Chapter_4 - Econ

Chapter 4

Demand Elasticity

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

The demand curve sloped downward to the right (the lowered the price, the greater the quantity demanded)

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

A firm contemplating lowering its price to counteract new competition

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

Price %

Quantity %E

p

Measurement of Price Elasticity 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

PP

PP

QQ

QQEp

Example

P1=11 P2=12 Q1=7 Q2=6

Then what is EP ?


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

1

1

εP

PdQx

dP Q=


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

1

1

Q

P

P

Q

p

Example

Q=18-P at when P=$12 and Q=6then what is EP ?

Q=100-P2 when P1=5, then Q=75 then what is EP ?


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)

The Price Elasticity of Demand 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

Special Cases

P

D

D

Q0 0 Q

Infinitely (price) elastic Infinitely price inelastic


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 Price Elasticity of Demand 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.

Example

Consider demand for residential housing (the final product) and the derived demand for one class of labor employed in construction , electricians ( the demand for electricians does not exist for its own sake) Assumptions: 1. can not build a house

without electricians 2. the cost of electricians is a relatively small percentage of the entire cost of the house

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

The Price Elasticity of Demand 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

The Price Elasticity of Demand For a straight-line

demand curve the marginal revenue curve is twice as steep as the demand

The Price Elasticity of 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

PP

QQ

QQE


Point Elasticity

B

B

A

AX P

P

Q

QE


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

Y

QEY

%

%

Income Elasticity

Arc Elasticity

2/)(2/)( 21

12

21

12

YY

YY

QQ

QQEY

Other Elasticity Measures Categories of

income elasticity Superior goods: EY

> 1 Normal goods: 0

>EY >1 Inferior goods –

demand decreases as income increases: EY < 0

Elasticity of Supply

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

Elasticity of Supply

Arc elasticity

2/)(2/)( 21

12

21

12

PP

PP

QQ

QQEs

Demand Elasticity

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.

Global application

Example: price elasticities in Asia

imports almost always price inelastic if exports price inelastic, export

earnings will rise as prices rise if exports price elastic, export

earnings will rise with world incomes

Chapter_4 - Econ

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