4 ELASTICITY

C h a p t e r K e y I d e a sPredicting Prices

A. To predict the quantitative effects of changes in demand and supply on prices and quantities, we need to know how responsive demand and supply are to price and other influences on buying plans and selling plans.

B. This chapter explains how we measure the responsive demand and supply to price and other influences on buying plans and selling plans using the concept of elasticity. It explains how we calculate, interpret, and use elasticity.

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I. Price Elasticity of DemandA. Figure 4.1 shows how the demand curve influences the price and

quantity responses that result from a given change in supply. The figure highlights the need for a measure of the responsiveness of the quantity demanded to a price change.

B. The price elasticity of demand is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price when all other influences on buyers’ plans remain the same.

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C. Calculating Elasticity1. The price elasticity of demand is equal to

.

2. To calculate the price elasticity of demand, we express the change in price as a percentage of the average price—the midpoint between the initial and new price.

3. Similarly we express the change in the quantity demanded as a percentage of the average quantity demanded—the average of the initial and new quantity.

4. Figure 4.2 shows what is needed to calculate the price elasticity of demand for pizza: The percentage change in quantity demanded is %Q, and the percentage change in price is %P. We calculate %Q as Q/Qave and we calculate %P as P/Pave so we calculate the price elasticity of demand as (Q/Qave)/(P/Pave).a) By using the average

price and average quantity, the elasticity is the same value whether the price rises or falls.

b) The ratio of two proportionate changes is the same as the ratio of two percentage changes. The measure is “units-free” because it is a ratio of two percentage changes and the percentages cancel out. Changing the units of measurement of price or quantity leave the value of the elasticity the same.

c) The demand elasticity formula yields a negative value, because price and quantity move in opposite directions. However, it is the magnitude, or absolute value, of the measure that reveals how responsive the quantity change has been to a price change. So we use the magnitude or the absolute value of the price elasticity of demand.

D. Inelastic and Elastic DemandDemand can be inelastic, unit elastic, or elastic, and can range from zero to infinity.1. If the quantity demanded doesn’t change when the price changes,

the price elasticity of demand is zero and demand is perfectly inelastic. The demand curve is vertical. Figure 4.3a illustrates this case.

2. If the percentage change in the quantity demanded equals the percentage change in price, the value of the price elasticity of demand equals 1 and demand is unit elastic. Figure 4.3b illustrates this case—a demand curve with ever declining slope. (Note that a unit elastic demand curve is not linear.)

3. Between the two previous cases, the percentage change in the quantity demanded is smaller than the percentage change in price so that the value of the price elasticity of demand is less than 1 and demand is inelastic.

4. If the percentage change in the quantity demanded is infinitely large when the price barely changes, the value of the price elasticity of demand is infinite and demand is perfectly elastic. The demand curve is horizontal. Figure 4.3c illustrates this case.

5. If the percentage change in the quantity demanded is greater than the percentage change in price, the value of the price elasticity of demand is greater than 1 and demand is elastic.

E. Elasticity Along a Straight-Line Demand Curve1. While moving along a linear

demand curve, the demand becomes less elastic as the price falls. Figure 4.4 illustrates this fact.

2. Demand is unit elastic at the mid-point of the demand curve.

E. Total Revenue and Elasticity

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1. The total revenue from the sale of good equals the price of the good multiplied by the quantity sold.

2. The change in total revenue from a change in price depends upon the elasticity of demand:a) If demand is elastic, a 1 percent price cut increases the quantity

sold by more than 1 percent, and total revenue increases.b) If demand is inelastic, a 1 percent price cut decreases the

quantity sold by more than 1 percent, and total revenue decreases.

c) If demand is unitary elastic, a 1 percent price cut increases the quantity sold by 1 percent, and total revenue remains unchanged.

3. The total revenue test is a method of estimating the price elasticity of demand by observing the change in total revenue that results from a price change (when all other influences on the quantity demanded remain unchanged).a) If a price cut increases

total revenue, then demand is elastic.

b) If a price cut decreases total revenue, then demand is inelastic.

c) If a price cut leaves total revenue unchanged, then demand is unitary elastic.

4. Figure 4.5 shows the relationship between elasticity of demand for pizzas and the total revenues from pizza sales across the entire demand curve for pizza.

F. The Factors That Influence the Elasticity of DemandThe magnitude of the elasticity of demand depends on three factors:1. The closeness of

substitutes:

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a) The closer the substitutes for a good or service, the more elastic the demand for it.

b) Necessities, such as food or housing, generally have inelastic demand.

c) Luxuries, such as exotic vacations, generally have elastic demand.

2. The proportion of income spent on the good. a) The greater the proportion of income consumers spend on a

good, the larger is the demand elasticity for that good.

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b) Figure 4.6 shows the proportion of income spent on food in different countries. This table shows how the magnitude of the price elasticity of demand for food rises as the fraction of income spent on food increases.

3. The time elapsed since a price change. a) The more time

consumers have to adjust to a price change the more elastic the demand for that good.

II. More Elasticities of DemandA. Cross Elasticity of Demand

1. The cross elasticity of demand is a measure of the responsiveness of demand for a good to a change in the price of a substitute or a compliment, other things remaining the same.

2. The formula for the cross elasticity of demand is:

a) The cross elasticity of demand for a substitute is positive. Figure 4.7 shows the increase in the quantity of pizza demanded when the price of hamburger (a substitute for pizza) rises.

b) The cross elasticity of demand for a complement is negative. Figure 4.7 shows the decrease in the quantity of pizza demanded when the price of a soft drink (a complement of pizza) rises.

B. Income Elasticity of Demand1. The income elasticity of demand measures the responsiveness

of the demand for a good or service to a change in income, other things remaining the same.

2. The formula for the income elasticity of demand is:

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a) If the income elasticity of demand is greater than 1, demand is income elastic and the good is a normal good.

b) If the income elasticity of demand is positive but less than 1, demand is income inelastic and the good is a normal good.

c) If the income elasticity of demand is negative the good is an inferior good.

3. Table 4.2 shows estimates of income elasticity of demand for various goods and services.

4. Figure 4.8 shows estimates of the income elasticity for food in different countries. In countries with high average incomes per person, the size of the income elasticity of demand for food is smaller.

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III. Elasticity of SupplyA. Figure 4.9 shows how the supply

curve influences the price and quantity responses that result from a given change in demand and highlights the need for a measure of the responsiveness of the quantity supplied to a price change.

B. The elasticity of supply measures the responsiveness of the quantity supplied to a change in the price of a good when all other influences on selling plans remain the same.

C. Calculating the Elasticity of Supply1. The formula for the elasticity of supply is:

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2. Figure 4.10 shows three cases of the elasticity of supply.

a) Supply is perfectly inelastic if the elasticity of supply equals 0. In this case, as Figure 4.10a shows, the supply curve is vertical.

b) Supply is unit elastic if the elasticity of supply equals 1. In this case, as Figure 4.10b shows, the supply curve is linear and passes through the origin. The slope of the supply curve is irrelevant.

c) Supply is perfectly elastic if the elasticity of supply is infinite. In this case, as Figure 4.10c shows, the supply curve is horizontal.

D. The Factors That Influence the Elasticity of SupplyThe elasticity of supply depends on1. Resource substitution possibilities: The easier it is to substitute

among the resources used to produce a good or service, the greater is its elasticity of supply.

2. The time frame for supply decisions: The more time that passes after a price change, the greater is the elasticity of supply.

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E. Table 4.3 provides a glossary of the all elasticity measures.

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R e a d i n g B e t w e e n t h e L i n e sA news article discusses how a record company, Universal Music, is slashing prices on CDs in an attempt to increase its revenues. The analysis points out that using the data from Universal Music in the article, the demand for CDs is inelastic so that a price cut will decrease Universal’s revenue.

N e w i n t h e S e v e n t h E d i t i o nThere are only a few minor changes to this chapter.

Te a c h i n g S u g g e s t i o n s1. Teaching the Elements of Calculating Price Elasticity of Demand

a. Percentages and percentage changes. Many students need a refresher for calculating percentage changes. Don’t be afraid to start with this pre-elasticity warm up to assess the sharpness of your class. Ask: “Suppose that the campus bookstore increases the price of an economics text from $75 to $100. What is the percentage increase in price?” Many will say 25 percent instead of 33 percent.

b. Devise a Mnemonic for Elasticity Calculations. Many students have a hard time remembering whether quantity or price goes in the numerator of the elasticity formulas. Have the students create their own mnemonic. Suggest McDonald’s Quarter Pounder™ hamburgers. It’s silly, but it works, reminding the student that Q (quantity) appears before P (price) in the ratio of percentage changes. (Remind them that using the alphabet won’t work.)

2. Elasticity and slope along a linear demand curve. After covering the three categories of things which influence over the magnitude of the elasticity value, you can provide solid intuition on why demand becomes more elastic as we move up the linear demand curve and reinforce one of the categories. Note how the price of the good or service is increasing, purchasing that good or service will necessarily take up a larger and larger proportion of a fixed budget. Consumers will naturally become more responsive to an increase in price as we raise price along a demand curve.

3. Insights into the Cross Elasticities of DemandEmphasize the information content in the algebraic sign of the cross elasticity and the income elasticity. A negative sign indicates the goods are complements and a positive sign indicates they are substitutes. Compare this with the price elasticity of demand for which we focus only on the magnitude and not the sign.

4. Insights into the elasticity of SupplyThe unit elastic demand curve is a good one to use to emphasize that elasticity and slope are not equal. Have the students calculate the elasticity of

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supply on two linear demand curves that passes through the origin, one with a slope of 0.5 and the other with a slope of 2. They’ll get the message.

5. Testing their knowledge of the elasticity formula. For each of the following goods, the price increase was caused by a 10 percent decrease in quantity supplied. Which good has an inelastic demand and which has an elastic demand?

The price of gasoline increased from $1.00 to $1.50 per gallon. (Inelastic)

The price of coffee increases from $5.00 to $6.00 per pound. (Inelastic) The price of a theater ticket increased from $7.50 to $8.00. (Elastic) The price of a large pizza increased from $10.00 to $11.00 (Unit elastic)

6. Testing their knowledge of the income elasticity formula. For each of the following goods, assume the change in quantity resulted from a student receiving a 50 percent increase in her income upon becoming employed full time after graduation. Which of these goods does she consider as inferior goods? Which are normal and income elastic? Which are normal and income inelastic?

The quantity of Raman Noodles eaten declined from five boxes per day to one box per month. (Inferior)

The quantity of margaritas consumed increased from 1 per week to 2 per week. (Income elastic)

The square feet of apartment space rented per month increased from 1000 to 1250 square feet per month. (Income inelastic)

The quantity of food consumed was unchanged. (Perfectly income inelastic)

T h e B i g P i c t u r eWhere we have been:The student can now use the demand and supply model to generate predictions and can supplement this knowledge with the ability to provide richer predictions based on the elasticities of demand and supply.

Where we are going:Demand, supply, and demand elasticity get an extensive work out in Chapter 6, where we use them to explain the division of a tax burden between buyer and seller in the market for illegal drugs and the volatile revenues received by agricultural firms. However, before doing that analysis, we study the efficiency and fairness of markets in Chapter 5. Chapter 11 also uses elasticity to contrast the long-run versus short-run response to a change in demand in perfect competition. And the relationship between total revenue and the price elasticity of demand is used in Chapter 12 to show that a monopoly never operates on the inelastic part of the demand curve.

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O v e r h e a d Tr a n s p a r e n c i e sTransparency Text figure Transparency title

20 Figure 4.2 Calculating the Elasticity of Demand21 Figure 4.3 Inelastic and Elastic Demand22 Figure 4.4 Elasticity Along a Straight-Line Demand

Curve23 Figure 4.5 Elasticity and Total Revenue24 Figure 4.7 Cross Elasticity of Demand25 Table 4.3 A Compact Glossary of Elasticities

E l e c t r o n i c S u p p l e m e n t sMyEconLabMyEconLab provides pre- and post-tests for each chapter so that students can assess their own progress. Results on these tests feed an individualized study plan that helps students focus their attention in the areas where they most need help. Instructors can create and assign tests, quizzes, or graded homework assignments that incorporate graphing questions. Questions are automatically graded and results are tracked using an online grade book.

PowerPoint Lecture NotesPowerPoint Electronic Lecture Notes with speaking notes are available and offer a full summary of the chapter.PowerPoint Electronic Lecture Notes for students are available in MyEconLab.

Instructor CD-ROM with Computerized Test BanksThis CD-ROM contains Computerized Test Bank Files, Test Bank, and Instructor’s Manual files in Microsoft Word, and PowerPoint files. All test banks are available in Test Generator Software.

A d d i t i o n a l D i s c u s s i o n Q u e s t i o n s1. Is the demand for higher education price elastic or price inelastic?

Use the student’s familiarity with college life to make them comfortable in using an economic model to describe the demand for a college education. Ask the students to assume that a survey of 100 state universities revealed how real tuition price per class credit has increased an average of 20 percent over the past five years while that total class credits purchased over the same period declined an average of only 5 percent. Ask the students what assumptions would be necessary to ensure this measure of

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the price elasticity of demand for college is valid. They should recognize that ceteris paribus conditions should be observed: The price of alternative education/training opportunities (substitutes)

was held constant. The price of the amenities of college life like dorms, meal programs,

etc. (compliments) was held constant. The income of the students or their parents was held constant.If the tuition hike was in response to an increase in education costs per class credit, should schools receive supplemental revenues from the state taxpayers? Assume that many of these schools lobbied their respective state governments to receive additional revenues, citing a small but significant decrease in the number of students taking course credits. If the demand for college education is truly inelastic, ask the students to provide a possible justification for refusing this request. The students should recognize that school enrollment is not the issue, but total tuition revenues collected by the school that matters most. They should recognize that even though the total number of student credits declined, inelastic demand implies that the total tuition revenues received from those fewer students must have increased along with the tuition price.

2. Economic analysis and various law enforcement issues: The students may be surprised to see how economic concepts can explain much of what we observe happening in the area of law enforcement: How does inelastic student demand for parking hinder police efforts at preventing illegal student parking? Illegal student parking is a hassle that every university police force must deal with. Ask the students whether the campus police will have more success with doubling the current parking fine, or liberally using the “boot,” which is a heavy iron clamp locked to the wheel of a car, rendering it immobile. Students will understand that raising the parking ticket fees is simply raising the price for illegal parking, and if quantity demanded does not decrease very much, demand for those choice parking spots is inelastic. To significantly decrease the incidence of illegal parking, the price must be raised substantially. Having their personal transportation severely restricted for a period of time is a much higher “price” with a more effective result. How does the inelastic demand for drugs help the police to monitor the effectiveness of drug interdiction operations? Tell students that if the demand for illegal drugs were very elastic, the difference in the street price of drugs resulting from a relatively small decrease in the supply would be difficult to discern from the “noise” of the observed market data. Because the demand for drugs is very inelastic, even a small decrease in supply will generate an easily discernable increase in the street price. This is why the police commonly state how much the street price increased after a drug bust. The police can easily get feedback to learn which interdiction techniques and operations were the most effective.

D. Fuel for thought: Getting some intuition on what determines whether demand is inelastic or elastic:

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The demand for gasoline and junk food in general. Students love their cars and to eat junk food and they know that the demand for both in general is inelastic, because there are no good substitutes for personal transportation or for a quick snack. Ask them if they think the demand for these is elastic or inelastic. They’ll likely say that demand for fast access junk food and gasoline is inelastic.The demand for convenience store gasoline. Ask your students if Joe’s Quick-Mart (substitute your actual local one) convenience store would lose much business and total revenues if he raised the price of gasoline more than a penny or two compared to the other three gas stations at the same street intersection. When the students conclude he’d lose much of his gasoline sales, ask them to reconcile this large quantity decrease to a small increase in price (elastic demand) with the fact that they earlier stated that demand for gasoline is very inelastic. They will recognize that gasoline from the other corner stations is a very good substitute for Joe’s gasoline. The demand for convenience store junk food. After students recognize that demand elasticity is high when abundant substitutes are available, ask the students why Joe’s Quick-Mart junk food (and all other convenience stores’ junk food) is priced so much higher than the near-by grocery store’s junk food. Students will conclude that “convenience” stores are well named. Most people aren’t willing to wait in the grocery store check-out line behind the frazzled mother of three screaming kids, each hanging on the over-loaded basket that will take 15 minutes of coupon validating and price checking to complete the sale. The grocery store is not a good substitute for people in a hurry who are looking for a fast snack and a quick gas fill.

3. How can the owner of The Burger Barn determine if a one-day promotional sale on milkshakes will affect the total revenues generated by hamburger sales? This question will exercise student knowledge of cross elasticities. First the students need to assume that the price of burgers remains unchanged (ceteris paribus conditions must be satisfied). Next, the students need to determine whether the cross elasticity is positive (substitutes) or negative (compliments). If burgers are substitutes, then burger revenues will decrease during the sale. However, if burgers are compliments, then burger revenues will increase.

4. Lessons Learned from the 9-11 terrorist attacks: In the ensuing months after the terrorist attacks, security concerns in the United States were heightened when rumors and further proclamations of pending chemical and biological attacks on the United States were reported in the media. Ask the students if it would be important for the government to know what the elasticity of supply would be for super-strength antibiotic medicines (like the popularized medicine Ciprofloxacine) available on the world market.

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A n s w e r s t o t h e R e v i e w Q u i z z e sPage 88

1. The elasticity of demand is a unit-free measure, which is a better measure than the slope ratio for the responsiveness of quantity changes to price changes. The slope of the demand curve will change as the units measuring the same quantity of the good change (going from pounds to ounces, for example). The value of the elasticity is independent of the units used to measure the price and quantity of the product and can be compared across the same good when quantity is measured in different units, or can be compared across different goods when they are measured in different units.

2. The price elasticity of demand is the absolute value (or magnitude) of the ratio of the percentage change in the quantity demanded to the percentage change in the price. The percentage change in quantity (price) is measured as the change in quantity (price) divided by the average quantity (price). The ratio of two percentages causes the unit measures to disappear, leaving a unit-free measure.

3. Using the average of both price and quantity gives the elasticity at the midpoint between the original price and the new price. If we only used percentage change from the original price, we would have a larger value for the elasticity between two prices when calculating for a price rise than when calculating for a price fall. Using the average price and quantity measures avoids the value of elasticity being dependent upon whether a price change reflects a price increase or decrease.

4. The total revenue test is a method of estimating the price elasticity of demand by observing the change in total revenue, given a change in price, holding all other things constant. The total revenue test shows that a price cut increases total revenue if demand is elastic, decreases total revenue if demand is inelastic, and does not change total revenue if demand is unit elastic.

5. The magnitude of the price elasticity of demand for a good depends on three main influences:

Closeness of substitutes. The more easily people can substitute other items for a particular good, the larger is the price elasticity of demand for that good.

The proportion of income spent on the good. The larger the portion of the consumer’s budget being spent on a good, the greater is the price elasticity of demand for that good.

The time elapsed since a price change. Usually, the more time that has passed after a price change, the greater is the price elasticity of demand for a good.

6. Demand for a necessity is generally less elastic than demand for a luxury because: i) there are fewer substitutes for a necessity, and ii) the proportion of our budgets spent on necessities is usually relatively larger than on luxuries.

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Page 911. Cross elasticity of demand measures how the quantity demanded of a

good responds to a change in the price of another good. The formula for cross price elasticity is the percentage change in the quantity of the good demanded divided by the percentage change in the price of the related good.

2. The sign of the cross elasticity of demand reveals whether two goods are substitutes or compliments: The cross elasticity of demand is positive for substitute goods and negative for complement goods.

3. Income elasticity of demand measures how the quantity demanded of a good responds to a change in income. The formula for income elasticity is the percentage change in the quantity of the good demanded divided by the percentage change in income.

4. The sign of income elasticity of demand reveals whether a good is a normal good or an inferior good: The income elasticity of demand is positive for normal goods and negative for inferior goods.

5. The level of a person’s income can influence the income elasticity of demand by changing how a good or service is perceived. Some goods, such as automobiles, might seem like a luxury when a person’s income is very low, but seem like a necessity when income is very high. Therefore, the income elasticity for some goods, like automobiles, might decrease (become less elastic) as incomes increase.

Page 941. Supply elasticity is an important component of understanding how

resources will be allocated when changes in the market lead producers to adjust their level of output. For example, how much additional antibiotics will be available if a sudden outbreak of anthrax is detected in our country, resulting in a significant increase the demand for such drugs?

2. The elasticity of supply measures the responsiveness of the quantity supplied to a change in the price of a good when all other influences on selling plans remain the same. The elasticity of supply is calculated by the percentage change in the quantity supplied divided by the percentage change in the price.

3. The main influences on the elasticity of supply are: Resource substitution possibilities: the greater the suppliers’ ability to

substitute resources, the greater will be their ability to react to price changes and the greater the elasticity of supply.

Time frame for the supply decision: the greater the amount of time available after the price change, the greater is the supplier’s ability to adjust quantity supplied, and the greater the elasticity of supply.

4. Students’ answers will vary. Here are some examples:a) The momentary supply of wheat is perfectly inelastic. Once farmers

have brought their wheat to market, there is no other alternative use for it and they sell it all regardless of the going price.

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b) The short-run supply of wheat. If the farmers already have a mature wheat crop but have not yet harvested it, farmers with both relatively high and low yield fields may chose to harvest both types of fields if the price for wheat is high. However, the farmers will not harvest their low yield fields when the price of wheat is relatively low, in order to economize on added labor costs.

c) The supply of wheat to an individual buyer. Any one buyer can purchase as much wheat at the going price as he or she desires. However, no quantity of wheat will be supplied at a lower price.

5. The momentary supply, short-run supply, and long-run supply all illustrate the response of suppliers to changes in the price, but they differ according to how much time has elapsed after the price change.

The momentary supply curve is frequently the least elastic and shows how suppliers cannot easily respond to a price change immediately after the price change occurs. Changing the quantity produced means changing the inputs into the production process, which takes time to complete. Sometimes the momentary supply is perfectly inelastic.

The short-run supply shows suppliers’ response after enough time has elapsed for some, but not all, of the possible technological adjustments have been made. Short-run supply generally is intermediate in elasticity between the momentary supply and the long-run supply.

The long-run supply shows how suppliers react after enough time has passed that all possible adjustments to productive factors have been made to accommodate the price change. It usually is the most elastic of the three supply curves.

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A n s w e r s t o t h e P r o b l e m s1. a. The price elasticity of demand is 1.25.

The price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price. The price rises from $4 to $6 a box, a rise of $2 a box. The average price is $5 a box. So the percentage change in the price equals $2 divided by $5, which equals 40 percent.The quantity decreases from 1,000 to 600 boxes, a decrease of 400 boxes. The average quantity is 800 boxes. So the percentage change in quantity equals 400 divided by 800, which equals 50 percent.The price elasticity of demand for strawberries equals 50 divided by 40, which is 1.25.

b. The price elasticity of demand exceeds 1, so the demand for strawberries is elastic.

2. a. The price elasticity of demand is 1.5.The price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price. The price falls from $7 to $5 a basket, a fall of $2 a basket. The average price is $6 a basket. So the percentage change in the price equals $2 divided by $6, which equals 33.3 percent.The quantity increases from 300 to 500 baskets, an increase of 200 baskets. The average quantity is 400 baskets. So the percentage change in quantity equals 200 divided by 400, which equals 50 percent.The price elasticity of demand for tomatoes equals 50 divided by 33.3, which is 1.5.

b. The price elasticity of demand exceeds 1, so the demand for tomatoes is elastic.

3. a. The price elasticity of demand is 2.When the price of a videotape rental rises from $3 to $5, the quantity demanded of videotapes decreases from 75 to 25 a day. The price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price.The price increases from $3 to $5, an increase of $2 a videotape. The average price is $4 a videotape. So the percentage change in the price equals $2 divided by $4, which equals 50 percent.The quantity decreases from 75 to 25 videotapes, a decrease of 50 videotapes. The average quantity is 50 videotapes. So the percentage change in quantity equals 50 divided by 50, which equals 100 percent.The price elasticity of demand for videotape rentals equals 100 divided by 50, which is 2.

b. The price elasticity of demand equals 1 at $3 a videotape. The price elasticity of demand equals 1 at the price halfway between the origin and the price at which the demand curve hits the y-axis. That price is $3 a videotape.

4. a. The price elasticity of demand is 2.

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When the price of a pen rises from $6 to $10, the quantity demanded of pens decreases from 60 to 20 a day. The price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price. The price rises from $6 to $10, an increase of $4 a pen. The average price is $8 a pen. So the percentage change in the price equals $4 divided by $8, which equals 50 percent.The quantity decreases from 60 to 20 pens, a decrease of 40 pens. The average quantity is 40 pens. So the percentage change in quantity equals 40 divided by 40, which equals 100 percent.The price elasticity of demand for pens equals 100 divided by 50, which is 2.

b. The price elasticity of demand equals 1 at $6 a pen. The price elasticity of demand is greater than 1 at prices greater than $6 a pen. The price elasticity of demand is less than 1 at prices less than $6 a pen. The price elasticity of demand equals 1 at the price halfway between the origin and the price at which the demand curve hits the y-axis. That price is $6 a pen.The demand curve is linear. Along a linear demand curve, the price elasticity of demand is greater than 1 at points above the midpoint and less than 1 at points below the midpoint. The price elasticity of demand is greater than 1 at prices above $6 a pen and less than 1 at prices below $6 a pen.

5. The demand for dental services is unit elastic.The price elasticity of demand for dental services equals the percentage change in the quantity of dental services demanded divided by the percentage change in the price of dental services.The price elasticity of demand equals 10 divided by 10, which is 1. The demand is unit elastic.

6. The demand for haircuts is elastic.The price elasticity of demand for haircuts equals the percentage change in the quantity of haircuts demanded divided by the percentage change in the price of a haircut.The price elasticity of demand equals 10 divided by 5, which is 2. The demand for haircuts is elastic.

7. a. Total revenue increases.When the price of a chip is $400, 30 million chips are sold and total revenue equals $12,000 million. When the price of a chip falls to $350, 35 million chips are sold and total revenue is $12,250 million. Total revenue increases when the price falls.

b. Total revenue decreases.When the price is $350 a chip, 35 million chips are sold and total revenue is $12,250 million. When the price of a chip is $300, 40 million chips are sold and total revenue decreases to $12,000 million. Total revenue decreases as the price falls.

c. Total revenue is maximized at $350 a chip.

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When the price of a chip is $300, 40 million chips are sold and total revenue equals $12,000 million. When the price is $350 a chip, 35 million chips are sold and total revenue equals $12,250 million. Total revenue increases as the price rises from $300 to $350 a chip. When the price is $400 a chip, 30 million chips are sold and total revenue equals $12,000 million. Total revenue decreases as the price rises from $350 to $400 a chip. Total revenue is maximized when the price is $350 a chip.

d. The demand for chips is unit elastic.The total revenue test says that if the price changes and total revenue remains the same, the demand is unit elastic at the average price. For an average price of $350 a chip, cut the price from $400 to $300 a chip. When the price of a chip falls from $400 to $300, total revenue remains at $12,000 million. So at the average price of $350 a chip, demand is unit elastic.

8. a. Total revenue increases.When the price of a pound of sugar is $5, 25 million pounds are sold and total revenue equals $125 million. When the price of a pound of sugar rises to $15, 15 million pounds are sold and total revenue is $225 million. Total revenue increases.

b. Total revenue does falls.When the price of a pound of sugar is $15, 15 million pounds are sold and total revenue is $225 million. When the price of a pound of sugar is $25, 5 million pounds are sold and total revenue is $125 million. Total revenue falls.

c. Total revenue is maximized at $15 a pound.The total revenue test says that if the price rises and total revenue remains the same, total revenue is maximized and demand is unit elastic at the average price. Total revenue is maximized at the price at which price elasticity of demand is 1. Draw the graph and extend the demand (which is linear) until it cuts the y-axis. The price halfway between the origin and the price at which the demand curve cuts the y-axis is the price at which elasticity is 1. The demand curve will cut the y-axis at $30 a pound. So the elasticity of demand for sugar equals 1 at a price of $15 a pound.You can check your answer by calculating the elasticity at an average price of $15 a pound. When the price rises from $10 to $20 a pound, the average price is $15 a pound.The price rises from $10 to $20, an increase of $10 a pound. The average price is $15 a pound. So the percentage change in the price equals $10 divided by $15, which equals 66.67 percent.The quantity decreases from 20 to 10 pounds, a decrease of 10 pounds. The average quantity is 15 pounds. So the percentage change in quantity equals 10 divided by 15, which equals 66.67 percent.The price elasticity of demand equals 66.7/66.7, which is 1.

d. The demand for sugar is elastic.The total revenue test says that if the price rises and total revenue decreases, the demand is elastic at the average price. For an average

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price of $20 a pound, raise the price from $15 to $25 a pound. Question 8(b) has calculated the change in total revenue when the price rises from $15 to $25 a pound. Total revenue decreases from $225 million to $125 million. So at the average price of $20 a pound, demand is elastic.

9. The demand for chips is inelastic.The total revenue test says that if the price falls and total revenue falls, the demand is inelastic. When the price falls from $300 to $200 a chip, total revenue decreases from $12,000 million to $10,000 million. So at an average price of $250 a chip, demand is inelastic.

10. The demand for sugar is inelastic.The total revenue test says that if the price rises and total revenue increases, the demand is inelastic at the average price. For an average price of $10 a pound, raise the price from $5 to $15 a pound. Question 8(a) has calculated the change in total revenue when the price rises from $5 to $15 a pound. Total revenue increases from $75 million to $225 million. So at the average price of $10 a pound, demand is inelastic.

11. The cross elasticity of demand between orange juice and apple juice is 1.17.The cross elasticity of demand is the percentage change in the quantity demanded of one good divided by the percentage change in the price of another good. The rise in the price of orange juice resulted in an increase in the quantity demanded of apple juice. So the cross elasticity of demand is the percentage change in the quantity demanded of apple juice divided by the percentage change in the price of orange juice. The cross elasticity equals 14 divided by 12, which is 1.17.

12. The cross elasticity of demand between chicken and beef is 4.The cross elasticity of demand is the percentage change in the quantity demanded of one good divided by the percentage change in the price of another good. The fall in the price of chicken resulted in a decrease in the quantity demanded of beef. So the cross elasticity of demand is the percentage change in the quantity demanded of beef divided by the percentage change in the price of chicken. The cross elasticity equals 20 divided by 5, which is 4.

13. Income elasticity of demand for (i) bagels is 1.33 and (ii) donuts is 1.33.Income elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in income. The change in income is $2,000 and the average income is $4,000, so the percentage change in income equals 50 percent.(i) The change in the quantity demanded is 4 bagels and the average quantity demanded is 6 bagels, so the percentage change in the quantity demanded equals 66.67 percent. The income elasticity of demand for bagels equals 66.67/50, which is 1.33.(ii) The change in the quantity demanded is 6 donuts and the average quantity demanded is 9 donuts, so the percentage change in the quantity demanded is 66.67. The income elasticity of demand for donuts equals 66.67/50, which is 1.33.

E L A S T I C I T Y 9 7

14. Income elasticity of demand for (a) concert tickets is 0.56 and (b) bus rides is 0.375.Income elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in income. The change in income is $4,000 and the average income is $15,000, so the percentage change in income equals 26.67 percent.(a) The change in the quantity demanded of concert tickets is 15 percent. The income elasticity of demand for concert tickets equals 15/26.67, which is 0.56.(b) The change in the quantity demanded of bus rides is 10 percent. The income elasticity of demand for bus rides equals 10/26.67, which is 0.375.

15. a. The elasticity of supply is 1. The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in the price. When the price falls from 40 cents to 30 cents, the change in the price is 10 cents and the average price is 35 cents. The percentage change in the price is 28.57. When the price falls from 40 cents to 30 cents, the quantity supplied decreases from 800 to 600 calls. The change in the quantity supplied is 200 calls, and the average quantity is 700 calls, so the percentage change in the quantity supplied is 28.57.The elasticity of supply equals 28.57/28.57, which equals 1.

b. The elasticity of supply is 1. The formula for the elasticity of supply calculates the elasticity at the average price. So to find the elasticity at an average price of 20 cents a minute, change the price such that 20 cents is the average price—for example, a fall in the price from 30 cents to 10 cents a minute.When the price falls from 30 cents to 10 cents, the change in the price is 20 cents and the average price is 20 cents. The percentage change in the price is 100. When the price falls from 30 cents to 10 cents, the quantity supplied decreases from 600 to 200 calls. The change in the quantity supplied is 400 calls and the average quantity is 400 calls. The percentage change in the quantity supplied is 100.The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in the price. The elasticity of supply is 1.

16. a. The elasticity of supply is 3.25. The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in the price. When the price rises from $125 to $135, the change in the price is $10 and the average price is $130. The percentage change in the price is 7.7. When the price rises from $125 to $135, the quantity supplied increases from 2,800 to 3,600 million pairs. The change in the quantity supplied is 800 million pairs, and the average quantity is 3,200 million pairs, so the percentage change in the quantity supplied is 25.The elasticity of supply equals 25/7.7, which equals 3.25.

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b. The elasticity of supply is 3.57. The formula for the elasticity of supply calculates the elasticity at the average price. So to find the elasticity at $125, change the price such that $125 is the average price—for example, a fall in the price from $130 to $120.When the price falls from $130 to $120, the change in the price is $10 and the average price is $125. The percentage change in the price is 8. When the price falls from $130 to $120, the quantity supplied decreases from 3,200 to 2,400 million pairs. The change in the quantity supplied is 800 millions pairs and the average quantity is 2,800 million pairs. The percentage change in the quantity supplied is 28.57.The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in the price. The elasticity of supply is 3.57.

A d d i t i o n a l P r o b l e m s1. Better-than-average weather brings a bumper tomato crop. The price of

tomatoes falls from $7 to $5 a basket, and the quantity demanded increases from 300 to 500 baskets a day. Over this price range,a. What is the price elasticity of demand?b. Describe the demand for tomatoes.

2. The figure shows the demand for pens.a. Calculate the elasticity of

demand for a rise in price from $2 to $4.

b. At what prices is the elasticity of demand equal to 1, greater than 1, and less than 1?

3. If the quantity of fish demanded decreases by 5 percent when the price of fish rises by 10 percent, is the demand for fish elastic, inelastic, or unit elastic?

4. The table gives the demand schedule for coffee.

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Price Quantity demanded

(dollars per

pound)

(millions of pounds per year)

10 3015 2520 2025 15

a. What happens to total revenue if the price of coffee rises from $10 to $20 per pound?

b. What happens to total revenue if the price rises to $15 to $25 per pound?

c. What is the price when total revenue at a maximum?d. What quantity of coffee will be sold at the price that answers problem

8(c)?e. At an average price of $15 a pound, is the demand for coffee elastic or

inelastic? Use the total revenue test to answer this question.5. In problem 4, at $15 a pound, is the demand for coffee elastic or inelastic?

Use the total revenue test to answer this question.6. If a 5 percent fall in the price of beef increases the quantity of beef

demanded by 20 percent and decreases the quantity of chicken demanded by 15 percent, calculate the cross elasticity of demand between beef and chicken.

7. Judy’s income has increased from $10,000 to $12,000. Judy increased her demand for concert tickets by 10 percent and decreased her demand for bus rides by 5 percent. Calculate Judy’s income elasticity of demand for (a) concert tickets and (b) bus rides.

8. The table gives the supply schedule for shoes.Price Quantity

supplied(dollars per

pair)(millions of pairs

per year)120 1,200125 1,400130 1,600135 1,800

Calculate the elasticity of supply whena. The price rises from $125 to $135 a pair.b. The price is $125 a pair.

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S o l u t i o n s t o A d d i t i o n a l P r o b l e m s1. a. The price elasticity of demand is 1.67.

The price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price. The price falls from $6 to $4 a basket, a fall of $2 a basket. The average price is $5 a basket. So the percentage change in the price equals $2 divided by $5, which equals 40 percent.The quantity increases from 200 to 400 baskets, an increase of 200 baskets. The average quantity is 300 baskets. So the percentage change in quantity equals 200 divided by 300, which equals 66.7 percent.The price elasticity of demand for tomatoes equals 66.7 divided by 40, which is 1.67.

b. The price elasticity of demand exceeds 1, so the demand for tomatoes is elastic.

2. a. The price elasticity of demand is 0.33.When the price of a pen rises from $2 to $4, the quantity demanded of pens decreases from 100 to 80 a day. The price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price. The price increases from $2 to $4, an increase of $2 a pen. The average price is $3 a pen. So the percentage change in the price equals $2 divided by $3, which equals 66.7 percent.The quantity decreases from 100 to 80 pens, a decrease of 20 pens. The average quantity is 90 pens. So the percentage change in quantity equals 20 divided by 90, which equals 22 percent.The price elasticity of demand for pens equals 22 divided by 66.7, which is 0.33.

b. The price elasticity of demand equals 1 at $6 a pen. The price elasticity of demand is greater than 1 at prices greater than $6 a pen. The price elasticity of demand is less than 1 at prices less than $6 a pen. The price elasticity of demand equals 1 at the price halfway between the origin and the price at which the demand curve hits the y-axis. That price is $6 a pen.The demand curve is linear. Along a linear demand curve, the price elasticity of demand is greater than 1 at points above the midpoint and less than 1 at points below the midpoint. The price elasticity of demand is greater than 1 at prices above $6 a pen and less than 1 at prices below $6 a pen.

3. The demand for fish is inelastic.The price elasticity of demand for fish equals the percentage change in the quantity of fish demanded divided by the percentage change in the price of fish.The price elasticity of demand equals 5 divided by 10, which is 0.5. The demand is inelastic.

4. a. Total revenue increases.

E L A S T I C I T Y 1 0 1

When the price of a pound of coffee is $10, 30 million pounds are sold and total revenue equals $300 million. When the price of a pound of coffee rises to $20, 20 million pounds are sold and total revenue is $400 million. Total revenue increases.

b. Total revenue does not change.When the price of a pound of coffee is $15, 25 million pounds are sold and total revenue is $375 million. When the price of a pound of coffee is $25, 15 million pounds are sold and total revenue is $375 million. Total revenue does not change.

c. Total revenue is maximized at $20 a pound.When the price of a pound of coffee is $20, 20 million pounds are sold and total revenue equals $400 million. When the price is $15 a pound, 25 million pounds are sold and total revenue equals $375 million. Total revenue increases as the price rises from $15 to $20 a pound. When the price is $25 a pound, 15 million pounds are sold and total revenue equals $375 million. Total revenue decreases as the price rises from $20 to $25 a pound. Total revenue is maximized when the price is $20 a pound.

d. The quantity will be 20 million pounds a year.The demand schedule tells us that when the price is $20 a pound, the quantity of coffee demanded is 20 million pounds a year.

e. The demand for coffee inelastic.The total revenue test says that if the price rises and total revenue increases, the demand is inelastic at the average price. For an average price of $15 a pound, raise the price from $10 to $20 a pound. When the price of a pound rises from $10 to $20, total revenue increases from $300 million to $400 million. So at the average price of $15 a pound, demand is inelastic.

5. The demand for coffee inelastic.The total revenue test says that if the price rises and total revenue increases, the demand is inelastic at the average price. For an average price of $15 a pound, raise the price from $10 to $20 a pound. When the price of a pound rises from $10 to $20, total revenue increases from $300 million to $400 million. So at the average price of $15 a pound, demand is inelastic

6. The cross elasticity of demand between beef and chicken is 2.The cross elasticity of demand is the percentage change in the quantity demanded of one good divided by the percentage change in the price of another good. The fall in the price of beef resulted in a decrease in the quantity demanded of chicken. So the cross elasticity of demand is the percentage change in the quantity demanded of chicken divided by the percentage change in the price of beef. The cross elasticity equals 20 divided by 10, which is 2.

7. Income elasticity of demand for (a) concert tickets is 0.55 and (b) bus rides is 0.275.Income elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in income. The change in

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income is $2,000 and the average income is $11,000, so the percentage change in income equals 18.2 percent.(a) The change in the quantity demanded of concert tickets is 10 percent.

The income elasticity of demand for concert tickets equals 10/18.2, which is 0.55.

(b) The change in the quantity demanded of bus rides is 5 percent. The income elasticity of demand for bus rides equals 5/18.2, which is 0.275.

8. a. The elasticity of supply is 1. The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in the price. When the price rises from $125 to $135, the change in the price is $10 and the average price is $130. The percentage change in the price is 7.7. When the price rises from $125 to $135, the quantity supplied increases from 1,400 million to 1,800 million pairs. The change in the quantity supplied is 400 million pairs, and the average quantity is 1,600 million pairs, so the percentage change in the quantity supplied is 25.The elasticity of supply equals 25/7.7, which equals 3.25.

b. The elasticity of supply is 1. The formula for the elasticity of supply calculates the elasticity at the average price. So to find the elasticity at $125, change the price such that $125 is the average price—for example, a fall in the price from $130 to $120.When the price falls from $130 to $120, the change in the price is $10 and the average price is $125. The percentage change in the price is 8. When the price falls from $130 to $120, the quantity supplied decreases from 1,600 million to 1,200 million pairs. The change in the quantity supplied is 400 millions pairs and the average quantity is 1,400 million pairs. The percentage change in the quantity supplied is 28.57.The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in the price. The elasticity of supply is 3.57.

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