Chapter 4

Elasticity

Elasticity:

The responsiveness of dependent variable to change in independent variable

A measure of the extent to which quantity demanded and quantity supplied respond to variations in price, income, and other factors.

Price Elasticity of Demand

Definition: % change in Qd due to 1% change in P.

Application: change in price on – total revenue for sellers– total expenditure for buyers– effectiveness of policy in influencing indi

vidual behaviors

Exercise: 4.1, P.99

Known:– P=$400, Qd=10K;– P=$380, Qd=12K

Solve for: Ed Is D elastic? Should P go down from $400 to $380?

Elastic Demand

|Ed| > 1: (|Ed| →∞) Elastic

– price changes by 1%, quantity demanded changes by more than 1%.

– price and total revenue are negatively related

Inelastic Demand :

|Ed| < 1, (|Ed| = 0) Inelastic

– price changes by 1%, quantity demanded changes by less than 1%

– price and total revenue are positively related

Unit Elastic Demand

|Ed| = 1, Unit Elastic

– price changes by 1%, quantity demanded also changes by 1%

– total revenue is maximized

Perfectly Elastic and Perfectly Inelastic Demand Curves

Figure 4.8, P.106

Mid-Point Method

Change in Q = Q2 - Q1 Change in P = P2 - P1 E = {(Q2-Q1)/[(Q2+Q1)/2]}

/ {(P2-P1)/[(P2+P1)/2]}

Example:

1998 1999

P $3.70 $2.72

Qd 1.74B 1.9B

Calculation

Change in Qd = 1.9 – 1.74 = 0.16 Change in P = 2.72 – 3.70 = - 0.98 Average Qd = (1.74 + 1.9) / 2 = 1.82 Average P = (3.70 + 2.72) / 2 = 3.21 E = (0.16/1.82) / (-0.98/3.21) = - 0.29 TR1998 = 6.438, TR1999 = 5.168

What does it mean?

Elastic? (Ed = -0.29 absolute value < 1)

Impact on TR when P decreases Possible type of good

Factors Affecting Elasticity of Demand

Substitutability Share in budget Necessity vs. Luxury Time span: short term vs. long term

Price Elasticity of Demand

Definition: % change in Qd due to 1% change in P.

Formula: Ed = %ΔQd / %ΔP

= (ΔQd / Qd ) / (ΔP/P)

= (Δ Qd /ΔP) x P/QdSlope of D Initial position

Determinants of Elasticity

Slope of the demand curve at the price Position of the point (price level) on the

demand curve

Price Elasticity and the Steepness of the Demand Curve

Figure 4.5, P.104

Fig. 4.5, P.104

Elasticity affected by both slope and position– At (4,4)

• Ed on D1=1/2• Ed on D2=2

– On D2• Ed at (4,4) = 2• Ed at (1, 10) = 1/5

Price Elasticity Regions along a Straight-Line Demand Curve

Figure 4.7

Conclusions:

For Straight-line Demand Curves: Ed at mid-point = 1

– P > Pm Elastic– P < Pm Inelastic

To increase TR– P > Pm: Lower P Higher TR– P < Pm: Higher P Higher TR

Total Expenditure as a Function of PriceFigure 4.12

Cross-Price Elasticity

Responsiveness of demand for one good to changes in the price of a related goods.

Ec = (Δ Qx/ ΔPy) x (Py/Qx)

Ec > 0, substitutes

Ec < 0, complements

Income Elasticity of Demand

The responsiveness of demand to changes in consumer income

% change in Q divided by % change in Y Em = (Δ Q/ ΔY) x (Y/Q)

Income Elasticity of Demand

0 < Em < 1: (Em = 0) Income Inelastic

Income changes by 1%, quantity demanded changes by less than 1%.

Em > 1: Income Elastic

Income changes by 1%, quantity demanded changes by more than 1%.

Income Elasticity of Demand

Em = 1: Income Unit Elastic

Income changes by 1%, quantity demanded changes by 1%.

Categories based on elasticity

Em > 0: Normal goods

– Em > 1: Luxury goods

– Em < 1: Necessity

Em < 0: Inferior goods

Engel’s Law

with a given set of tastes and preferences, as income rises, the proportion of income spent on food falls, even if actual expenditure on food rises

the income elasticity of demand of food is less than 1 (necessity)

Engel’s Coefficient

% change in food expenditure / % change in total expenditure

% change in food expenditure / % change in income

– EC > 59%: absolutely poverty (绝对贫困 ); – 50% < EC <59%: barely enough food and clothing （温饱） ;

– 40% < EC < 50%: moderately well-off （小康）– 30% <EC < 40%: well-to-do （富足）– EC < 30%: wealthy （富裕）

Summary: Elasticity of Demand

Price Elasticity Cross-Price

ElasticityIncome Elasticity

%ΔQd / %ΔP %ΔQd(x)/ %ΔP(y) %ΔQd / %ΔY

Elastic (horizontal)

Inelastic (vertical)

Unitary elastic

Complements

Substitutes

Normal vs. inferior

Luxury vs.necessity

Luxury/necessity

Substitutability

Price Elasticity of Supply

Definition: % change in Qs due to 1% change in P.

Formula: Es = %ΔQs / %ΔP

= (ΔQs / Qs ) / (ΔP/P)

= (Δ Qs /ΔP) x P/Qs

Again: slope and position

S’

Es at Point A:On S: (8/2)(1/2)=2On S’: (14/2)(1/6)=7/6

Es on S:At A: (8/2)(1/2)=2At B: (10/3)(1/2)=5/3

Conclusions:Es declines as Q increasesEs declines faster if slope is steeper

14

Special Case: fig.4.14, P.113

Es = 1 everywhere If S is straight and

passes through origin

Special cases:Perfectly inelastic and Perfectly elastic supply curves

Fig.4.15, P. 113 Fig. 4.16, P.114

Price Elasticity of Supply

Es > 1: (Es →∞) Elastic

price changes by 1%, quantity supplied changes by more than 1%.

Es < 1, (Es = 0) Inelastic

price changes by 1%, quantity supplied changes by less than 1%

Unit Elastic Supply

Es = 1, Unit Elastic

price changes by 1%, quantity supplied also changes by 1%

Factors Affecting Elasticity of Supply

Availability of inputs:

– Flexibility; mobility; substitute Length of production period Difficulty of production Technology

Incidence of Excise Tax

Who bears the real burden of tax, the buyer or the seller?

Effect of an Excise Tax Levied on the Sales of Taxi Rides

Effect of an Excise Tax Levied on Purchases of Taxi Rides

The Revenue from an Excise Tax