Chapter 4 Elasticity Elasticity n The responsiveness of

Chapter 4 Elasticity

Elasticity: n The responsiveness of dependent variable to change in independent variable n 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 n Definition: % change in Qd due to 1% change in P. n 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 n Known: – P=$400, Qd=10 K; – P=$380, Qd=12 K n Solve for: Ed n Is D elastic? n Should P go down from $400 to $380?

Elastic Demand n |Ed| > 1: (|Ed| →∞) Elastic – price changes by 1%, quantity demanded changes by more than 1%. – price and total revenue are negatively related

Inelastic Demand : n |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 n |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 n Change in Q = Q 2 - Q 1 n Change in P = P 2 - P 1 n E = {(Q 2 -Q 1)/[(Q 2+Q 1)/2]} / {(P 2 -P 1)/[(P 2+P 1)/2]}

Example: 1998 1999 P $3. 70 $2. 72 Qd 1. 74 B 1. 9 B

Calculation n Change in Qd = 1. 9 – 1. 74 = 0. 16 n Change in P = 2. 72 – 3. 70 = - 0. 98 n Average Qd = (1. 74 + 1. 9) / 2 = 1. 82 n Average P = (3. 70 + 2. 72) / 2 = 3. 21 n E = (0. 16/1. 82) / (-0. 98/3. 21) = - 0. 29 n TR 1998 = 6. 438, TR 1999 = 5. 168

What does it mean? n Elastic? (Ed = -0. 29 absolute value < 1) n Impact on TR when P decreases n Possible type of good

Factors Affecting Elasticity of Demand n Substitutability n Share in budget n Necessity vs. Luxury n Time span: short term vs. long term

Price Elasticity of Demand n Definition: % change in Qd due to 1% change in P. n Formula: Ed = %ΔQd / %ΔP = (ΔQd / Qd ) / (ΔP/P) = (Δ Qd /ΔP) x P/Qd Slope of D Initial position

Determinants of Elasticity n Slope of the demand curve at the price n 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 n Elasticity affected by both slope and position – At (4, 4) • Ed on D 1=1/2 • Ed on D 2=2 – On D 2 • Ed at (4, 4) = 2 • Ed at (1, 10) = 1/5

Figure 4. 7 Price Elasticity Regions along a Straight-Line Demand Curve

Conclusions: For Straight-line Demand Curves: n Ed at mid-point = 1 – P > Pm Elastic – P < Pm Inelastic n To increase TR – P > Pm: Lower P Higher TR – P < Pm: Higher P Higher TR

Figure 4. 12 Total Expenditure as a Function of Price

Cross-Price Elasticity n Responsiveness of demand for one good to changes in the price of a related goods. n Ec = (Δ Qx/ ΔPy) x (Py/Qx) n Ec > 0, substitutes n Ec < 0, complements

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

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

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

Categories based on elasticity n Em > 0: Normal goods – Em > 1: Luxury goods – Em < 1: Necessity n Em < 0: Inferior goods

Engel’s Law n 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 n the income elasticity of demand of food is less than 1 (necessity)

Engel’s Coefficient % change in food expenditure / % change in total expenditure n % 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） n

Summary: Elasticity of Demand Price Elasticity Cross-Price Elasticity Income Elasticity %ΔQd / %ΔP %ΔQd(x)/ %ΔP(y) %ΔQd / %ΔY Elastic (horizontal) Complements Inelastic (vertical) Substitutes Unitary elastic Luxury/necessity Substitutability Normal vs. inferior Luxury vs. necessity

Price Elasticity of Supply n Definition: % change in Qs due to 1% change in P. n Formula: Es = %ΔQs / %ΔP = (ΔQs / Qs ) / (ΔP/P) = (Δ Qs /ΔP) x P/Qs

Again: slope and position S’ 14 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

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 n Es > 1: (Es →∞) Elastic price changes by 1%, quantity supplied changes by more than 1%. n Es < 1, (Es = 0) Inelastic price changes by 1%, quantity supplied changes by less than 1%

Unit Elastic Supply n Es = 1, Unit Elastic price changes by 1%, quantity supplied also changes by 1%

Factors Affecting Elasticity of Supply n Availability of inputs: – Flexibility; mobility; substitute n Length of production period n Difficulty of production n Technology

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The Revenue from an Excise Tax