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 Q d due to 1% change in P. Application: change in price on –total revenue for sellers –total expenditure for buyers –effectiveness of policy in influencing individual 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 |E d | > 1: (|E d | →∞) Elastic –price changes by 1%, quantity demanded changes by more than 1%. – price and total revenue are negatively related

Inelastic Demand : |E d | < 1, (|E d | = 0) Inelastic –price changes by 1%, quantity demanded changes by less than 1% – price and total revenue are positively related

Unit Elastic Demand |E d | = 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: P$3.70$2.72 Qd1.74B1.9B

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

What does it mean? Elastic? (Ed =  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 Q d due to 1% change in P. Formula:E d = %ΔQ d / %ΔP = (ΔQ d / Q d ) / (ΔP/P) = (Δ Q d /ΔP) x P/Q d Slope of DInitial 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 Price Figure 4.12

Cross-Price Elasticity Responsiveness of demand for one good to changes in the price of a related goods. E c = (Δ Q x / ΔP y ) x (P y /Q x ) E c > 0, substitutes E c < 0, complements

Income Elasticity of Demand The responsiveness of demand to changes in consumer income % change in Q divided by % change in Y E m = (Δ Q/ ΔY) x (Y/Q)

Income Elasticity of Demand 0 < E m < 1: (E m = 0) Income Inelastic Income changes by 1%, quantity demanded changes by less than 1%. E m > 1: Income Elastic Income changes by 1%, quantity demanded changes by more than 1%.

Income Elasticity of Demand E m = 1: Income Unit Elastic Income changes by 1%, quantity demanded changes by 1%.

Categories based on elasticity E m > 0: Normal goods –E m > 1: Luxury goods –E m < 1: Necessity E m < 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 ElasticityCross-Price Elasticity Income Elasticity %ΔQ d / %ΔP%ΔQ d (x)/ %ΔP(y)%ΔQ d / %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 Q s due to 1% change in P. Formula:E s = %ΔQ s / %ΔP = (ΔQ s / Q s ) / (ΔP/P) = (Δ Q s /ΔP) x P/Q s

Again: slope and position S’ Es at Point A: On S: (8/2)(1/2)=2 On S’: (14/2)(1/6)=7/6 Es on S: At A: (8/2)(1/2)=2 At B: (10/3)(1/2)=5/3 Conclusions: Es declines as Q increases Es 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 E s > 1: (E s →∞) Elastic price changes by 1%, quantity supplied changes by more than 1%. E s < 1, (E s = 0) Inelastic price changes by 1%, quantity supplied changes by less than 1%

Unit Elastic Supply E s = 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