CHAPTER-3-ELASTICITY-OF-DEMAND-AND-SUPPLY.pdf

Written by: Edmund Quek

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CHAPTER 3

ELASTICITY OF DEMAND AND SUPPLY

LECTURE OUTLINE

1 INTRODUCTION

2 PRICE ELASTICITY OF DEMAND

2.1 Definition and formula of price elasticity of demand

2.2 Interpreting price elasticity of demand

2.3 Use of price elasticity of demand

2.4 Linear downward-sloping demand curve (optional)

2.5 Determinants of price elasticity of demand

3 INCOME ELASTICITY OF DEMAND

3.1 Definition and formula of income elasticity of demand

3.2 Interpreting income elasticity of demand

3.3 Use of income elasticity of demand

3.4 Determinants of income elasticity of demand

4 CROSS ELASTICITY OF DEMAND

4.1 Definition and formula of cross elasticity of demand

4.2 Interpreting cross elasticity of demand

4.3 Use of cross elasticity of demand

4.4 Determinants of cross elasticity of demand

5 PRICE ELASTICITY OF SUPPLY

5.1 Definition and formula of price elasticity of supply

5.2 Interpreting price elasticity of supply

5.3 Linear upward-sloping supply curve (optional)

5.4 Determinants of price elasticity of supply

6 LIMITATIONS OF THE CONCEPTS OF ELASTICITY OF DEMAND

References

John Sloman, Economics

William A. McEachern, Economics

Richard G. Lipsey and K. Alec Chrystal, Positive Economics

G. F. Stanlake and Susan Grant, Introductory Economics

Michael Parkin, Economics

David Begg, Stanley Fischer and Rudiger Dornbusch, Economics



1 INTRODUCTION

We have learnt that a fall in price will lead to a rise in quantity demanded and vice versa.

However, given any change in price, in addition to the direction of the change in quantity

demanded, economists are also interested to find the magnitude of the change. To measure

this, economists use the concept of price elasticity of demand. This chapter gives an

exposition of the concepts of price elasticity of demand, income elasticity of demand, cross

elasticity of demand and price elasticity of supply.

2 PRICE ELASTICITY OF DEMAND

2.1 Definition and formula of price elasticity of demand

Definition

The price elasticity of demand (PED) for a good is a measure of the degree of

responsiveness of the quantity demanded to a change in the price, ceteris paribus.

Formula

% Quantity Demanded

PED -------------------------------

% Price

2.2 Interpreting price elasticity of demand

Due to the law of demand, the PED for a good is always negative. However, the common

practice among economists is to omit the negative sign.

If the PED for a good is greater than one, the demand is price elastic which means that a

change in the price will lead to a larger percentage change in the quantity demanded. A

good with an elastic demand has a relatively flat demand curve.

If the PED for a good is less than one, the demand is price inelastic which means that a

change in the price will lead to a smaller percentage change in the quantity demanded. A

good with an inelastic demand has a relatively steep demand curve.

If the PED for a good is equal to one, the demand is unit price elastic which means that a

change in the price will lead to the same percentage change in the quantity demanded. The

demand curve for a good with a unit elastic demand is a rectangular hyperbola.



If the PED for a good is zero, the demand is perfectly price inelastic which means that a

change in the price will not lead to any change in the quantity demanded. A good with a

perfectly inelastic demand has a vertical demand curve.

If the PED for a good is infinity, the demand is perfectly price elastic which means that a

rise (not a fall) in the price will lead to an infinite decrease in the quantity demanded. A

good with a perfectly elastic demand has a horizontal demand curve.

2.3 Use of price elasticity of demand

If the demand for the good produced by a firm is price elastic, the firm can decrease its

price to increase its total revenue as its quantity demanded will rise by a larger percentage.

In the above diagram, area A represents the gain in revenue resulting from the increase in

the quantity demanded (Q) from Q0 to Q1 and area B represents the loss in revenue

resulting from the fall in the price (P) from P0 to P1. Since the gain exceeds the loss, total

revenue rises.

If the demand for the good produced by a firm is price inelastic, the firm can increase its

price to increase its total revenue as its quantity demanded will fall by a smaller percentage.



In the above diagram, area C represents the gain in revenue resulting from the rise in the

price (P) from P0 to P1 and area D represents the loss in revenue resulting from the decrease

in the quantity demanded (Q) from Q0 to Q1. Since the gain exceeds the loss, total revenue

rises.

If the demand for the good produced by a firm is unit price elastic, the firm cannot change

its price to increase its total revenue as its quantity demanded will change by the same

percentage.

2.4 Linear downward-sloping demand curve (optional)

Along a linear downward-sloping demand curve, PED is different at different points along

the demand curve. As we move down along a linear downward-sloping demand curve,

PED falls from infinity to zero. If the demand curve is linear, the total revenue curve will

be Hill-shaped.

Example

Price Quantity

demanded

Total

revenue

Average

revenue

Marginal

revenue

PED

6 0 0 - - ∞

5 1 5 5 5 5

4 2 8 4 3 2

3 3 9 3 1 1

2 4 8 2 -1 0.5

1 5 5 1 -3 0.2

0 6 0 0 -5 0

Total revenue (TR) Price (P) x Quantity (Q)

Average revenue (AR) TR/Q P (∴ Demand curve AR curve)

Marginal revenue (MR) ΔTR/ΔQ



In the above table, as quantity rises, TR rises from zero to nine and then falls back to zero.

MR is the additional revenue resulting from selling one more unit of a good. TR is

maximised where PED is 1 since any change in price will lead to the same percentage

change in quantity demanded. If we assume that quantity is continuously divisible, this will

happen where MR is equal to zero.

TR curve and MR curve that correspond to a linear downward-sloping demand curve

Note: MR is lower than AR because if the firm wants to sell one more unit of the good, not

only must it lower the price of the unit, but it must also lower the price of all the

previous units. With the use of differential calculus, we can show that the slope of

the MR curve is twice that of the AR curve.

When economists speak of elastic demand, what they mean is that PED is greater

than one at all the points along the demand curve and a necessary condition for this

to happen is that the demand curve is not linear.



2.5 Determinants of price elasticity of demand

Number of substitutes

The larger the number of substitutes for a good, the higher the PED for the good.

Conversely, the smaller the number of substitutes for a good, the lower the PED for the

good. The number of substitutes for a good depends, in part, on how narrowly, and for that

matter, how broadly the good is defined. The more narrowly a good is defined (e.g. carrots,

cabbages), the more elastic the demand for the good. Conversely, the more broadly a good

is defined (e.g. vegetables or even food), the less elastic the demand for the good.

Closeness of substitutes

The closer the substitutes for a good, the higher the PED for the good. Conversely, the

farther the substitutes for a good, the lower the PED for the good.

Degree of necessity

The higher the degree of necessity of a good, the lower the PED for the good. Conversely,

the lower the degree of necessity of a good, the higher the PED for the good.

Proportion of income spent on the good

The larger the proportion of income spent on the good, the higher the PED for the good.

Conversely, the smaller the proportion of income spent on a good, the lower the PED for

the good.

Time period

The longer the time period after a change in the price of a good, the higher the PED for the

good.

3 INCOME ELASTICITY OF DEMAND

3.1 Definition and formula of income elasticity of demand

Definition

The income elasticity of demand (YED) for a good is a measure of the degree of

responsiveness of the quantity demanded to a change in income, ceteris paribus.

Formula

% Quantity Demanded

YED --------------------------------

% Income



3.2 Interpreting income elasticity of demand

If the YED for a good is positive, the good is a normal good. A normal good is a good

whose demand rises when consumers’ income rises. There are two types of normal goods:

necessity and luxury. If the YED for a good is positive but less than one, the good is a

necessity. In other words, the demand for a necessity is income inelastic. If the YED for a

good is greater than one, the good is a luxury. In other words, the demand for a luxury is

income elastic.

If the YED for a good is negative, the good is an inferior good. An inferior good is a good

whose demand falls when consumers’ income rises.

The concepts of normal and inferior goods can be depicted by an Engel’s curve. The

Engel’s curve of a good shows the quantity of the good demanded at each income level.

Engel’s Curve

In the above diagram, the good is normal between income levels Y0 and Y1 and inferior

between income levels Y1 and Y2.

3.3 Use of income elasticity of demand

The concept of YED allows a firm to determine the future size of the market for its good

and hence its production capacity. Suppose that the YED for a good is positive. If a firm

that produces the good predicts an economic boom, it can consider increasing its

production capacity to meet the increase in demand if the boom arrives. Conversely, if the

firm predicts a recession, it can consider decreasing its production capacity or holding back

any expansion plan to minimise excess production capacity if the recession arrives.



3.4 Determinants of income elasticity of demand

The YED for a good will be lower the higher the level of income and wealth of consumers.

4 CROSS ELASTICITY OF DEMAND

4.1 Definition and formula of cross elasticity of demand

Definition

The cross elasticity of demand (XED) for a good with respect to another good is a measure

of the degree of responsiveness of the quantity of the first good demanded to a change in

the price of the second good, ceteris paribus. Let the two goods be good A and good B.

Formula

% Quantity Demanded of Good A

XEDAB = -----------------------------------------------

% Price of Good B

4.2 Interpreting cross elasticity of demand

If the XEDAB is positive, good A and good B are substitutes, which means that the two

goods are alternatives to each other.

In the above diagram, the demand curve (DAB) relating the quantity demanded of good A to

the price of good B is upward-sloping. If the price of good B rises, consumers will buy less

of it. Since good A and good B are substitutes, they will buy more good A.



If the XEDAB is negative, good A and good B are complements, which means that the two

goods are consumed together.

In the above diagram, the demand curve (DAB) relating the quantity demanded of good A to

the price of good B is downward-sloping. If the price of good B rises, consumers will buy

less of it. Since good A and good B are complements, they will buy less good A.

4.3 Use of cross elasticity of demand

The concept of XED allows a firm to determine how a change in the price of a related good

produced by another firm will affect the demand for its good. For instance, if a firm that

produces a substitute decreases its price, the firm will also need to decrease its price to

avoid suffering a decrease in demand and this is due to the positive XED between

substitutes. However, it should take into consideration the possibility of a price war. If a

firm that produces a substitute increases its price, the firm can increase total revenue by

keeping its price unchanged. However, if does not have excess production capacity, it may

need to increase its price to increase total revenue.

If a firm produces more than one good, let’s say two goods, the concept of XED also allows

the firm to determine how the demand for one good will be affected if it changes the price

of the other good.

4.4 Determinants of cross elasticity of demand

The XED between two goods will be higher the more closely they are related. Hence, a

large positive XED indicates very close substitutes and a large negative XED indicates

very close complements.



5 PRICE ELASTICITY OF SUPPLY

5.1 Definition and formula of price elasticity of supply

Definition

The price elasticity of supply (PES) of a good is a measure of the degree of responsiveness

of the quantity of the good supplied to a change in the price, ceteris paribus.

Formula

% Quantity Supplied

PES ------------------------------

% Price

5.2 Interpreting price elasticity of supply

Due to the law of supply, the PES of a good is always positive.

If the PES of a good is greater than one, the supply of the good is price elastic which means

that a change in the price of the good will lead to a larger percentage change in the quantity

supplied. A good with an elastic supply has a relatively flat supply curve.

If the PES of a good is less than one, the supply of the good is price inelastic which means

that a change in the price of the good will lead to a smaller percentage change in the

quantity supplied. A good with an inelastic supply has a relatively steep supply curve.

If the PES of a good is equal to one, the supply of the good is unit price elastic which means

that a change in the price of the good will lead to the same percentage change in the

quantity supplied.

If the PES of a good is zero, the supply of the good is perfectly price inelastic which means

that a change in the price of the good will not lead to any change in the quantity supplied. A

good with a perfectly inelastic supply has a vertical supply curve.

If the PES of a good is infinity, the supply of the good is perfectly price elastic which

means that a fall (not a rise) in the price of the good will lead to an infinite decrease in the

quantity supplied. A good with a perfectly elastic supply has a horizontal supply curve.

5.3 Linear upward-sloping supply curve (optional)

Along a linear upward-sloping supply curve, PES is different at different points along the

supply curve, unless the supply curve intersects the origin as a linear upward-sloping



supply curve which intersects the origin has a unit price elasticity of supply at all points

along the supply curve, regardless of the slope.

A linear upward-sloping supply curve which intersects the price-axis has a PES greater

than one at all points along the supply curve, regardless of the slope. Although all the

points along such a supply curve has a PES greater than one, the value of PES decreases as

we move up along the supply curve.

A linear upward-sloping supply curve which intersects the quantity-axis has a PES less

than one at all points along the supply curve, regardless of the slope. Although all the

points along such a supply curve has a PES less than one, the value of PES increases as we

move up along the supply curve.

5.4 Determinants of price elasticity of supply

Definition of the good

The PES of a good is higher the more narrowly the good is defined. For instance, the PES

of a crop is higher than the PES of crops as a whole as it is easier to obtain factor inputs to

produce a crop within the agricultural sector than from other industries.

Time period

The longer the time period after an increase in the price of a good, the higher the PES of the

good as firms are able to increase output by a larger amount with more time. Time period

can be divided into the immediate run, the short run and the long run. The immediate run is

the time period that is so short that output is fixed. The supply curve of the good is perfectly

inelastic, assuming firms do not keep stocks of the good. The short run is the time period

during which at least one of the factor inputs used in the production process is fixed. In the

short run, when the price of a good rises, firms can increase output only by employing more

of the variable factor inputs used in the production process. The long run is the time period

after which all the factor inputs used in the production process are variable. The PES of a

good in the long run is higher than the PES in the short run as firms can increase output by

employing more of all the factor inputs used in the production process and potential firms

can enter the industry in the long run.

Nature of the good

The supply of a non-perishable good is normally more price elastic than the supply of a

perishable good. If a good is non-perishable, such as a manufactured good, firms can keep

stocks of the good. Therefore, if the price rises, firms can increase the quantity supplied by

increasing output and by running down their stocks. However, if a good is perishable, such

as an agricultural product, firms cannot keep stocks of the good. Therefore, if the price

rises, firms can only increase the quantity supplied by increasing output. Further, the

growing time of a perishable good is normally longer than the production time of a

non-perishable good.



Behaviour of marginal cost as firms change output

Given a change in price of a good, the lower the output level and hence capacity utilisation,

the less rapidly marginal cost will change as firms change output. The less rapidly marginal

cost will change as firms change output, the larger the change in output. Therefore, the

lower the output level of a good, the higher the PES of the good.

Mobility of factor inputs

The ease with which factor inputs can move from the production of one good to another

will influence PES. The higher the mobility of factor inputs, the higher the PES of a good.

The mobility of factor inputs depends to some extent on the time period.

6 LIMITATIONS OF THE CONCEPTS OF ELASTICITY OF DEMAND

The concepts of elasticity of demand are subject to several limitations.

First, data from past records may no longer be relevant to calculating elasticities of demand

as some of the determinants of demand may have changed.

Second, although data from current surveys are relevant to calculating elasticities of

demand, they may not be reliable because the respondents may not be truthful in their

answers. Further, if the sample size of the surveys is small, the results may not be reflective

of the actual market for the good. Having a larger sample size will result in a higher cost.

Third, the assumption of ceteris paribus that is made in calculating elasticities of demand is

unlikely to hold in reality.

Note: More advanced applications of the concepts of elasticity of demand will be

discussed in the essays. In addition, students must also know the usefulness of the

concepts of elasticity of demand to the government which will also be discussed in

the essays.

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CHAPTER-3-ELASTICITY-OF-DEMAND-AND-SUPPLY.pdf