Demand Elasticity

Chapter 4Chapter 4Demand

Elasticity Managerial Economics: Economic Tools for Today’s Decision

Makers, 5/e By Paul Keat and Philip Young

2006 Prentice Hall Business Publishing Managerial Economics, 5/e Keat/Young

Demand Elasticity

• The Economic Concept of Elasticity• The Price Elasticity of Demand• The Cross-Elasticity of Demand• Income Elasticity• Other Elasticity Measures• Elasticity of Supply


Learning Objectives

• Define and measure elasticity• Apply concepts of price elasticity, cross-

elasticity, and income elasticity• Understand determinants of elasticity• Show how elasticity affects revenue


The Economic Concept of Elasticity

• Elasticity: the percentage change in one variable relative to a percentage change in another.

Bin changepercent Ain changepercent Elasticity oft Coefficien


The Price Elasticity of Demand

• Price elasticity of demand: The percentage change in quantity demanded caused by a 1 percent change in price.

Price %Quantity %E

p



• Arc elasticity: Elasticity which is measured over a discrete interval of a demand (or a supply) curve.

• Ep = Coefficient of arc price elasticity

• Q1 = Original quantity demanded

• Q2 = New quantity demanded

• P1 = Original price

• P2 = New price

2/)(2/)( 21

12

21

12

PPPP

QQQQEp



• Point elasticity: Elasticity measured at a given point of a demand (or a supply) curve.

1

1

εP

PdQ xdP Q

=



The point elasticity of a linear demand function can be expressed as:

1

1

QP

PQ

p



• Some demand curves have constant elasticity over the relevant range

• Such a curve would look like:Q = aP-b

where –b is the elasticity coefficient• This equation can be converted to linear

by expressing it in logarithms:log Q = log a – b(log P)



• Elasticity differs along a linear demand curve.



• Categories of Elasticity• Relative elasticity of demand: EP > 1

• Relative inelasticity of demand: 0 < EP < 1

• Unitary elasticity of demand: EP = 1

• Perfect elasticity: EP = ∞

• Perfect inelasticity: EP = 0



• Factors affecting demand elasticity• Ease of substitution• Proportion of total expenditures• Durability of product

• Possibility of postponing purchase• Possibility of repair• Used product market

• Length of time period



• Derived demand: The demand for products or factors that are not directly consumed, but go into the production of a final product.

• The demand for such a product or factor exists because there is demand for the final product.



• The derived demand curve will be more inelastic:• the more essential is the component in question.• the more inelastic is the demand curve for the

final product.• the smaller is the fraction of total cost going to

this component.• the more inelastic is the supply curve of

cooperating factors.


The Price Elasticity of Demand• A long-run demand

curve will generally be more elastic than a short-run curve.

• As the time period lengthens consumers find way to adjust to the price change, via substitution or shifting consumption



• There is a relationship between the price elasticity of demand and revenue received.• Because a demand curve is downward sloping, a

decrease in price will increase the quantity demanded

• If elasticity is greater than 1, the quantity effect is stronger than the price effect, and total revenue will increase



• As price decreases• Revenue rises when

demand is elastic.• Revenue falls when

it is inelastic.• Revenue reaches it

peak when elasticity of demand equals 1.



• Marginal Revenue: The change in total revenue resulting from changing quantity by one unit.

QuantityMR

Revenue Total



• For a straight-line demand curve the marginal revenue curve is twice as steep as the demand.



• At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum.



• Some sample elasticities• Coffee: short run -0.2, long run -0.33• Kitchen and household appliances: -0.63• Meals at restaurants: -2.27• Airline travel in U.S.: -1.98• Beer: -0.84, Wine: -0.55


The Cross-Elasticity of Demand

• Cross-elasticity of demand: The percentage change in quantity consumed of one product as a result of a 1 percent change in the price of a related product.

B

AX P

QE

%%



• Arc Elasticity

2/)(2/)( 21

12

21

12

BB

BB

AA

AAx PP

PPQQQQE



• Point Elasticity

B

B

A

AX P

PQQE



• The sign of cross-elasticity for substitutes is positive.

• The sign of cross-elasticity for complements is negative.

• Two products are considered good substitutes or complements when the coefficient is larger than 0.5.


Income Elasticity

• Income Elasticity of Demand: The percentage change in quantity demanded caused by a 1 percent change in income.

• Y is shorthand for Income

YQEY

%%


Income Elasticity

• Arc Elasticity

2/)(2/)( 21

12

21

12

YYYY

QQQQEY


Income Elasticity• Categories of income

elasticity• Superior goods: EY > 1

• Normal goods: 0 >EY >1• Inferior goods – demand

decreases as income increases: EY < 0


Other Elasticity Measures

• Elasticity is encountered every time a change in some variable affects quantities.• Advertising expenditure• Interest rates• Population size


Elasticity of Supply

• Price Elasticity of Supply: The percentage change in quantity supplied as a result of a 1 percent change in price.

• If the supply curve slopes upward and to the right, the coefficient of supply elasticity is a positive number.

Price %SuppliedQuantity %E

S



• Arc elasticity

2/)(2/)( 21

12

21

12

PPPP

QQQQEs



• When the supply curve is more elastic, the effect of a change in demand will be greater on quantity than on the price of the product.

• With a supply curve of low elasticity, a change in demand will have a greater effect on price than on quantity.

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Demand Elasticity