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Elasticity Measures Lecture 10 Dr. Jennifer P. Wissink ©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved. March 1, 2017 i>clicker questions Can I use a cell phone or a smart phone or graphing calculator or anything like that for the prelim? A.Yes B.No Can I use a help sheet during the prelim? A.Yes B.No Should I buy a simple function calculator before Prelim 1? A.Yes B.No i>clicker question The own price elasticity of demand between points A and B on the graph below (and reported using absolute values) is 1.6. If we calculate the own price elasticity of demand using points A and C we would expect that A. the elasticity would be the same, that is 1.6, silly, since it’s a straight line! B. the elasticity would now be smaller than 1.6. C. the elasticity would now be larger than 1.6. Linear Demand Curve 42 41 40 B 39 Price 38 A 37 36 C 35 34 33 32 31 30 10 11 12 Quantity 13 14 POINT Own Price Elasticity of Demand at A, where P=$36 and QD=30-1/2P Recall the (midpoint) arc formula using points A and B. D X , PX Q D /[(Q D A Q D B )/2] 100 P/[(PA PB )/2] 100 Linear Demand Curve 42 41 40 Now let’s make B get closer and closer to A. – In the limit we would get the exact elasticity at point A. D X ,P X dQ /Q A 100 dP/PA 100 D D 38 Price B 39 A 37 36 C 35 34 33 32 31 30 10 Rearranging, you get: 11 12 Quantity D X , P [dQ D X / dPX ]( PX / Q D X ) evaluated at A X 13 14 Slope Compared to Elasticity The slope measures the rate of change of one variable (P, for example) in terms of another (Q, for example). An elasticity measures the percentage change of one variable (Q) in terms of percentage change in another (P). Point Elasticity As We Move Down a Linear Demand Curve ηDx,Px=[dQDx/dPx]•(Px/QDx) Price Own price elasticity of demand $P QD = 30 – 1/2P $60 Demand 36 A 12 30 Q i>clicker question At their respective market equilibriums, in which of the markets below would you expect market demand to be the most price elastic? A. The market for fruit. B. The market for fresh fruit. C. The market for fresh fruit you do not have to peel. D. The market for fresh apples. E. The market for fresh Gala variety apples. Determinants of Own Price Demand Elasticity What are the major determinants of the own price elasticity of demand? – Availability of substitutes in consumption. » thumb drives versus Lexar thumb drives – The importance of the item in individual budgets. » baby food versus textbooks (for you guys) – The time frame in question. » over a day versus over a year Perfectly Elastic Demand Demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded. Example: Price Perfectly Elastic Demand (elasticity = -) Quantity Perfectly Inelastic Demand Demand is perfectly inelastic when a 1% change in the price would result in no change in quantity demanded. Example: Price Perfectly Inelastic Demand (elasticity = 0) Quantity i>clicker question At their respective market equilibriums, in which of the markets below would you expect market demand to be the most price elastic? A. The market for fruit. B. The market for fresh fruit. C. The market for fresh fruit you do not have to peel. D. The market for fresh apples. E. The market for fresh Gala variety apples. Real World Example Gas taxes in Washington DC, 1980 – extra 6% tax imposed Aug 16, 1980 to raise much needed revenue for D.C. – increased price at pump by 8¢ (a nearly 6% increase) – By end of first month, QD down by 27.5% – elasticity = 27.5÷6 = 4.5 pretty darn elastic! – Way off on expected revenue, too. – By October, sales had dropped by 40% and 242 gas station workers were laid off. – Tax lifted by Mayor Marion Barry on November 24, 1980 i>clicker question What went wrong with the Barry administration’s model concerning gas taxes in Washington D.C.? A.People are too poor in D.C. so they can not pay taxes. B.They should have collected the taxes directly from demanders and not the suppliers. C.Gas station owners in D.C. are just not very good entrepreneurs. D.Mayor Barry’s economic advisers were pretty mediocre. E.Someone stole all the revenue before it got to the mayor. Own Price Elasticity of Demand & Total Expenditures (TE) Suppose: Current toll for the George Washington Bridge is $15/trip. Suppose: The quantity demanded at $15/trip is 1,000 trips/hour. TE on trips per hour = $15,000/hour i>clicker question If the own price elasticity of demand for bridge trips is known to be equal to -2.0, then what is the effect on TE of a 10% toll increase? A. TE increase B. TE stay the same C. TE decrease A 10% toll increase means the price is now $16.50 per trip. – If η = -2, a toll increase of 10% implies a 20% decline in the quantity demanded. – If there is a 20% decline in trips, number of trips falls to 800 trips/hour. TE are now only $13,200/hour (= 800 x $16.50), so TE decreased! Own Price Elasticity of Demand & Total Expenditures What happens to total expenditures (TE) made by buyers in a market when market price increases? Note: TE = PD•QD Price Perfectly Inelastic Demand (elasticity = 0) – PD↑ tends to increase TE. – QD↓ tends to decreases TE. – So what happens to TE? Knowing own price elasticity will help! – If demand is price ELASTIC, then TE ↓ » Why? – If demand is price INELASTIC, then TE ↑ » Why? Quantity On you own: reverse this argument to determine the relationship between total expenditure and elasticity when you consider a price decrease! Own Price Elasticity of Demand & Total Expenditure with Linear Demand $TE=P•Q Price Price elastic Demand Price inelastic Quantity Quantity Starting at the “top” of the demand curve, where demand is price elastic, as price falls, and quantity demanded rises, total expenditures rise, but increase at a decreasing rate. At the midpoint, where demand is unit elastic, total expenditures will be at their maximum value. As you continue down the demand curve, where demand is now price inelastic, as price falls, and quantity demanded rises, total expenditures fall. Own Price Elasticity of Demand & Total Expenditure with Linear Demand $TE=P•Q Price Price elastic Demand Price inelastic Quantity Quantity Example: Demand Function, Demand Curve & Own Price Elasticity of Demand Suppose you know the demand function for compact disc players (X) is: QDX = (T&P)(Pop) + 3I – 2PCD + 3PB – (5,145/T&P)PX Now… to go from the demand function to the demand curve, plug in values for everything BUT PX – So suppose: T&P=7; Pop=1,000; I=5,000; PCD=9; PB=15 – You get: – Now find own price elasticity of demand at PX=$7