C H A T E R In 5 this chapter, look for the answers to these questions: Elasticity and its Application R I N C I L E O F Microeonomics N. Gregory Mankiw remium oweroint lides by Ron Cronovich 2009 outh-western, a part of Cengage Learning, all rights reserved What is elasticity? What kinds of issues can elasticity help us understand? What is the price elasticity? How is it related to the demand curve? How is it related to revenue & expenditure? What is the price elasticity? How is it related to the supply curve? What are the income and cross-price elasticities of demand? 1 A scenario You design websites for local businesses. You charge $200 per website, and currently sell 12 websites per month. Your costs are rising (including the opportunity cost of your time), so you consider raising the price to $250. The law says that you won t sell as many websites if if you raise your price. How many fewer websites? How much will your revenue fall, or might it it increase? Elasticity Basic idea: Elasticity measures how much one variable responds to changes in another variable. One type of elasticity measures how much demand for your websites will fall if you raise your price. efinition: Elasticity is a numerical measure of the responsiveness of d or s to one of its determinants. 2 ELATICITY AN IT ALICATION 3 1
rice Elasticity of emand rice Elasticity of emand rice elasticity ercentage change in d ercentage change in rice elasticity ercentage change in d ercentage change in rice elasticity measures how much d responds to a change in. Loosely speaking, it measures the pricesensitivity of buyers demand. Example: rice elasticity equals 15% 10% 1.5 rises 2 1 falls by 15% 2 1 ELATICITY AN IT ALICATION 4 ELATICITY AN IT ALICATION 5 rice Elasticity of emand Calculating ercentage Changes rice elasticity Along a curve, and move in in opposite directions, which would make price elasticity negative. We will drop the minus sign and report all all price elasticities as as positive numbers. ercentage change in d ercentage change in 2 1 2 1 $250 $200 emand for your websites 8 B 12 A tandard method of computing the percentage (%) change: end value start value start value x 100% Going from A to B, the % change in equals ($250 $200)/$200 25% ELATICITY AN IT ALICATION 6 ELATICITY AN IT ALICATION 7 2
$250 $200 Calculating ercentage Changes emand for your websites 8 B 12 A roblem: The standard method gives different answers depending on where you start. From A to B, rises 25%, falls 33%, elasticity 33/25 1.33 From B to A, falls 20%, rises 50%, elasticity 50/20 2.50 Calculating ercentage Changes o, we instead use the midpoint method: end value start value midpoint x 100% The midpoint is the number halfway between the start & end values, the average of those values. It doesn t matter which value you use as the start and which as the end you get the same answer either way! ELATICITY AN IT ALICATION 8 ELATICITY AN IT ALICATION 9 Calculating ercentage Changes Using the midpoint method, the % change in equals $250 $200 $225 The % change in equals 12 8 10 x 100% 22.2% x 100% 40.0% The price elasticity equals 40/22.2 1.8 A C T I V E L E A R N I N G 1 Calculate an elasticity Use the following information to calculate the price elasticity for hotel rooms: if $70, d 5000 if $90, d 3000 ELATICITY AN IT ALICATION 10 11 3
A C T I V E L E A R N I N G 1 Answers Use midpoint method to calculate % change in d (5000 3000)/4000 50% % change in ($90 $70)/$80 25% The price elasticity equals 50% What determines price elasticity? To learn the determinants of price elasticity, we look at a series of examples. Each compares two common goods. In each example: uppose the prices of both goods rise by 20%. The good for which d falls the most (in percent) has the highest price elasticity. Which good is it? Why? What lesson does the example teach us about the determinants of the price elasticity? 25% 2.0 12 ELATICITY AN IT ALICATION 13 EXAMLE 1: Breakfast cereal vs. unscreen The prices of both of these goods rise by 20%. For which good does d drop the most? Why? Breakfast cereal has close substitutes (e.g., pancakes, Eggo waffles, leftover pizza), so buyers can easily switch if the price rises. unscreen has no close substitutes, so consumers would probably not buy much less if its price rises. Lesson: rice elasticity is higher when close substitutes are available. ELATICITY AN IT ALICATION 14 EXAMLE 2: Blue Jeans vs. Clothing The prices of both goods rise by 20%. For which good does d drop the most? Why? For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, peedos). There are fewer substitutes available for broadly defined goods. (There aren t too many substitutes for clothing, other than living in a nudist colony.) Lesson: rice elasticity is higher for narrowly defined goods than broadly defined ones. ELATICITY AN IT ALICATION 15 4
EXAMLE 3: Insulin vs. Caribbean Cruises The prices of both of these goods rise by 20%. For which good does d drop the most? Why? To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no decrease in demand. A cruise is a luxury. If the price rises, some people will forego it. Lesson: rice elasticity is higher for luxuries than for necessities. EXAMLE 4: Gasoline in the hort Run vs. Gasoline in the Long Run The price of gasoline rises 20%. oes d drop more in the short run or the long run? Why? There s not much people can do in the short run, other than ride the bus or carpool. In the long run, people can buy smaller cars or live closer to where they work. Lesson: rice elasticity is higher in the long run than the short run. ELATICITY AN IT ALICATION 16 ELATICITY AN IT ALICATION 17 The eterminants of rice A ummary The price elasticity depends on: the extent to which close substitutes are available whether the good is a necessity or a luxury how broadly or narrowly the good is defined the time horizon elasticity is higher in the long run than the short run The Variety of emand Curves The price elasticity is closely related to the slope of the demand curve. Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity. Five different classifications of curves. ELATICITY AN IT ALICATION 18 ELATICITY AN IT ALICATION 19 5
erfectly inelastic demand (one extreme case) rice elasticity curve: vertical Consumers none 0 % change in % change in falls ELATICITY AN IT ALICATION 20 1 2 1 0% 10% 0 changes by 0% Inelastic demand rice elasticity curve: relatively steep Consumers relatively low < 1 % change in % change in falls ELATICITY AN IT ALICATION 21 1 2 < 10% 10% < 1 1 2 rises less than 10% Unit elastic demand rice elasticity % change in % change in 10% 10% 1 Elastic demand rice elasticity % change in % change in > 10% 10% > 1 curve: intermediate slope Consumers intermediate 1 falls ELATICITY AN IT ALICATION 22 1 2 1 2 rises curve: relatively flat Consumers relatively high falls 1 2 > 1 rises more than 10% ELATICITY AN IT ALICATION 23 1 2 6
erfectly elastic demand (the other extreme) rice elasticity curve: horizontal Consumers extreme infinity % change in % change in 2 changes by 0% ELATICITY AN IT ALICATION 24 1 any % 0% infinity 1 2 changes by any % Elasticity of a Linear emand Curve $30 20 10 E 200% 40% 5.0 E $0 0 20 40 60 67% 67% 1.0 E 40% 200% 0.2 The slope of a linear demand curve is constant, but its elasticity is not. ELATICITY AN IT ALICATION 25 rice Elasticity and Total Revenue Continuing our scenario, if you raise your price from $200 to $250, would your revenue rise or fall? Revenue x A price increase has two effects on revenue: Higher means more revenue on each unit you sell. But you sell fewer units (lower ), due to Law of emand. Which of these two effects is bigger? It depends on the price elasticity. ELATICITY AN IT ALICATION 26 rice Elasticity and Total Revenue rice elasticity ercentage change in ercentage change in Revenue x If demand is elastic, then price elast. > 1 % change in > % change in The fall in revenue from lower is greater than the increase in revenue from higher, so revenue falls. ELATICITY AN IT ALICATION 27 7
rice Elasticity and Total Revenue Elastic demand (elasticity 1.8) If $200, 12 and revenue $2400. If $250, 8 and revenue $2000. When is elastic, a price increase causes revenue to fall. $250 $200 increased emand for revenue due your websiteslost to higher revenue due to lower ELATICITY AN IT ALICATION 28 8 12 rice Elasticity and Total Revenue rice elasticity ercentage change in ercentage change in Revenue x If demand is inelastic, then price elast. < 1 % change in < % change in The fall in revenue from lower is smaller than the increase in revenue from higher, so revenue rises. In our example, suppose that only falls to 10 (instead of 8) when you raise your price to $250. ELATICITY AN IT ALICATION 29 rice Elasticity and Total Revenue Now, demand is inelastic: elasticity 0.82 If $200, 12 and revenue $2400. If $250, 10 and revenue $2500. $250 $200 When is inelastic, a price increase causes revenue to rise. increased emand for ELATICITY AN IT ALICATION 30 revenue your websites due A. harmacies raise the price of insulin. to higher lost revenue oes total expenditure on insulin rise or fall? due to lower B. As a result of a fare war, the price of a luxury cruise falls 20%. oes luxury cruise companies total revenue rise or fall? 10 12 A C T I V E L E A R N I N G 2 Elasticity and expenditure/revenue 31 8
A C T I V E L E A R N I N G 2 Answers A. harmacies raise the price of insulin. oes total expenditure on insulin rise or fall? Expenditure x ince demand is inelastic, will fall less than 10%, so expenditure rises. 32 A C T I V E L E A R N I N G 2 Answers B. As a result of a fare war, the price of a luxury cruise falls 20%. oes luxury cruise companies total revenue rise or fall? Revenue x The fall in reduces revenue, but increases, which increases revenue. Which effect is bigger? ince demand is elastic, will increase more than 20%, so revenue rises. 33 ALICATION: oes rug Interdiction Increase or ecrease rug-related Crime? One side effect of illegal drug use is crime: Users often turn to crime to finance their habit. We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime. For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs. emand for illegal drugs is inelastic, due to addiction issues. ELATICITY AN IT ALICATION 34 Interdiction reduces the supply of drugs. ince demand for drugs is inelastic, rises proportionally more than falls. olicy 1: Interdiction rice of rugs 2 1 Result: an increase in total spending on drugs, and in drug-related crime new value of drugrelated crime ELATICITY AN IT ALICATION 35 1 2 1 2 1 initial value of drugrelated crime uantity of rugs 9
Education reduces the demand for drugs. and fall. Result: A decrease in total spending on drugs, and in drug-related crime. olicy 2: Education rice of rugs 1 2 new value of drugrelated crime uantity of rugs ELATICITY AN IT ALICATION 36 2 1 2 1 initial value of drugrelated crime rice Elasticity of upply rice elasticity ercentage change in s ercentage change in rice elasticity measures how much s responds to a change in. Loosely speaking, it measures sellers price-sensitivity. Again, use the midpoint method to compute the percentage changes. ELATICITY AN IT ALICATION 37 rice Elasticity of upply rice elasticity Example: rice elasticity equals 16% 8% 2.0 ercentage change in s ercentage change in rises by 8% 2 1 ELATICITY AN IT ALICATION 38 rises by 16% 1 2 The Variety of upply Curves The slope of the supply curve is closely related to price elasticity. Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity. Five different classifications. ELATICITY AN IT ALICATION 39 10
erfectly inelastic (one extreme) rice elasticity % change in % change in 0% 10% 0 Inelastic rice elasticity % change in % change in < 10% 10% < 1 curve: vertical ellers none 0 rises ELATICITY AN IT ALICATION 40 2 1 1 changes by 0% curve: relatively steep ellers relatively low < 1 rises ELATICITY AN IT ALICATION 41 2 1 1 2 rises less than 10% Unit elastic rice elasticity % change in % change in 10% 10% 1 Elastic rice elasticity % change in % change in > 10% 10% > 1 curve: intermediate slope ellers intermediate 1 rises ELATICITY AN IT ALICATION 42 2 1 1 2 rises curve: relatively flat ellers relatively high > 1 rises ELATICITY AN IT ALICATION 43 2 1 1 2 rises more than 10% 11
erfectly elastic (the other extreme) rice elasticity curve: horizontal ellers extreme infinity % change in % change in 2 changes by 0% ELATICITY AN IT ALICATION 44 1 1 any % 0% infinity 2 changes by any % The eterminants of upply Elasticity The more easily sellers can change the quantity they produce, the greater the price elasticity of supply. Example: upply of beachfront property is harder to vary and thus less elastic than supply of new cars. For many goods, price elasticity is greater in the long run than in the short run, because firms can build new factories, or new firms may be able to enter the market. ELATICITY AN IT ALICATION 45 A C T I V E L E A R N I N G 3 Elasticity and changes in equilibrium The supply of beachfront property is inelastic. The supply of new cars is elastic. uppose population growth causes demand for both goods to double (at each price, d doubles). For which product will change the most? For which product will change the most? A C T I V E L E A R N I N G 3 Answers When supply is inelastic, an increase in demand has a bigger impact on price than on quantity. 2 1 1 Beachfront property (inelastic supply): 2 A B 46 1 2 47 12
A C T I V E L E A R N I N G 3 Answers How the rice Elasticity of upply Can Vary When supply is elastic, an increase in demand has a bigger impact on quantity than on price. 2 1 1 2 New cars (elastic supply): A 1 B 2 48 $15 4 $3 12 elasticity > 1 100 200 elasticity < 1 500 ELATICITY AN IT ALICATION 49 525 upply often becomes less elastic as rises, due to capacity limits. Other Elasticities Income elasticity : measures the response of d to a change in consumer income Income elasticity ercent change in d ercent change in income Recall from Chapter 4: An increase in income causes an increase in demand for a normal good. Hence, for normal goods, income elasticity > 0. For inferior goods, income elasticity < 0. ELATICITY AN IT ALICATION 50 Other Elasticities Cross-price elasticity : measures the response for one good to changes in the price of another good Cross-price elast. % change in d for good 1 % change in price of good 2 For substitutes, cross-price elasticity > 0 (e.g., an increase in price of beef causes an increase in demand for chicken) For complements, cross-price elasticity < 0 (e.g., an increase in price of computers causes decrease in demand for software) ELATICITY AN IT ALICATION 51 13
Cross-rice Elasticities in the News As Gas Costs oar, Buyers Flock to mall Cars -New York Times, 5/2/2008 Gas rices rive tudents to Online Courses -Chronicle of Higher Education, 7/8/2008 Gas prices knock bicycle sales, repairs into higher gear -Associated ress, 5/11/2008 Camel demand soars in India (as a substitute for gas-guzzling tractors ) -Financial Times, 5/2/2008 High gas prices drive farmer to switch to mules -Associated ress, 5/21/2008 ELATICITY AN IT ALICATION 52 CHATER UMMARY Elasticity measures the responsiveness of d or s to one of its determinants. rice elasticity equals percentage change in d divided by percentage change in. When it s less than one, demand is inelastic. When greater than one, demand is elastic. When demand is inelastic, total revenue rises when price rises. When demand is elastic, total revenue falls when price rises. 53 CHATER UMMARY CHATER UMMARY emand is less elastic in the short run, for necessities, for broadly defined goods, or for goods with few close substitutes. rice elasticity equals percentage change in s divided by percentage change in. When it s less than one, supply is inelastic. When greater than one, supply is elastic. rice elasticity is greater in the long run than in the short run. 54 The income elasticity measures how much quantity demanded responds to changes in buyers incomes. The cross-price elasticity measures how much demand for one good responds to changes in the price of another good. 55 14