging the use of other energy sources like gas.

• Proportion of income spent on the good. The lower the proportion of

income spent on the good, the more inelastic the demand is likely to be. In

contrast, the higher the percentage of income spent on the good, the more

elastic the demand is likely to be. If a consumer with a yearly income of

£39,000, for instance, buys 5p worth of chewing gum every morning, she is

not likely to stop buying chewing gum when its price goes up by 100 per cent

to 10p because 10p represents a minute percentage of total income. In contrast,

a miniscule percentage change in the price of a car, which constitutes a high

percentage of her yearly income, would have a large effect on the consumer’s

decision to buy it.

• Habit creating and addictive goods. When consumers are addicted to some

products, they are not likely to reduce their consumption much when their

price increases. Thus, goods such as cigarettes, alcohol or drugs are consumed

even when their prices increase. Their demand is inelastic. Governments who

need a quick source of income tend to increase indirect taxes in these goods

because due to their inelastic demand, consumers will buy them even when

their prices increase.

• Luxuries and necessities. The demand for luxuries tends to be more elastic

than the demand for necessities. Consumers could stop buying luxuries should

their price increase but must buy necessities even when their price is

increased.

3.2.6 The income elasticity of demand

The income elasticity of demand is useful in analysing the response of customers to

changes in their incomeu. The income elasticity of demand measures the percentage

response of the quantity demanded to a percentage change in income as summarised

by expression (3.6)

Y

qd

y∆

∆=

%

%ε (3.6)

where yε is the income elasticity of demand, dq∆% is the percentage change in the

quantity demanded, and Y∆% is the percentage change in the income of the

consumer.

When an increase (decrease) in the consumer’s income results in a decrease (increase)

in the quantity demanded, the value of the income elasticity demand is negative.

Products that have a negative income elasticity of demand are known as inferior

goods. Examples include low quality food or cheap clothes.

In contrast, when an increase (decrease) in the consumer’s income results in an

increase (decrease) in the quantity demanded, the value of the income elasticity of

demand is positive. Goods that have a positive income elasticity of demand are known

as normal goods. These goods can be further divided into subsistence or luxury goods

depending on whether a change in consumer’s income results in a less or a more than

proportionate change in the quantity demanded respectively. The income elasticity of

demand of subsistence goods thus is smaller than 1. Examples of subsistence goods

include computers or books. In contrast, the income elasticity of demand of luxuries is

greater than 1. Examples of luxuries include designer products.

Note that the sign of the income elasticity of demand is important in order to

determine whether goods are inferior or normal. While in the computation of the price

elasticity of demand, the sign is ignored for simplicity, it is crucial to indicate whether

there is a positive or a negative relationship between income and the quantity

demanded.

Table 3.3 summarises the types of goods depending on the value of the price elasticity

of demand.

Table 3.3 Income elasticity of demand

Income elasticity of

demand value

relationship Type of good

0<yε negative Inferior good

10 << yε positive Subsistence good

1>yε positive luxuries

Some organisations include a number of types of goods in their product portfolios to

minimise the risk of the business cycle fluctuations. Thus in booming phases of the

business cycle, sales of normal goods increase as income levels increase. In contrast,

firms can increase sales of inferior goods during economy recessions.

3.2.7 The cross price elasticity of demand

In some cases goods are related to each other in such a way that changes in the price

of one good results in changes in the quantity demanded of another good. In this

sense, when goods are related, they can be complements or substitutes. The ‘cross

price elasticity of demand’ indicates whether or not any goods are related and

measures the strength of the relationship.

The cross price elasticity of demand measures the response of the quantity demanded

of one good B to changes in the price of good A. the formula that measures the cross

price elasticity of demand is expressed below.

A

B

ABp

q

∆

∆=

%

%ε (3.8)

where ABε is the cross price elasticity of demand, Bq∆% is the percentage change in

the quantity demanded of product B, and Ap∆% is the percentage change in the price

of good A.

When an increase (reduction) in the price of good A results in a reduction (increase)

in the quantity demanded of good B, the value of the cross price elasticity of demand

is subsequently negative. The goods are complements. Computers and printers

represent an example of complement goods.

In contrast, when an increase (reduction) in the price of good A results in an increase

(reduction) in the quantity demanded of good B, the value of the cross price elasticity

of demand is subsequently positive. The goods are substitutes. Examples of

complement goods include coffee and tea (although in some cultures they are taken

together).

The closer the cross elasticity of demand is to 0, the less related two products are. The

more negative and the more positive the cross price elasticity of demand, the stronger

complements and substitutes the pair of goods are respectively.

Table 3.4 summarises the relationships depending on the cross price elasticity of

demand.

Table 3.4 Cross price elasticity of demand

Cross price elasticity of demand

ABε

relationship

0<ABε complements

0=ABε unrelated

0>ABε substitutes

The cross elasticity of demand is useful in determining which are the products

competing in the same industry. It is crucial for example to know any firms’ substitute

products in the analysis of the likely response of competitors to the implementation of

any strategy.

The cross price elasticity is also used in the study of a relevant market as a first step in

antitrust investigations. Thus, for example, should a firm report a competitor for

anticompetitive practices such as predatory pricing or abuse of dominant position to

the competition authorities, it will firstly need to prove that they compete in the same

market. The cross price elasticity of demand is used to determine whether or not the

goods produced by the two firms are substitutes.

3.3 Conclusion

This unit has presented some crucial concepts in Economics related to the consumer.

On the one hand, the contribution of indifference curve analysis to decision making

was highlighted. Indifference curves will be used in Unit 1 in the Managerial

Economics course to describe the behaviour of the firm in a world where management

and ownership are divorced. On the other hand, the concept of the price elasticity of

demand and its application to revenue optimising pricing were outlined. The unit also

included the study of the income elasticity of demand and the cross price elasticity of

demand. These concepts will be used in Unit 3 in the Managerial Economics course

to study the response of customers and competitors to the implementation of

strategies.

References and further reading

Baumol, ‘On the theory of Oligopoly’, Economica, N.S. 25, 1985, p.187-98.

Cook, M. and Farquharson, C., Business Economics, United Kingdom, Financial

Times Prentice Hall, 1998.

Davies,H. and Lam, Managerial Economics. An Analysis of Business Issues, United

Kingdom, Financial Times Prentice Hall, 2001.

Katz, M. and Rosen, H., Microeconomics, United States of America, Mc Graw-Hill,

1998.

McNutt, P., Managerial Economics Unit 1. Management Objectives and Stakeholder

value, Bangor, U.K., Business & Management Education Limited, 2005.

McNutt, P., Managerial Economics Unit 2. Cost Leadership and the Production

Process, Bangor, U.K., Business & Management Education Limited, 2005.

McNutt, P., Managerial Economics Unit 3. Strategic Rivalry and the Competitive

Process, Bangor, U.K., Business & Management Education Limited, 2005.

Sloman, Essentials of Economics, United Kingdom, Financial Times Prentice Hall,

2004.