Download With a price elastic demand

OHT 2.1
CHAPTER 2.
The analysis of consumer demand
•
The market demand curve.
•
Utility and the demand curve.
•
Consumer surplus.
•
The determinants of demand.
•
The classification of goods.
•
Concepts of elasticity.
•
The relationship between price elasticity and
sales revenue.
Learning outcomes
OHT 2.2A
This chapter will help you to:
• Understand why changes in price affect consumer demand and, in
particular, why demand curves are normally downward sloping, i.e.
the law of demand.
•
Understand why demand curves may shift in response to changes
in various factors, other than price, which impact upon demand
(known as the conditions of demand).
•
Analyse the nature of the relationship between marginal utility and
the demand curve for any product or service.
•
Appreciate the meaning and importance of consumer surplus in the
context of pricing strategies.
Learning outcomes
OHT 2.2B
•
Interpret the relative importance of income and substitution effects
on demand when the price of a good or service changes.
•
Classify goods and services according to how demand responds
to changes in price and income, giving rise to the terms normal,
inferior, Giffen and Veblen goods or services.
•
Calculate price, cross-price and income elasticities of demand
and interpret the significance of the results.
•
Appreciate the relationship between price elasticity, marginal
revenue and total revenue arising from the sale of goods or
services.
The market demand curve
OHT 2.3
A consumer’s demand curve relates the amount
the consumer is willing to buy to each conceivable
price for the product.
The market demand curve for a good or service is
derived by summing the individual demand curves
of consumers horizontally for any given price.
OHT 2.4
Figure 2.1 Derivation of the market demand curve
OHT 2.5
The law of demand
In general there is a central law of demand, which
states that there is an inverse relationship
between the price of a good and the quantity
demanded assuming all other factors that might
influence demand are held constant .
OHT 2.6
Figure 2.2 Linear and non-linear demand relationships
Utility and the demand curve
OHT 2.7
The term utility describes the pleasure, satisfaction or benefit derived
by a person from the consumption of goods or services.
Marginal utility is the addition to total utility as a consumer purchases
each extra unit of a good or service.
Consumer equilibrium
MU z
MU a MU b

... 
Pa
Pb
Pz
where
MU =marginal utility
P =price
a ,b ,...,z =various goods and services consumed
Consumer surplus
OHT 2.8
Consumer surplus is the excess of the price which a person would
be willing to pay rather than go without the good, over that which he
or she actually does pay.
Marginal utility and water shortages
OHT 2.9A
Determinants of demand
• The ‘own price of the good itself (P0 ).
•
The price of substitute goods (Ps ).
•
The price of complementary goods (Pc ).
•
The level of advertising expenditure on the
product in question, a , as well as on
complementary and substitute products, b,...,
z (denoted Aa,b,…..z).
•
The level and distribution of consumers
disposable incomes (Yd ),i.e.income after
state direct taxes and benefits.
Determinants of demand
OHT 2.9B
•
Wealth effects (W )caused by, for example, stock
market booms, rising house prices, windfall gains,etc.
•
Changes in consumers tastes and preferences (T ).
•
The cost and availability of credit (C ).
•
Consumers expectations concerning future price rises
and availability of the product (E ).
•
Changes in population (POP),if we are examining the
total market demand.
Demand function
Qd  f P0 , Ps , Pc , Aa ,b... z , Yd ,W , T , C , E , POP 
OHT 2.10
Figure 2.3 Shift in the demand curve
When the own price of a product changes, the outcome is a movement along the
demand curve and when any other determinants of demand change, there will
be a shift of the demand curve (either to the left, showing a fall in the quantity
demanded, or to the right, showing a rise) depending on the nature of the
change.
OHT 2.11
Figure 2.4 Examples of changes in the conditions of demand (demand curves
DD refer to the good in question)
OHT 2.12
Classification of products
•
Normal products.
•
Inferior products.
•
Giffen products.
•
Veblen products.
Classification of products
OHT 2.13
Normal products
Goods and services may be classified as ‘ normal products段if the quantity
demanded rises as incomes rise and falls as incomes fall.
Inferior products
Certain products are classified as ‘inferior’ because the demand for them falls as
incomes rise (and vice versa).
Giffen products
A special case of the inferior product arises when,as price rises ,more of the
good in question is bought 睦resulting seemingly in an upward sloping demand
curve,contrary to the normal law of demand.
Veblen products
It has been suggested that ‘ luxury type恥products also display perverse price
謀demand relationships,though for different reasons to that of the Giffen
products case.These are sometimes referred to as Veblen products,
Concepts of elasticity
OHT 2.14
•
Price elasticity of demand.This measures the responsiveness of
quantity demanded of a product to changes in its ‘ own price. For
example,if the price of alcohol increases,what happens to the quantity of
alcohol demanded?
•
Cross-price elasticity of demand.This measures the responsiveness of
quantity demanded to changes in the prices of other goods (both
complements and substitutes).For example,if the price of one brand of
coffee rises,what happens to the demand for another coffee brand?Or,if
the price of petrol falls,what happens to the demand for cars?
•
Income elasticity of demand.This measures the responsiveness of
demand to a change in the income of consumers.For example,if incomes
are rising,on average, by $50 per month,what will happen to the demand
for housing?
Coefficient of elasticity = Percentage change in quantity demanded
Percentage change in the relevant variable
OHT 2.15
Price elasticity of demand
E d = Percentage change in quantity demanded
Percentage change in the price of the product
Two different types of price elasticity (E d )can be
calculated,as follows:
•
•
Arc elasticity of demand.
Point elasticity of demand.
Arc elasticity of demand
Arc Ed =

Q2  Q1  / 1 Q2  Q1 
2
P2  P1  / 1 P2  P1 
2
Q2  Q1  x P2  P1 
P2  P1  Q2  Q1 
Figure 2.5 Arc elasticity of demand
OHT 2.12
OHT 2.17
Point elasticity of demand
Point
Ed

Q2  Q1  / Q1

P2  P1  / P1

Q2  Q1  P1

x
P2  P1  Q1
OHT 2.18
Degrees of elasticity
•
Products with a price elasticity of demand
of less than 1 are said to have a relatively
inelastic demand with respect to price 釦
they are said to be price inelastic .
•
Products with a price elasticity of demand
greater than 1 are said to have a relatively
elastic demand 釦they are said to be price
elastic .
•
Products with a price elasticity of demand
exactly equal to 1 are said to have a unit
(or unitary)elasticity of demand.
OHT 2.19
Figure 2.6 Degrees of elasticity of demand
OHT 2.20
Cross-price elasticity of demand
Cross-price Ed = Percentage change in the demand for A
Percentage change in the price of B
The terminology regarding the degree of cross-price
elasticity (ignoring the sign)is the same as for price
elasticity,namely:
•
•
•
1 =unit cross-price elasticity.
Less than 1 =inelastic cross-price elasticity.
Greater than 1 =elastic cross-price elasticity.
OHT 2.21A
Income elasticity of demand
Income Ed = Percentage change in demand
Percentage change in real income
Inferior goods
These are goods of which consumers buy less when real
incomes rise.The value of income elasticity is,
therefore,negative.Examples might be potatoes,
unbranded clothing,cheap package holidays,etc.
Normal goods
These are the most common goods with demand
generally rising as real income rises. They can
themselves be further subdivided into two categories:
OHT 2.21B
Necessities .These are goods and services which exhibit
a positive income elasticity of demand,though the value
will tend to be less than 1. Articles such as basic
foodstuffs and ordinary day-to-day clothing fall into this
category.Consumers will purchase a certain amount of
these goods at very low levels of income,but they will
tend for any given percentage increase in real income to
increase their spending on the goods by a smaller
proportion.
Luxuries . At very low income levels,nothing will be
spent on these but,once a certain threshold income level
is reached,the proportionate rise in demand for luxury
goods is greater than the proportionate rise in real
income,e.g.foreign holidays,dining out and DVD players.
The relationship between price elasticity
and sales revenue
Total revenue = price x quantity sold
TR = P x Q
Figure 2.7 Demand and total revenue
OHT 2.22
OHT 2.23
Price elasticity and total revenue
•
•
With a price inelastic demand:
(a)an increase in price causes a reduction in
quantity demanded,but total revenue increases;
(b)a fall in price causes an increase in quantity
demanded,but total revenue earned declines.
With a price elastic demand:
(a)an increase in price causes such a large fall in
quantity demanded that total revenue falls;
(b)a reduction in price causes such a large increase
in the quantity demanded that the total revenue
rises.
OHT 2.24
Marginal revenue
Marginal revenue (MR) is defined as the change in ()
total revenue (TR) as a firm sells one more or one less
unit of its output (Q ).
TR
MR =
Q
Average revenue (AR)is the total revenue (TR) divided by
output (Q )or the revenue earned on average for each unit
sold.
TR
AR =
Q
OHT 2.25
Figure 2.8 Elasticity, marginal revenue and total revenue
OHT 2.26A
Elasticity, marginal revenue and total revenue - key
relationships
•
Marginal revenue falls as output rises. Since the demand curve
slopes downwards, the addition to total revenue from producing
and selling extra units declines.
•
Average revenue exceeds marginal revenue. When the demand
curve is downward sloping,the marginal revenue from selling one
more unit falls faster than the average revenue from selling the
total output.
•
The marginal revenue curve declines at twice the rate of the
demand (average revenue)curve. Hence, the marginal revenue
curve cuts the horizontal axis at a point midway between the origin
and point C in Figure 2.8.A proof of this mathematical relationship
is given in Appendix 2.2 at the end of the chapter.
OHT 2.26B
Elasticity, marginal revenue and total revenue key relationships
•
When total revenue is increasing,marginal revenue is
positive. This results from the fact that demand is elastic
between points A and B on the demand curve DD in Figure
2.8.
•
When total revenue is falling,marginal revenue is
negative.A negative marginal revenue results from demand
being inelastic between points B and C in Figure 2.8.
•
Total revenue is maximised when marginal revenue is
zero which occurs when the price elasticity is
unitary.Therefore,further attempts to increase total revenue
by lowering price below P *will fail because the sales
volume will not increase sufficiently to compensate for the
price fall.
Key learning points
OHT 2.27A
•
A demand curve relates the amount that consumers are
willing to buy to each conceivable price for the product.
•
In general, the law of demand states that there is an
inverse relationship between the price of a good and the
quantity demanded,assuming all other factors that might
influence demand are held constant (i.e.ceteris paribus ).
•
Utility theory helps explain why consumers buy more of
something the lower its price.
Key learning points
OHT 2.27B
•
Marginal utility is the addition to total utility as a consumer
purchases each extra unit of a good or service.
•
The law of diminishing marginal utility is concerned with
the tendency for marginal utility to fall as more units of a
good or service are consumed at any given time.
•
Consumer equilibrium describes how consumers
maximise their total utility by distributing expenditure so
that the ratio of marginal utilities for all the goods and
services they consume,at any given time, is equal to their
relative prices.
•
Consumer surplus is reflected by the excess of the price
which a person would be willing to pay rather than go
without the good,over that which he or she actually
does pay.
OHT 2.27C
•
When the own price of a good changes,the outcome is a
movement along the demand curve and when any other
determinant or condition of demand changes, there will be a shift
of the demand curve .
•
The impact of a change in price on quantity demanded is made up
of two distinct effects:an income effect and a substitution
effect. The income effect arises from the fact that as the own
price of a good falls,consumers are in effect better off and hence
able to buy more of the good.The substitution effect reflects the
fact that as the price falls, the product becomes relatively cheaper
than alternatives and hence there will be a tendency for
consumers to substitute more of it for other goods.
•
Goods and services are classified as normal products if the
quantity demanded rises as (real)incomes and falls as incomes
fall.
OHT 2.27D
•
In contrast, goods and services are classified as inferior
products if the quantity demanded falls (rises)as incomes
rise (fall).
•
A Giffen product is a special case of an inferior product and
has what appears to be an upward sloping demand
curve,contrary to the normal law of demand,because the
income effect outweighs the substitution effect.
•
A Veblen product also has seemingly an upward sloping
demand curve because of ‘snob’ effects, i.e.it is demanded
because it is expensive and therefore exclusive. Many luxury
products fit into this category.
OHT 2.27E
The (own) price elasticity of demand for a product may be
defined in general terms as:
Ed = Percentage change in quantity demanded
Percentage change in the price of the product
The value of Ed may be calculated on the basis of a
movement along a section of the demand curve,giving rise
to a value of the arc elasticity .This is expressed on the
basis of the average quantity and average price,as follows:
Arc Ed
Q2  Q1  x P2  P1 
P2  P1  Q2  Q1 
OHT 2.27F
•
For very small price changes,elasticity may be calculated with
reference to a single point on the demand curve,giving rise to a
value of the point elasticity ,as follows:
Point Ed =
Q2  Q1  x P1
P2  P1  Q1
•
Products with a price elasticity of demand of less than 1 (in
absolute terms)are said to have a relatively inelastic demand
with respect to price 釦hey are said to be price inelastic .In this
case,total sales revenue will tend to rise (fall)as price rises
(falls).
•
Products with a price elasticity of demand greater than 1 (in
absolute terms)are said to have a relatively elastic demand 釦
they are said to be price elastic. In this case,total sales
revenue will tend to fall (rise)as price rises (falls).
OHT 2.27G
•
Products with a price elasticity of demand equal to 1 (in
absolute terms)are said to have a unit or unitary elasticity of
demand. In this case, total sales revenue will remain
unchanged as price rises or falls.
•
The value of price elasticity of demand can range from infinity
(in absolute terms)to 0. A product with a perfectly inelastic
demand will have a value of Ed equal to 0 at every price,while
a product with a perfectly elastic demand will have a value of
Ed equal to infinity at a particular price.
•
Cross-price elasticity of demand indicates the
responsiveness of the demand for one product to changes in
the prices of other goods and services and may be calculated
as:
Cross-price Ed = Percentage change in the demand for A
Percentage change in the price of B
OHT 2.27H
•
Substitutes will tend to have a positive value for cross-price
Ed ,while complements will tend to have a negative value.
•
Income elasticity of demand measures the responsiveness
of quantity demanded with respect to (real) income variations
as follows:
Income Ed = Percentage change in quantity demanded
Percentage change in real income
Necessities exhibit a positive income elasticity of demand
though the value will tend to be less than 1. In contrast,
luxuries will tend to have an income elasticity of demand
greater than 1.
•
Marginal revenue is defined as the incremental change in
total revenue and is usually measured as a firm sells one more
or one less unit of its output.
OHT 2.27I
•
The marginal revenue curve declines at twice the rate of the
demand (average revenue)curve.
•
When total revenue is increasing (decreasing),marginal revenue
is positive (negative)such that total revenue is maximised
when marginal revenue is zero .This occurs when the price
elasticity of demand is equal to 1.
•
An indifference curve shows all combinations of two goods or
services that yield the same level of utility or satisfaction so that
the consumer is indifferent between each combination.
•
The slope of the budget line is determined by the relative
prices of the two goods or services and the position of the line
by the consumer 痴income.
OHT 2.27J
•
Together, the indifference curve mapping and the
budget line determine the combination of the goods or
services that the consumer will choose to buy.
•
Indifference curve analysis can be used to show the
income and substitution effects of a price change.
Appendix 2.1 Indifference curve analysis
The meaning of indifference curves
An indifference curve details all combinations of two goods or
services that yield the same level of utility or satisfaction.
Figure A2.1 A typical indifference curve
OHT A2.28
OHT A2.29
Figure A2.2 An indifference curve map
The budget constraint
OHT A2.30
Budget constraint
PxQx + PyQym
The slope of the budget line is determined by the relative prices of the two goods
and the position of the line by the consumer’s income.
Figure A2.3 The budget constraint
OHT A2.31
Figure A2.4 Illustrating the effects of price and income changes
OHT A2.32
Figure A2.5 Utility maximisation with a budget constraint
OHT A2.33
Figure A2.6 Substitution and income effects of a price change for a normal good
OHT A2.34
Figure A2.7 Income and substitution effects for an inferior good
OHT 2.35A
Appendix 2.2 Marginal revenue and the demand
curve
Proof that the marginal revenue curve declines at twice the rate of
the demand curve
The equation of a linear demand relationship is:
P = a - bQ
(2.1)
Total revenue (TR) = P x Q
Total revenue (TR) = (a - bQ) x Q (substituting for P = a - bQ)
Total revenue (TR) = aQ - bQ2
OHT 2.35B
Appendix 2.2 Marginal revenue and the demand curve
Marginal revenue (MR) is defined as the change in total revenue with
respect to a unit change in sales. In terms of differential calculus:
TR
TR
MR 

Q
Q

=  aQ  bQ
2

(substituting for TR = aQ - bQ2)
Q
= a - 2bQ
2.2)