Elasticity Claudia Garcia-Szekely 9/26/2011 1 The Price Elasticity of Demand • Measures the response of the quantity demanded to a change in price. • Compare how responsive to price changes is the quantity demanded of prescription drugs and that of strawberries. 9/26/2011 2 Consumers barely notice Consumers Overreact 110 110 100 100 Big change in Q 100 130 100 105 9/26/2011 3 Consumers barely notice Consumers Overreact 110 110 100 100 Big change in Q 100 130 100 105 9/26/2011 4 Calculating the Elasticity Price Quantity Demanded Point 0 25 A Midpoint Formula. 0.5 22 B The elasticity is 1 19 C measured between 1.5 16 D two points along a 2 13 E given demand 2.36 11 F curve. 2.5 10 G 3 7 H The elasticity between B 3.5 4 I and C measures the response to a $0.50 4 1 J change in the price. 4.5 0 K 9/26/2011 5 Midpoint Formula 1. Compute the Price Quantity Demanded Point difference 0 25 A between the two 0.5 22 B quantities: 22-19 = 1 19 C 3 2. Compute the 1.5 16 D average of the two 2 13 E quantities: (22 + 2.36 11 F 19)/2 = 41/2 = 20.5 2.5 10 G 3. Divide the answer 3 7 H you got in (1) by the 3.5 4 I answer in (2). This is 4 1 J the Percentage 4.5 0 K change in the quantity demanded: 3/20.5 = 0.146 9/26/2011 6 The Midpoint Formula Price Quantity Demanded Point 0 25 A 4. Compute the 0.5 22 B difference between 1 19 C the two prices: (1- 1.5 16 D 0.5) = 0.5 2 13 E 5. Compute the 2.36 11 F average of the two 2.5 10 G prices: (1+0.5)/2 = 3 7 H 0.75 3.5 4 I 6. Divide the answer in 4 1 J (4) by the answer in (5). This is the 4.5 0 K percentage change in the price: 0.5/0.75 =0.667. 9/26/2011 7 The Midpoint Formula 8. Divide the percentage change in the quantity demanded: the answer you got in (3), by the percentage change in the price: the answer you got in (6). The answer is the Price Elasticity of Demand between B and C. 0.146 / 0.667 = 0.21 9/26/2011 8 The Midpoint Formula Percentage Change Quantity Demanded epd = Percentage Change in price Change in Quantity / Average Quantity epd = Change in Price / Average Price 9/26/2011 9 The Price Elasticity of Demand • Measures the responsiveness of the quantity demanded to a change in price. • There is a negative relationship between the price and the quantity demanded. • The price elasticity of demand is ALWAYS NEGATIVE. 9/26/2011 10 Price elasticity of demand is ALWAYS NEGATIVE Always write a negative sign in front! Change in Quantity / Average Quantity epd = Change in Price / Average Price 9/26/2011 11 Three Types of Elasticities Consider only the absolute value of the elasticity: |E| The absolute value of the elasticity can be • |e|>1 Elastic • |e|=1 Unitarily Elastic • |e|<1 Inelastic 9/26/2011 12 Sensitive Demands are Elastic Demands (e > 1) Percentage Change in Quantity Demanded epd = Percentage Change in price If the numerator (DQ%) is larger than the denominator (DP%) then epd is greater than one. A relatively small change in price causes a relatively large change in quantity demanded. 9/26/2011 13 Insensitive Demands are Inelastic Demands (e < 1) Percentage Change in Quantity Demanded epd = Percentage Change in price If the numerator (DQ%) is smaller than the denominator (DP%), then epd is less than one. A relatively large change in price causes a relatively small change in quantity demanded. 9/26/2011 14 Example Elasticity It has been observed that 20% ahas no units! decrease in the price of good X, caused a 5% increase in the quantity demanded of X. epd = 5% / -20% = - 0.25 Elasticity of Demand is less than one: Inelastic 9/26/2011 15 Example It has been observed that a 5% increase in the price, caused a 10% reduction in the quantity demanded. epd = -10% / 5% = - 2 Elasticity of Demand is greater than one: Elastic 9/26/2011 16 1. Compute price elasticity PRICE QUANTITY 3 4 1 e = -1 12 9/26/2011 17 1. Compute price elasticity PRICE QUANTITY 5 4 1 e = - 0.75 12 9/26/2011 18 1. Compute price elasticity PRICE QUANTITY 3 3 1 e = -1.2 12 9/26/2011 19 At Midpoint Calculate the elasticity of demand between A and E E 9/26/2011 20 A is the Midpoint Calculate the elasticity AT A E 9/26/2011 21 The Elasticity Changes Along the Demand Curve As you move along a Quantity demand curve -as price Price Demanded Point Elasticity changes- the elasticity changes in absolute value. 0 25 A Elasticity Increases 0.5 22 B -0.06 As Price Increases 1 19 C -0.22 For low prices (at the 1.5 16 D -0.43 At of the bottomthe demand 2 13 E -0.72 midpoint, is curve) demand relatively inelastic 2.5 10 G -1.17 3 7 H -1.94 1 |e| =prices (at the top For high 3.5 4 I -3.55 of the demand curve) 4 1 J -9.00 demand is relatively elastic 4.5 0 K -17.00 The Elasticity Changes Along the Demand Curve |e| > 1 |e| = 1 |e| < 1 0 0 100 1000 100/2 == 500 1000/2 50 Midpoint 9/26/2011 23 Without calculating the elasticity: a. Is the elasticity at A > B? A < B? A=B? b. Is the elasticity at F F > 1? F < 1? F=1? c. Is the elasticity at E E = 1? 9/26/2011 24 Perfectly Elastic Demand • When the elasticity is a very large |e| = number (close to infinity) 0.61 • A perfectly elastic 0.6 demand shows that at the slightest increase in the price, the quantity demanded would drop to zero. 0 Units 100 Units Perfectly Inelastic Demand • When the elasticity is a very small number (close to 1.20 zero) • A perfectly inelastic demand shows that |e| = 0 even after a large change in the price 0.6 the quantity demanded would not change at all. 100 Units The demand curve with the smallest elasticity is _______ The demand curve with the largest elasticity is _______ Demand curve _______ is perfectly elastic Demand curve _______ is perfectly inelastic 9/26/2011 27 If the price elasticity of demand for good X is 0.5. In order to induce a 10% reduction in consumption of this good, the government would need to tax this good until the price rises by how much? edp= % D Q / % D P 0.5= 10%/ % D P 10 /0.5 =% D P 20 =% D P 28 What Determines the Elasticity? • The number of substitutes available. • The Definition of the market. • The length of time consumers have to react to a price change. • Necessities tend to have inelastic demands, whereas luxuries have elastic demands. – Example: Doctor visits, sailboats. 9/26/2011 29 The number of Substitutes Available. The more substitutes The more exist for a sensitive given good, the (elastic) easier it would demand would be for be to price consumers to changes switch. 9/26/2011 30 Definition of Common mistake: The more the market. + + = specific the more inelastic because only Ben and Jerry’s chocolate ice cream “will do” Narrowly defined markets have Ben and Jerry’s more elastic Chocolate demands. Ice Cream |epd | > 1 9/26/2011 31 Common mistake: The The Definition of the larger the set the more market. elastic because there are lots of “choices” HDz Broadly Ice Cream defined markets have B&J less elastic demands Food Cookies Beverages | epd | < 1 9/26/2011 32 2. Which product will be more elastic? Why? 2. Which product has more substitutes? a) All frozen desserts b) Ice cream c) Chocolate ice cream d) Ben and Jerry’s chocolate ice cream 9/26/2011 33 The Amount of Time to React • The longer the time allowed, the easier it is for consumers to find an alternative or modify their behavior. • Goods have more elastic demands over longer time horizons. Example: Gasoline. 9/26/2011 34 Two ways to increase revenue 1. Increase price, in order to make more per unit 2. Decrease price, in order to sell more units. 9/26/2011 35 Inelastic Demand Increase Price Decrease Price • Quantity sold drops • Quantity sold increase • Decrease in Q is • Increase in Q is SMALLER than increase SMALLER than in price decrease in price • Total Revenue increase. • Total Revenue decrease If demand is Inelastic, increase price to increase TR 9/26/2011 36 Elastic Demand Increase Price Decrease Price • Quantity sold drops • Quantity sold increase • Decrease in Q is • Increase in Q is LARGER than increase in LARGER than decrease price in price • Total Revenue decrease. • Total Revenue increase If demand is Elastic, decrease price to increase TR 9/26/2011 37 The Price Elasticity of Demand and Revenues • Total Revenues = Price x Quantity • An increase in price will increase TR only if the quantity demanded does not fall “too much”. • If the increase in price is larger than the drop in quantities, TR will increase. • This is precisely what happens if demand is _____________ Inelastic 9/26/2011 38 When Demand is Inelastic TR follow the change in P If the drop in quantities is smaller than the increase in price, total revenues will increase. TR = P x Q epd = D%Q / D%P epd = small/ Large |epd | < 1 This is the case when |e| < 1. 9/26/2011 39 When Demand is Elastic TR follow the change in Q If the drop in quantities sold is larger than the increase in price, total revenues will fall after a price increase. TR = Px Q epd = D%Q / D%P epd = Large/ small |epd | > 1 This is the case when |e| > 1 9/26/2011 40 Elasticity and Total Revenues TR = P x Q This is the case when |e| > 1. TR = P x Q This is the case when |e| < 1. 9/26/2011 41 Price Quantity Total Revenue elasticity 0 1,200 0 2 1,100 2200 0.0 4 1,000 4000 If total Revenues -0.1 6 900 5400 increase with a -0.3 Demand is 8 800 price increase 6400 Inelastic -0.4 10 700 7000 -0.6 12 600 7200 -0.8 14 500 7000 -1.2 16 400 6400 If total Revenues -1.7 18 300 5400 decrease with a -2.4 Demand is elastic 20 200 4000 price increase -3.8 22 100 2200 -7.0 24 0 0 -23.0 If a company increases prices and as a result: • Total Revenues • Total Revenues Decrease. Increase. • Then the effect of • Then the quantity higher prices, was sold did not drop completely offset enough to offset by the drop in the increase in Demand is quantities sold. Elastic price. Demand is Inelastic 9/26/2011 43 3. Is this demand elastic or inelastic? PRICE TOTAL ELASTICITY REVENUE 1 1,950,000 Demand is Inelastic 1.25 2,062,500 9/26/2011 44 The Elasticity Changes Along the Demand Curve Decrease Price to Increase TR |e| > 1 An increase/decrease in price |e| = 1 would leave TR unchanged Increase Price to Increase TR |e| < 1 Midpoint 9/26/2011 45 When Demand is Inelastic S1 S0 P1 P0 Gain L Gain > L o s o s s s D0 TR increase Q1 Q 0 9/26/2011 46 When Demand is Inelastic S0 S1 > P0 Loss Loss Gain P1 Gain D0 Q0 Q1 9/26/2011 TR decrease 47 When Demand is Elastic > S0 Gain S1 Loss P0 P1 Loss Gain D0 TR Increase Q0 Q1 9/26/2011 48 When Demand is Elastic S1 S0 > Loss Gain P1 Gain P0 Loss D0 TR Decrease Q1 Q0 9/26/2011 49 Elasticity and Price Controls • When supply and demand are both elastic, a price floor will cause a larger surplus than when supply and demand are inelastic • When supply and demand are both elastic, a price ceiling will cause a a larger shortage than when supply and demand are inelastic. 50 Questions to prepare for the Quiz 1. Assume that currently, a book publisher charges one price for a novel by author B. An economist determines that the price elasticity of demand for die hard fans of this author is – 0.4 and that the price elasticity of demand for regular buyers is –3. The advertising department comes up with the idea of publishing the same book in a hard cover version to be published first, and a soft cover version to be released two months after the release of the hard cover version. This would allow the publisher to charge different prices to these two groups. How would you advise them to set prices in order to increase total revenues? 2. Assume that currently, all customers pay the same price for a packet of cigarettes “Generic” brand D. An economist determines that the price elasticity of demand by adults is –0.4 and that the price elasticity of demand by teenagers is –3. The advertising department comes up with the idea of packaging cigarettes differently to target different groups: Target teenagers with “Cool” brand A and adults with “less tar” brand B. How would you adjust prices in order to increase your total revenues? You must provide a clear explanation for your answer. 2. Determine whether demand is elastic, inelastic, unit elastic or can’t tell: a. Chapped Hands Community College’s tuition increased from $20 per unit to $25 per unit. a. Inelastic Enrollment dropped from 8,000 to 7,200 0.47 students. b. Unit elastic b. Washington apple growers sell a 10% larger crop c. Can’t tell than last year’s , but the revenue they earned is d. Inelastic unchanged. e. Elastic c. Honda offers a $100 rebate on its largest rider 1.67 lawn mowers, and their sales rise 5%. f. Perfectly d. The price of doctor services falls and your Inelastic E=0 family’s total expenditures are less on doctor services and more on other things. e. The price of carnations rises by 15%. Florists substitute daisies and ferns ant the quantity used of carnations drop by 25%. f. The price of coffee drops by 25 cents per pound, but you continue to drink the same amount as before. Tax Soda to Fight Obesity? • Reducing soda intake by a 100 calories a day results in a half a pound of weight loss after 18 months. • A 10% tax on sodas, sport sodas and fruit juice cocktails would prompt consumers to reduce consumption by 8%. 9/26/2011 54 Demand Supply Demand Demand Price of Quantity Quantity Demand Demand Point X X good X X good X Complement Substitute good N good R A 20 200 120 350 1050 B 40 180 140 340 1065 C 60 160 160 330 1080 D 80 140 180 320 1095 E 100 120 200 310 1110 F 120 100 220 300 1125 3. Use the table above to answer the following questions: a. Calculate the elasticity of demand and the elasticity of supply at point B b. Should this producer increase, decrease or leave the price the same? Why? Use a supply and demand diagram to explain why… • Oil producing countries enjoy increases in their total revenues when they restrict supply. • Farmers suffer declines in their total revenues when they become more productive as a group. • Fresh tomato farmers enjoy increases in their total revenues when they become more productive as a group. • Oil producing countries would see their total revenues decrease if they were to increase oil production. • Restaurant owners see an increase in total revenues as competition from new restaurants increases. 9/26/2011 56 Table 5. Estimated Price Elasticities of Demand for Various Goods and Services Goods Estimated Elasticity of Demand Inelastic Salt 0.1 Matches 0.1 Toothpicks 0.1 Airline travel, short-run 0.1 Gasoline, short-run 0.2 Gasoline, long-run 0.7 Residential natural gas, short-run 0.1 Residential natural gas, long-run 0.5 Coffee 0.25 Fish (cod) consumed at home 0.5 Tobacco products, short-run 0.45 Legal services, short-run 0.4 Physician services 0.6 Taxi, short-run 0.6 Automobiles, long-run 0.2 Approximately Unitary Elasticity Movies 0.9 Housing, owner occupied, long-run 1.2 Shellfish, consumed at home 0.9 Oysters, consumed at home 1.1 Private education 1.1 Tires, short-run 0.9 Tires, long-run 1.2 Radio and television receivers 1.2 9/26/2011 58 Elastic Restaurant meals 2.3 Foreign travel, long-run 4 Airline travel, long-run 2.4 Fresh green peas 2.8 Automobiles, short-run 1.2 - 1.5 Chevrolet automobiles 4 Fresh tomatoes 4.6 9/26/2011 59 Types of Elasticity • Price elasticity of demand. • Price elasticity of supply. • Income elasticity of demand. • Cross Price elasticity of demand. 9/26/2011 60 The Price Elasticity of Supply • Measures the sensitivity of the quantity supplied to changes in the price. • Since there is a direct relationship between the price and the quantity supplied • The price elasticity of supply is always positive. 9/26/2011 61 Price Elasticity of Supply: eps D in Quantity Supplied / Average Quantity eps = Change in Price / Average Price Percentage Change in Quantity Supplied epd = Percentage Change in price 9/26/2011 62 Calculating the Price Elasticity of Supply • To calculate the price Price Q Supplied Elasticity elasticity of supply, 40 140 follow the same steps 50 160 0.60 60 180 0.65 as for the price 70 200 0.68 elasticity of demand. 80 220 0.71 • The only difference is 90 240 0.74 100 260 0.76 that the price 110 280 0.78 elasticity of supply is 120 300 0.79 always POSITIVE. 130 320 0.81 140 340 0.82 150 360 0.83 160 380 0.84 9/26/2011 63 Extreme Cases eps = infinity P D0 D1 Perfectly Elastic Supply suppliers can easily Po Supply increase or decrease production to match demand, Q0 Q1 Qs Perfectly Inelastic Supply P Supply suppliers cannot increase production eps = 0 to match demand. Supply is “fixed”. D1 D0 Qs 9/26/2011 Fixed Quantity 64 Perfectly Inelastic Supply The quantity supplied of DaVinci paintings doesn't change regardless of what the price is. The number of seats in a stadium/theater does not change regardless of price 9/26/2011 65 Elasticity changes along a P Supply Curve eps = infinity S S S eps = 0 Q 9/26/2011 66 Calculate the Elasticity at point B. 9/26/2011 67 Refer to the graph above. When price rises by 20%, Refer to the graph above. When price rises by 20%, quantity supplied remains the Which curve best quantity supplied rises by 20%.same. Which curve best 30% demonstrates the elasticity of supply in this example? demonstrates the elasticity of supply in this example? 9/26/2011 68 Without calculating the elasticity: a. Is the elasticity at A > B? A < B? A=B? b. Is the elasticity at E F > 1? F < 1? F=1? F c. Is the elasticity at C > D? C < D? C =D? d. Is the elasticity at E > 1? E < 1? E=1? e. Is the elasticity at C > 1? C < 1? C =1? 9/26/2011 69 Refer to the graph above. When price rises by 20%, quantity supplied increases by 5%. Which curve best demonstrates the elasticity of supply in this example? 9/26/2011 70 The Income Elasticity of Demand • Measures the sensitivity of Demand to changes in INCOME. • The relationship between Demand and INCOME depends on whether the good is normal or inferior. 9/26/2011 71 The Income Elasticity Formula Change in Quantity / Average Quantity epd = Change in Income / Average Income Percentage Change in Demand epd = Percentage Change in Income 9/26/2011 72 Normal Goods • The Demand for normal goods INCREASES when income INCREASES. • There is a positive relationship between income and demand for normal goods. • The sign of the income elasticity for normal goods is positive. 9/26/2011 73 Calculating Average Quantity Change in Quantity / the Income ey = d Elasticity (Normal Goods) Change in Income / Average Income 1. Find the Percentage Income DemandedEdy Q. change in quantity demanded = 100 / 1000 300 350 = 0.286 2000 400 0.43 2. Find the percentage 3000 500 0.56 change in income = 1000/1500 = 0.667 4000 600 0.64 3. The Income Elasticity = 5000 700 0.69 0.286/0.667 = 0.429 6000 800 0.73 7000 900 0.76 + 8000 1000 0.79 9/26/2011 74 Inferior Goods • Demand for inferior goods DECREASES when income INCRESES. • There is a negative relationship between income and demand for inferior goods. • The sign of the income elasticity for inferior goods is negative. 9/26/2011 75 Inferior Good Income Elasticity Income Q. Demanded Ed y 1000 1000 2000 900 -0.16 3000 800 -0.29 4000 700 -0.47 5000 600 -0.69 6000 500 -1.00 7000 400 -1.44 8000 300 -2.14 9/26/2011 76 The Cross Price Elasticity • Measures the sensitivity of the quantity demanded of one good to changes in the price of ANOTHER GOOD. • Goods can be either Complements or Substitutes. 9/26/2011 77 Cross Price Elasticity Formula % Change in Quantity demanded of Coke X epd = %Change in price of Pepsi Y. 9/26/2011 78 Cross Price Elasticity for Complements • The quantity demanded of a good decreases when the price of a complement increases, Example: When the price of PRINTERS increases, the quantity demanded of INK decreases. • The price of one good and the Demand of the other good move in opposite directions. • The cross price elasticity between complements is NEGATIVE. 9/26/2011 79 Cross Price Elasticity Complements ( Negative) Price X Qua ntity Y Cross Price Elasticity x,y 100.00 600.00 130.00 580.00 -0.130 160.00 All Negative! 560.00 -0.170 190.00 540.00 -0.212 220.00 520.00 -0.258 250.00 500.00 -0.307 280.00 480.00 -0.361 310.00 460.00 -0.418 340.00 440.00 -0.481 370.00 420.00 -0.550 9/26/2011 400.00 400.00 -0.626 80 Cross Price Elasticity for Substitutes • When the price of a substitute INCREASES, the quantity demanded of the good INCREASES. Example: When the price of movie tickets increases, the quantity demanded of video tapes increases too. • The price of one good and the Demand of the other move in the SAME direction. • The cross price elasticity between substitutes is POSITIVE. 9/26/2011 81 Cross Price Elasticity Substitutes (Positive) Price X Qua ntity Y Cross Price Elasticity x,z 100.00 600.00 130.00 620.00 0.126 160.00 640.00 0.153 190.00 All Positive! 660.00 0.179 220.00 680.00 0.204 250.00 700.00 0.227 280.00 720.00 0.249 310.00 740.00 0.269 340.00 760.00 0.289 370.00 780.00 0.307 400.00 800.00 0.325 9/26/2011 82 Use the information in table 1 above to calculate: 1. Price elasticity of demand for good X between points B and D. 2. Price elasticity of demand for good X at C. 3. Price elasticity of supply between A and B. 4. Cross Price elasticity between X and N between points E and F. Are X and N substitutes? Or complements? 5. Cross Price elasticity between X and R between points E and F. Are X and R substitutes? Or complements? Your answer must have a value AND A SIGN! Solutions 9/26/2011 84 Solutions 9/26/2011 85 Solutions 9/26/2011 86 Solutions 9/26/2011 87 9/26/2011 88

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