Chapter 5 Elasticity of Demand and Supply © 2009 South-Western/Cengage Learning

22 Price Elasticity of Demand Elasticity A measure of the responsiveness of Q d or Q s to a change in price or other economic variable Price elasticity of demand % change in Q d for a 1% change in price

Price Elasticity of Demand ε d = %ΔQ d / %ΔP = ΔQ d / Q d ΔP / P = ΔQ d x P ΔP Q d Law of demand ε d negative 3

Categories of Elasticities |ε| between 0 and 1 Inelastic |ε| greater than 1 Elastic |ε| = 1 Unit elastic |ε| = infinite Perfectly elastic |ε| = 0 Perfectly inelastic 4

Midpoint Formula Use the average Q and average P in the elasticity formula: average Q = (Q 1 + Q 2 ) / 2 average P = (P 1 + P 2 ) / 2 ε = ΔQ / (average Q) ΔP / (average P) = (Q 1 - Q 2 ) / (Q 1 + Q 2 ) (P 1 - P 2 ) / (P 1 + P 2 ) 5

Elasticity and Total Revenue Total revenue = price * quantity TR= p * q As p decreases –If D elastic, TR increases –If D inelastic, TR decreases –If D unit elastic, TR constant 6

Price Elasticity and the Linear D curve Linear D curve –Constant slope –Different elasticity –D becomes less elastic as we move downward D upper half: elastic D lower half: inelastic D midpoint: unit elastic 7

Exhibit 2 Demand, price elasticity and total revenue 8 D Price per unit $ b a d e Quantity per period1, Total revenue $25, Quantity per period1,000 0 (a) Demand and price elasticity (b) Total revenue Total revenue Unit elastic, E D =1 Elastic, E D >1 Inelastic, E D <1 Where D is elastic, a lower P increases TR Where D is inelastic, a lower P decreases TR TR reaches a maximum at the rate of output where D is unit elastic c

Exhibit 4 Summary of price elasticity of demand 9 Effects of a 10 percent increase in price Absolute value of price elasticity Type of demand What happens to quantity demanded What happens to total revenue 0 < ε d < 1InelasticDrops by less than 10 percent Increases by less than 10 percent ε d = 1Unit elasticDrops by 10 percent No change 1 < ε d <∞ElasticDrops by more than 10 percent Decreases

Determinants of Price Elasticity of D ε d is greater: –The greater the availability of substitutes, and the more similar the substitutes –The more important the good as a share of the consumer’s budget –The longer the period of adjustment (time) 10

Exhibit 5 Demand becomes more elastic over time 11 DwDw Price per unit $ DmDm Quantity per day DyDy e D w : one week after the price increase D m : one month after the price increase D y : one year after the price increase D y is more elastic than D m, which is more elastic than D w

Elasticity Estimates Short run –Consumers have little time to adjust Long run –Consumers can fully adjust to a price change Demand is more elastic in the long run 12

Exhibit 6 Selected price elasticities of D (absolute values) 13 ProductShort runLong run Cigarettes (among adults) Electricity (residential) Air travel Medical care and hospitalization Gasoline Milk Fish (cod) Wine Movies Natural gas (residential) Automobiles Chevrolets

Income Elasticity of Demand % change in Q d for a 1% change in income ε I = %ΔQ d / %ΔI Normal goods (Q d increases when I increases) –Positive income elasticity Inferior goods (Q d decreases when I increases) –Negative income elasticity 14

Income Elasticity of Demand Normal goods –Income inelastic Elasticity between 0 and 1 Necessities –Income elastic Elasticity > 1 Luxuries 15

Exhibit 10 Selected income elasticities of demand 16 Product Income ElasticityProduct Income Elasticity Wine Private education Automobiles Owner-occupied housing Furniture Dental service Restaurant meals Spirits (‘hard’ liquor) Shoes Chicken Clothing Physicians’ services Coca-Cola Beef Food Coffee Cigarettes Gasoline and oil Rental housing Pork Beer Flour

Cross-Price Elasticity of Demand % change in Q demanded of one good for a 1% change in the price of another good –ε X,Y = %ΔQ X / %ΔP Y –If positive: X and Y are substitutes –If negative: X and Y are complements –If zero: X and Y are unrelated 17

Price Elasticity of Supply Price elasticity of supply % change in Q s for a 1 percent change in price ε s = %ΔQ s / %ΔP Law of supply ε s positive 18

Constant Elasticity Supply Curves Perfectly elastic S curve –Horizontal; ε s = ∞ –Producers supply 0 at a price below P Perfectly inelastic S curve –Vertical; ε s = 0 –Goods in fixed supply Unit-elastic S curve – %∆p = %∆q –S is a ray from the origin 19

Determinants of Supply Elasticity ε s is greater: –cost and feasibility of storage –production process –the longer the period of adjustment (time) 20

Exhibit 9 Supply becomes more elastic over time 21 SwSw Price per unit 1.00 $1.25 Quantity per day SmSm SySy S w : one week after the price increase S m : one month after the price increase S y : one year after the price increase S w is less elastic than S m, which is less elastic than S y

Price Elasticity and Tax Incidence Tax –Decrease in S by the amount of tax S shifts upward by the tax Tax incidence –distribution of the tax burden 22

Price Elasticity and Tax Incidence The more price elastic the D: –The more tax producers pay –The less tax consumers pay The more elastic the S: –The less tax producers pay –The more tax consumers pay 23

Price Elasticity and Tax Incidence The issue of tax incidence depends on the relationship between ε d and ε s If | ε d | > ε s producers bear more of the burden of the tax If | ε d | < ε s consumers bear more of the burden of the tax 24