Economics 2017 (Hubbard/O'Brien)
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6.1 The Price Elasticity of Demand and Its Measurement (pages 184–190)
Define price elasticity of demand and understand how to measure it.
Price elasticity of demand is a measure of the responsiveness of quantity demanded to a change in price.
6.2 The Determinants of the Price Elasticity of Demand (pages 191–192)
List and explain the determinants of the price elasticity of demand.
The key determinants of the price elasticity of demand for a good are: the availability of close substitutes, the passage of time, whether the good is a luxury or a necessity, the definition of the market, and the share of the good in the consumer’s budget.
Revenue (pages 193–197)
Explain the relationship between the price elasticity of demand and total revenue.
When demand is inelastic, price and total revenue move in the same direction. When demand is elastic, price and total revenue move inversely.
6.4 Other Demand Elasticities (pages 197–199)
Define cross-price elasticity of demand and income elasticity of demand and understand their determinants and how they are measured.
The cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good; the income elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in income.
(pages 200–202)
Use price elasticity and income elasticity to analyze economic issues.
Elasticity can help us understand why the family farm has become an endangered species and the effects of raising the federal government’s tax on gasoline
(pages 202–208)
Define price elasticity of supply and understand its determinants and how it is measured.
The price elasticity of supply measures the responsiveness of the quantity supplied to a change in price.
Cross-price elasticity of demand, p. 197. The percentage change in quantity demanded of one good divided by the percentage change in the price of another good.
Elastic demand, p. 185. Demand is elastic when the percentage change in the quantity demanded is greater than the percentage change in price, so
the price elasticity is greater than 1 in absolute value.
Elasticity, p. 184. A measure of how much one economic variable responds to changes in another economic variable.
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Income elasticity of demand, p. 198. A measure of the responsiveness of the quantity demanded to changes in income, measured by the percentage change in quantity demanded divided by the percentage change in income.
Inelastic demand, p. 185. Demand is inelastic when the percentage change in quantity demanded is less than the percentage change in price, so the price elasticity is less than 1 in absolute value.
Perfectly elastic demand, p. 189. The case where the quantity demanded is infinitely responsive to price and the price elasticity of demand equals infinity.
Perfectly inelastic demand, p. 189. The case where the quantity demanded is completely unresponsive to price, and the price elasticity of demand equals zero.
Price elasticity of demand, p. 184. The responsiveness of the quantity demanded to
a change in price, measured by dividing the percentage change in the quantity demanded of a product by the percentage change in the product’s price.
Price elasticity of supply, p. 202. The responsiveness of the quantity supplied to a change in price, measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the product’s price.
Total revenue, p. 193. The total amount of funds a seller receives from selling of a good or service, calculated by multiplying price per unit by the number of units sold.
Unit-elastic demand, p. 185. Demand is unit elastic when the percentage change in quantity demanded is equal to the percentage change in price, so the price elasticity is equal to 1 in absolute value.
In the summer of 2008, the average price of a gallon of gasoline was $4.00; by the end of the year it was down to $1.50. The price rose to nearly $4.00 by 2011 before falling to below $2.00 at the beginning of 2015 and then rising again. Some people argue that consumers don’t vary the quantity of gas they buy as the price fluctuates because the number of miles they drive is roughly constant. But actual consumer behavior contradicts this. In December 2014, when the average price of gasoline was $2.50 per gallon, U.S. consumers bought about 7 percent more gasoline than they did in April 2014, when the average price of gasoline was $3.60 per gallon.
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6.1
184–190)
Learning Objective: Define price elasticity of demand and understand how to measure it.
Elasticity is a measure of how much one economic variable responds to changes in another economic variable. The price elasticity of demand is the responsiveness of the quantity demanded to a change in price, measured by dividing the percentage change in the quantity demanded of a product by the percentage change in the product’s price.
The slope of the demand curve is not used to measure elasticity because the measurement of slope is sensitive to the units chosen for quantity and price.
Price elasticity of demand
Percentage change in price
The price elasticity of demand is always negative. Because we are usually interested in the relative size of elasticities, we often compare their absolute values.
Elastic demand refers to when the percentage change in quantity demanded is greater than the percentage change in price, so the price elasticity is greater than 1 in absolute value.
Inelastic demand refers to when the percentage change in quantity demanded is less than the percentage change in price, so the price elasticity is less than 1 in absolute value.
Unit-elastic demand refers to when the percentage change in quantity demanded is equal to the percentage change in price, so the price elasticity is equal to 1 in absolute value.
In calculating the price elasticity between two points on a demand curve, we run into a problem because we get a different value for price increases than for price decreases.
We can use the midpoint formula to ensure that we have only one value for the price elasticity of demand between the same two points on a demand curve. The midpoint formula uses the average of the initial and final quantities and the average of the initial and final prices If Q1 and P1 are the initial quantity and price and Q2 and P2 are the final quantity and price, then the midpoint formula is:
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When two demand curves intersect, the curve with the smaller slope (in absolute value) is more elastic, and the one with the larger slope (in absolute value) is less elastic.
If a demand curve is a vertical line, then it is perfectly inelastic. Perfectly inelastic demand is the case where the quantity demanded is completely unresponsive to price and the price elasticity of demand equals zero. If a demand curve is a horizontal line, then it is perfectly elastic. Perfectly elastic demand is the case where the quantity demanded is infinitely responsive to price, and the price elasticity of demand equals infinity.
After illustrating a perfectly inelastic demand curve, ask your students to suggest examples. They may mention cigarettes, gasoline, or other goods that have relatively inelastic, but not perfectly inelastic, demands. Ask if the quantity demanded of the products they suggest would change if the price were not only higher but lower as well. Even students who claim they would not buy less gasoline if the price rose are unlikely to argue that they would not buy more gasoline at lower prices. This discussion will help your students understand that very few products actually have perfectly inelastic demand curves You don’t need to spend much time discussing perfectly elastic demand. It should be sufficient to make a brief reference to perfect competition, a topic covered in Chapter 12.
Your understanding of elasticity (E) may be increased by rewriting the elasticity formula. To make this explanation easier to follow, assume that we are interested in measuring the price elasticity of a linear demand curve. The elasticity formula in the textbook is:
Both “2”s can be dropped from this equation. Recall that (Q2 Q1) = ΔQ and (P2 P1) = ΔP. Substituting, we have:
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Because the elasticity equation divides one fraction by another fraction you can rewrite this expression by multiplying the numerator by the inverse, or reciprocal, of the denominator. The associative property of multiplication allows us to divide ΔQ by ΔP and (P1 + P2) by (Q1 + Q2). Therefore:
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Because the slope of a linear or straight line demand curve is constant and can be written as ΔP/ΔQ, the elasticity formula can now be written as:
Writing the elasticity formula this way makes it clear that the slope is not the same as the elasticity of a demand curve. Along a linear demand curve, the slope will have a constant value but the elasticity will not. The formula highlights this and also can be used to make another important point. Because the law of demand tells us that high prices are associated with relatively low values of quantity demanded (and vice versa), the absolute values for elasticity will be high at high prices (demand is elastic) and relatively low at low prices (demand is inelastic). This result can easily be shown by substituting in actual price and quantity values for a given demand curve into the rewritten formula and observing the change in the ratio of (P1 + P2) to (Q1 + Q2) as price is decreased.
There are five key determinants of the price elasticity of demand.
The availability of substitutes is the most important determinant of the price elasticity of demand. In general, if a product has more substitutes available, it will have a more elastic demand. If a product has fewer substitutes available, it will have a less elastic demand.
The more time that passes, the more elastic the demand for a product becomes.
The demand curve for a luxury is more elastic than the demand curve for a necessity.
The more narrowly we define a market, the more elastic demand will be.
In general, the demand for a good will be more elastic the larger the share of the good in the average consumer’s budget.
It is important to remember that estimates of the price elasticity of different goods vary depending on the data used and the time period over which the estimates were made.
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It is useful to emphasize two points. First, each of the five determinants of the price elasticity of demand should be considered separately from the others. A product that consumes a small part of a consumer’s budget (this suggests demand would be relatively inelastic) may have several good substitutes (this suggests demand would be relatively elastic). Second, changes in the market price of any product will result in different values for price elasticity. Estimates of the price elasticity of demand use market prices for products at a particular time. Different market prices from different timer periods would result in different elasticity estimates
Among the victims of the 2007–2009 recession were luxury restaurants in New York, Chicago, and other large cities. Rubicon, a top-rated San Francisco restaurant, closed in August 2008. The Blue Water Grill in Chicago also closed. Other restaurants attempted to survive by offering discounts. High-end New York restaurant Jean Georges slashed prices for three- and four-course meals. Other restaurants followed suit, some offering three-course meals for less than $20; the London Grill in Philadelphia offered a lobster or beef meal for $18.95. To avoid high labor costs, San Francisco’s Fifth Floor started an “Honor Bar” where customers placed money in a box on the honor system and poured their own wine. An article summarizing the woes of the restaurant industry commented:
Currently, consumers appear to be “trading down,” choosing lower-priced restaurants than they used to. The National Restaurant Association projects sales, adjusted for inflation, will decline by 2.5% in full service restaurants in 2009, while it predicts quick service will grow by 0.4%.
Stephen Hanson, who closed several of his once-successful restaurants in New York and Chicago, has had better luck with restaurants that offer less expensive meals. Mr. Hanson explained the success of his big restaurants that earn a small profit from a large number of customers: “I’m in the volume business.” By 2010, business at upscale and other restaurants began to recover as the recession ended.
Sources: Katy McLaughlin, “What’s Not Cooking,” Wall Street Journal, January 23, 2009, and Kevin P. Casey, “From fast food to fine dining, business is up at restaurants,” USA Today, November 22, 2010.
a. What are the key determinants of the price elasticity of demand for meals served at high-end restaurants?
b. Cite evidence that high restaurant prices resulted in a lower quantity demanded and a substitution by consumers to lower-priced alternatives
Step 1: Review the chapter material. This problem is about the determinants of the price elasticity of demand, so you may want to review the section “The Determinants of the Price Elasticity of Demand,” which begins on page 191.
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Step 2: What are the key determinants of the price elasticity of demand for meals served at high-end restaurants?
The key determinants are the availability of close substitutes (for example, “quick service” restaurants that serve less expensive meals) and the share of the restaurant meals in the consumer’s budget.
Step 3: Cite evidence that high restaurant prices resulted in a lower quantity demanded and a substitution by consumers to lower-priced alternatives.
High-end restaurants had their worst downturn in decades. San Francisco’s Rubicon and the Blue Water Grill in Chicago closed in 2008. But sales at “quick service” restaurants increased. Steven Hanson, owner of several restaurants, reported that he had greater success with restaurants that charge lower prices.
Learning Objective: Explain the relationship between the price elasticity of demand and total revenue.
A firm is interested in price elasticity of demand for its products because it allows the firm to calculate how changes in price will affect its total revenue. Total revenue is the total amount of funds a seller receives from selling a good or service, calculated by multiplying price per unit by the number of units sold. When demand is inelastic, price and total revenue move in the same direction: An increase in price raises total revenue, and a decrease in price reduces total revenue. When demand is elastic, price and total revenue move inversely: An increase in price reduces total revenue, and a decrease in price raises total revenue. If demand is unit elastic a change in price is exactly offset by a proportional change in quantity demanded, leaving revenue unaffected.
Along most demand curves, including linear demand curves, elasticity is not constant at every point. When the price is high and the quantity demanded is low, demand is elastic. When the price is low and the quantity demanded is high, demand is inelastic.
Firms usually have a good idea of the price elasticity of demand for products that have been on the market for at least a few years. For new products, however, firms often experiment with different prices to
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determine the price elasticity. For example, Apple introduced the first-generation iPhone in June 2007, at a price of $599. But demand for the iPhone was more elastic than Apple had expected, and when sales failed to reach Apple’s projections, the company cut the price to $399 just two months later. Similarly, when 3D televisions were introduced into the U.S. market in early 2010, Sony and other manufacturers believed that sales would be strong despite prices being several hundred dollars higher than for other high-end ultra-thin televisions. Once again, though, demand turned out to be more elastic than expected, and by December firms were cutting prices 40 percent or more in an effort to increase revenue.
Since electronic books (e-books) became popular after Amazon introduced the Kindle e-reader, firms have experimented with different prices in trying to determine the relevant price elasticity. Amazon had originally priced most best-selling e-books at $9.99, but when Apple introduced the iPad in 2010, Apple negotiated contracts with publishers that raised prices for e-books. Amazon and Barnes & Noble eventually signed similar contracts, and the prices for best selling e-books rose from $9.99 to $12.99 or $14.99. Publishers hoped that a low price elasticity of demand for e-books would result in the price increase leading to higher revenues. Many buyers, however, claimed that rather than pay higher prices, they would go back to reading printed books. Joel Waldfogel, an economist at the University of Pennsylvania, raised the possibility that the higher prices might lead some readers to illegally download pirated e-books, in violation of the publishers’ copyrights. Although piracy has been a problem with music and movies, it had not yet been a problem with books. Waldfogel argued that, “I would be scared to death about a culture of piracy taking hold. I wouldn’t mess around with price increases.” Whether the demand for e-books turns out to be elastic or inelastic may depend on how many readers consider printed books or pirated e-books to be close substitutes for legally downloaded e-books.
Source: Daisuke Wakabayashi and Miguel Bustillo, “TV Makers Can’t Hold Line on 3-D Prices,” Wall Street Journal, December 20, 2010; Motoko Rich and Brad Stone, “Cost of an e-Book Will Be Going Up,” New York Times, February 11, 2010; and Kate Hafner and Brad Stone, “iPhone Owners Crying Foul Over Price Cut,” New York Times, September 7, 2007.
A publisher was quoted as saying the following about the pricing of e-books: “We may introduce [an ebook] at $14.95 for a year and then move the book to $9.99 when we would have put out the trade paperback edition. I suspect you’re going to see a fair amount of experimentation.” Why would issuing a paperback version of a book affect the price a publisher would charge for an e-book? Why would publishers be experimenting with the prices of e-books?
Source: Motoko Rich and Brad Stone, “Cost of an e-Book Will Be Going Up,” New York Times, February 11, 2010.
The paperback edition is a reasonably good substitute for the e-book edition. Publishers are experimenting with the prices of e-books because they are relatively new products, which makes estimating price elasticity difficult.
In addition to price elasticity, two other demand elasticities are important: the cross-price elasticity of demand and the income elasticity of demand.
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The formula for the cross-price elasticity of demand is:
Percentage change in quantity demanded of one good
Percentage change in price of another good .
The cross-price 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. An increase in the price of a substitute will lead to an increase in quantity demanded, so the cross-price elasticity of demand will be positive. An increase in the price of a complement will lead to a decrease in the quantity demanded, so the crossprice elasticity of demand will be negative.
The income elasticity of demand of demand is a measure of the responsiveness of the quantity demanded to changes in income, measured by the percentage change in the quantity demanded divided by the percentage change in income:
Percentage change in quantity demanded .
Percentage change in income
If the quantity demanded of a good increases as income increases, then the good is a normal good. Normal goods are often further subdivided into luxuries and necessities The income elasticity of demand for a necessity is positive but less than 1. The income elasticity of demand for a luxury is greater than 1. A good is inferior if the quantity demanded falls as income increases.
Many students confuse one type of elasticity with another. Ask your students to solve the following problem. Assume that the absolute value of the price elasticity of demand for good X is 2.5. Is good X a normal good? (Answer: You cannot determine whether X is normal or inferior by knowing its price elasticity You need to know the income elasticity of demand for good X to answer this question).
Assume that two separate events affect the market for taxi rides in New York City:
a. There is a 20 percent increase in New York subway fares. As a result, the price of a taxicab ride increases by 5 percent.
b. An economic expansion causes a 5 percent increase in the incomes of tourists visiting New York City. As a result, the price of a taxicab ride increases by 2 percent.
Describe the cross-price and income elasticity formulas and use the formulas to determine the values of these elasticities for taxicab rides.
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Step 1: Review the chapter material.
This problem is about the determinants of the cross-price elasticity and income elasticity of demand, so you may want to review the section “Other Demand Elasticities,” which begins on page 197.
Step 2: State the cross-price elasticity formula and determine the value of this elasticity for taxicab rides.
The cross-price elasticity formula is:
Percentage change in quantity demanded of one good
Percentage change in price of another good
Because a 20 percent increase in subway fares raised the quantity demanded of taxi rides by 5 percent, the value of the cross-price elasticity is:
5 percent 0.25.
20 percent
The elasticity is positive, so subway and taxi rides are substitutes.
Step 3: State the income elasticity formula and determine the value of this elasticity for taxi rides.
The income elasticity is:
Percentage change in quantity demanded .
Percentage change in income
Because a 5 percent increase in income led to a 2 percent increase in taxi rides, the value of the income elasticity is:
2 percent 0.4.
5 percent
The elasticity is positive but less than 1. Therefore, a taxi ride is a normal good and a necessity.
6.5
Using Elasticity to Analyze the Disappearing Family Farm (pages 200–202)
Learning Objective: Use price elasticity and income elasticity to analyze economic issues.
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From 1950 to 2015, the number of farms decreased from 5 million to about 2 million, and the number of people who lived on farms fell from 23 million to fewer than 3 million. Rapid growth in farm output has combined with low price and income elasticities to make family farming difficult in the United States. In 1950, the average U.S. wheat farmer harvested about 17 bushels from each acre. By 2015, the average U.S. wheat farmer harvested 44 bushels per acre. This increase in wheat production resulted in a substantial decline in prices because: (1) the demand for wheat is inelastic, and (2) the income elasticity of demand for wheat is low.
An ongoing policy debate concerns whether to legalize the use of drugs such as marijuana and cocaine. Some researchers estimate that legalizing cocaine would cause its price to fall by as much as 95 percent. Proponents of legalization argue that legalizing drug use would lower crime rates by eliminating the main reason for the murderous gang wars that plague many big cities and by reducing the incentive for drug addicts to commit robberies and burglaries. Opponents of legalization argue that lower drug prices would lead more people to use drugs.
a. Suppose the price elasticity of demand for cocaine is −2. If legalization causes the price of cocaine to fall by 95 percent, what will be the percentage increase in the quantity of cocaine demanded?
b. If the price elasticity is −0.02, what will be the percentage increase in the quantity demanded?
c. Discuss how the size of the price elasticity of demand for cocaine is relevant to the debate over its legalization.
Step 1: Review the chapter material. This problem deals with applications of the price elasticity of demand formula, so you may want to review the section “Using Elasticity to Analyze the Disappearing Family Farm,” which begins on page 200 of the textbook, and the section “Measuring the Price Elasticity of Demand,” which begins on page 184.
Step 2: Answer part (a) using the formula for the price elasticity of demand.
Price elasticity of demand
Percentage change in quantity demanded .
Percentage change in price
We can plug into this formula the values given for the price elasticity and the percentage change in price:
Percentage change in quantitydemanded 2. 95%
Or rearranging:
Percentage change in quantity demanded = 2 × 95% = 190%
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Step 3: Use the same method to answer part (b)
We only need to substitute 0.02 for 2 as the price elasticity of demand:
Percentage change in quantity demanded = 0.02 × 95% = 1.9%
Step 4: Answer part (c) by discussing how the size of the price elasticity of demand for cocaine helps us to understand the effects of legalization. Clearly, the higher the absolute value of the price elasticity of demand for cocaine, the greater the increase in cocaine use that would result from legalization. If the price elasticity is as high as in part (a), legalization will lead to a large increase in use. If, however, the price elasticity is as low as in part (b), legalization will lead to only a small increase in use.
Extra Credit: One estimate puts the price elasticity at −0.28, which suggests that even a large fall in the price of cocaine might lead to only a moderate increase in cocaine use. However, even a moderate increase in cocaine use would have costs. Some studies have shown that cocaine users are more likely to commit crimes, to abuse their children, to have higher medical expenses, and to be less productive workers. Moreover, many people object to the use of cocaine and other narcotics on moral grounds and would oppose legalization even if it led to no increase in use. Ultimately, whether the use of cocaine and other drugs should be legalized is a normative issue. Economics can contribute to the discussion but cannot decide the issue.
Source for estimate of price elasticity of cocaine: Henry Saffer and Frank Chaloupka, “The Demand for Illicit Drugs,” Economic Inquiry, Vol. 37, No. 3, July 1999, pp. 401–411.
Learning Objective: Define price elasticity of supply and understand its main determinants and how it is measured.
To measure how much quantity supplied increases when price increases, we use the price elasticity of supply.
The price elasticity of supply is the responsiveness of the quantity supplied to a change in price, measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the product’s price. We calculate the price elasticity of supply using percentage changes:
Percentage change in quantity supplied
Percentage change in price
Because of the law of supply, price elasticity of supply will be a positive number. If the price elasticity of supply is less than 1, then supply is inelastic. If the price elasticity of supply is greater than 1, then supply is elastic. If the price elasticity of supply is equal to 1, then supply is unit elastic.
Whether the supply curve is elastic or inelastic depends on the ability and willingness of firms to alter the quantity they produce as price increases. The supply curve for most products will be inelastic if we
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measure it over a short period of time, but increasingly elastic the longer the period of time over which we measure it.
It is possible for supply to fall into one of the polar cases of price elasticity. If a supply curve is a vertical line, it is perfectly inelastic. If a supply curve is a horizontal line, it is perfectly elastic.
When demand increases, the amount that price increases depends on the price elasticity of supply. When the supply is inelastic, a change in demand results in a larger increase in price than when the supply is elastic.
In fall of 2015 New York City taxi medallions, some of which had sold for over $1 million each in 2013, were worth about $650,000 apiece. The New York City Taxi and Limousine Commission limits the number of medallions, which are required in order to legally operate a cab in New York City, to about 13,200. Because of the limit placed on the number of medallions, as demand for taxis and medallions rose from 1980 to 2013, the price of a medallion increased by about 1,000 percent. The number of medallions did not change from 2013 to 2015, but competition from Uber and other transportation alternatives was responsible for most of the decline in the price of medallions.
Sources: Jared Mayer, “New York’s Taxi King Is Going Down,” the Federalist, October 26, 2015; Ilya Marritz, “NYC Taxi Medallions Fetch ‘Unbelievable’ Returns,” National Public Radio, November 15, 2011; and “NYC Taxi Medallions Sell for $1.1 Million,” Economic Policy Journal, March 18, 2013.
a. What was the value of the price elasticity of supply of New York City taxi medallions between 1980 and 2015?
b. Describe some of the consequences of the New York City Taxi and Limousine Commission’s decision to limit the quantity of taxi medallions.
Step 1: Review the chapter material. This problem is about the determinants of the elasticity of supply, so you may want to review the section “The Price Elasticity of Supply and Its Measurement,” which begins on page 202 of the textbook.
Step 2: What was the value of the price elasticity of supply of New York City taxi medallions between 1980 and 2013?
The price elasticity of supply formula is:
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Because the quantity supplied of medallions did not change between 1980 and 2015, the percentage change in the quantity supplied of medallions was zero, as was the price elasticity of supply. The medallion supply curve was vertical at the quantity of about 13,200 medallions.
Step 3: Describe some of the consequences of the New York City Taxi and Limousine Commission limiting the quantity of taxi medallions.
The high cost of medallions has limited the number of taxi cabs available for residents and visitors to the city, which has raised the price of taxi rides. Another consequence is the high number of unlicensed cabs that break the law by offering their services. Economist Paul Krugman claims that a disproportionately high number of traffic accidents in New York City are caused by unlicensed and unregulated taxi drivers. The limited the number of medallions and taxis created an incentive for competitors such as Uber to offer its transportation services in New York City.
Question: After studying the material in this chapter, you should understand why knowing the income and price elasticities of their products is important to the owners and managers of firms. But what if you are not a manager or owner? If, for example, you were interested in investing some of your hard-earned savings in the stock market, how would knowing income and price elasticities help you?
Answer: The best advice for success in the stock market is still “buy low, sell high.” But what you learned about elasticity also may be helpful, at least in a general way. Firms that sell products with high income elasticities (for example, houses and automobiles) experience especially large fluctuations in sales as the overall economy moves through the business cycle. Consumers are reluctant to buy expensive products during a recession, especially if they must take out loans to do so. But sales of these same items tend to increase rapidly when the economy moves into an expansion.
Source: Ben McClure, “The Ups and Downs of Investing in Cyclical Stocks,” www.investopedia.com. October 22, 2002.
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how to measure it.
1.1 Price elasticity of demand = (percentage change in quantity demanded)/(percentage change in price). The price elasticity of demand isn’t measured by the slope of the demand curve because the slope depends on the units of measurement. The slope of the demand curve will change by a factor of 100 if you use cents instead of dollars, for example. Another example: consider sixpacks of soda versus cans of soda. If the price drops by $1.00 per six-pack and the quantity demanded increases by two six-packs, then that is the same thing as quantity demanded increasing by 12 cans. So, you could calculate the slope either as −1/2 six-packs, or as −1/12 cans. In addition, using percentage changes in the elasticity formula allows for meaningful comparisons of demand responsiveness between very different kinds of goods; for example, breakfast cereal versus health care.
1.2 The price elasticity of demand =
Percentage change in quantity demanded25% 2.5
Percentage change in price10%
The demand for Cheerios is elastic.
1.3 In calculating the percentage change in price and quantity, the midpoint formula divides the change in price and change in quantity by the average of their starting and ending values.
Midpoint()() formula:
Percentage changes can also be calculated by using the starting or ending value without averaging, but, unlike the midpoint formula, these methods gives different results depending on whether the starting or ending value is used.
1.4 A perfectly inelastic demand curve is a vertical line, as shown at the bottom of Table 6.1. Such a good will have no substitutes; for example, a life-saving drug. Therefore, an increase in price from $30 to $40 or decrease in price from $30 to $20 will have no effect on the quantity demanded (Qd) of the good, which remains at 16.
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1.5 If there is a 1.6 percent increase in gasoline consumption in response to a 32 percent decline in price (holding everything else constant) the price elasticity of demand would be:
Because the price elasticity of demand is less than one (in absolute value) the demand for gasoline would be price inelastic. The percentage change in quantity demanded is less than the percentage change in price.
1.6 a. 12,000,0008,000,000 4,000,000 $2.00$3.00
b. 128 4 $2.00$3.00 . This is a much smaller value than in (a)
c. We can calculate the price elasticity using the midpoint formula as follows:
Percentage change in quantity demanded = 12,000,0008,000,000 10040% 10,000,000
Percentage change in price = $2.00$3.00 10040% $2.50
So, the price elasticity of demand = 40% 1 40%
Notice that this value is significantly different from the values calculated in (a) and (b)
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1.7 For D1:
Percentage change in quantity demanded = 6030 10066.7% 45
Percentage change in price = $2$3 10040% $2.5
Percentage change in quantity demanded = 4030 10028.6%
Percentage change in price = $2$3 10040% $2.5
1.8 Step 1: Calculate average quantity and average price:
Step 2: Calculate percentage change in quantity demanded and percentage change price:
Percentage change in price = $29,454$24,751 10017.4%
Step 3: Divide the percentage change in the quantity demanded by the percentage change in price to arrive at the price elasticity for the demand curve:
Price elasticity of demand = 26% 1.5 17.4%
Demand for Pace University is therefore elastic.
Total tuition received in 2006 declined to $33,312,474 (= $29,454 × 1,131 students) from $36,359,219 (= $24,751 × 1,469 students) in 2005.
1.9 Suppose Ford did cut the price by $1 from $440 to $439 and quantity demanded increased by 1,000 cars from 500,000 to 501,000. The midpoint price would be $439.50 and the midpoint quantity would be 500,500. Then, the percentage change in quantity would equal: (1,000/500,500) × 100 = 0.20%. The percentage change in price would equal: (–$1/$439.50) × 100 =
0.23%. The price elasticity of demand is: 0.20%/–0.23% = –0.87. If Ford’s belief about the responsiveness of the quantity demanded for Model Ts to a change in their price was accurate, then the demand for Model Ts was price inelastic.
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1.10 At a higher price, quantity demanded will decrease, so the total revenue (price × quantity sold) will still be less than the total cost. Only in the very unlikely case where the demand for the magazine is perfectly inelastic would the publisher’s analysis be correct.
Learning Objective: List and explain the determinants of the price elasticity of demand.
2.1 The most important determinant of the price elasticity of demand is usually the availability of substitutes for the product. If there are close substitutes, elasticity will be high because people can switch to buying another good as the product’s price rises. Other factors determining the price elasticity of demand for a product include the passage of time, whether the good is a necessity or a luxury, how narrowly the market for the good is defined, and the share of the good in the consumer’s budget.
2.2 The demand for most agricultural goods is inelastic. Food is a necessity, and the demand for necessities tends to be less elastic than the demand for luxuries.
2.3 Milk (a) and prescription medicine (d) are likely to be price inelastic due to the lack of substitutes, but frozen cheese pizza (b) and cola (c) are likely to be price elastic because they have good substitutes, though we would expect a more narrowly defined product, such as Coca-Cola, to be more elastic than a broadly defined product such as cola.
2.4
Because the price elasticity of demand was less than one (in absolute value) the demand for bus rides was price inelastic. The five determinants of the price elasticity are: (a) the availability of substitutes, (b) the passage of time, (c) whether the good is a luxury or a necessity, (d) the definition of the market, and (e) the share of the good in a consumer’s budget. For many people who do not own their own automobiles, there are no good substitutes for bus transportation, which is more of a necessity than a luxury. These are probably the most important reasons why demand was price inelastic.
2.5 The more narrowly a market is defined, the more elastic demand will be, because more substitutes are available. The price elasticity of Coca-Cola (or any specific brand of soda) will be higher than for soda as a product because there are more substitutes available for a specific product like Coca-Cola than there are for a product category like soda.
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2.6 It usually takes consumers some time to adjust their buying habits when prices change. The more time passes, the more elastic the demand for a product becomes. In the case of oil prices, a good part of the demand is determined by the demand for gasoline. Consumers are slow to react to changes in gasoline prices because doing so often involves buying new cars, moving closer (or farther away) from work, and so on.
2.7 a. We can’t know with certainty from the information given whether in this case demand will be elastic or inelastic. We can say, though, that a family that has driven to Yellowstone with the intention of vacationing there is probably not going to be very responsive to changes in the admission price because that price would likely make up only a small fraction of the family’s vacation budget. So, it seems likely that demand for entry from someone driving a car, minivan, or motor home will be inelastic.
b. Once again, we can’t answer this question with certainty from the information given. As noted in part (a), someone arriving for a vacation in a private vehicle is likely to have an inelastic demand for entering the park. Someone who is entering by foot, bike, or on skis likely lives in the area or is staying close to the park. These people may have access to recreational opportunities outside of the park and so may choose not to enter the park if the price is too high. They are likely to have a more elastic demand for entering the park. People who arrive by motorcycle may be intending to vacation in the park, or they be from the local area and just planning a short visit. They are likely to have a price elasticity of demand that is between the two other groups. This ordering of the groups from highest price elasticity of demand to lowest corresponds to the ordering of prices charged by the National Park Service.
Learning Objective: Explain the relationship between the price elasticity of demand and total revenue.
3.1 If demand is inelastic, an increase in price will increase revenue because the price will increase proportionally more than the quantity sold will decrease.
3.2 If revenue increases when price falls, other things remaining equal, then demand must be elastic.
3.3 The sportswriter is assuming the price elasticity of demand for Indians’ tickets is inelastic. If the demand for Indians’ tickets is inelastic, then a decrease in price will lead to a decrease in total revenue.
3.4 a. The observation that an increase in ticket prices to the opera “backfired” means that total revenue from ticket sales decreased following the price increase.
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b. Assuming that there were no other reasons why ticket revenue fell (for example, because of bad weather on the dates of the performances or a negative reaction by the public to the operas performed in 2012), the decline in revenue means that demand for opera tickets was elastic.
3.5 Elasticity = (percentage change in quantity/percentage change in price). The article states that consumption decreases by 3 to 5 percent in response to a 10 percent increase in price, so the range of elasticity is: (−3%/10%) = −0.3 to (−5%/10%) = −0.5. The demand for cigarettes is inelastic because the elasticity values computed are both less than 1 in absolute value. Because demand is inelastic, if price increases, revenue will also increase.
3.6 a. The Coca-Cola executive’s comment suggests that he believes the demand for Coca-Cola is inelastic. If he believes that consumers don’t care at all about price, then he believes that the demand for Coke is perfectly inelastic. It is unlikely that the executive believes that demand is perfectly inelastic, because it’s implausible that however high the firm raised the price, consumers would buy the same quantity of Coke.
b. If the executive was correct, then by raising the per ounce price of Coca-Cola, the firm’s revenues should increase.
c. It may be that placing cans of Coke near checkout lines “within arm’s reach” results in more impulse buying on the part of shoppers. If this is true, then it could make the demand for Coke more price inelastic. If Coke is the only soda that is displayed near checkout lines, then shoppers who decide to buy soda at that point in their shopping trip would have no “close” substitutes for Coke.
3.7 a. We can calculate the price elasticity along D1 between points A and C as follows:
Similarly, the price elasticity of demand along D2 between points A and B can be calculated as follows:
Because the quantity response is much larger for the same price change, demand curve D1 is much more elastic.
b. Along D1, revenue increases from $3 × 200 = $600 to $2.50 × 300 = $750. Revenue rises by $150 as the price is cut because this demand curve is elastic between these prices. Along D2,
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revenue falls from $600 to $2.50 × 225 = $562.50. Revenue falls by $37.50 as the price is cut because D2 is inelastic between these prices
3.8 Manager 2 is wrong. Cutting the price will increase revenue if demand is price elastic. But notice that Manager 1 is just as wrong to say “only” as Manager 2 was to say “never.” Manager 1 says the only way to boost revenue is by cutting the price, but if demand is inelastic, then cutting the price will decrease revenue, not increase it.
3.9 a. Because Coca-Cola’s revenue rose while it sold 1 percent less soda in North America, it must have raised its prices. Lowering its prices would have resulted in its selling more soda, not less, holding all other factors constant.
b. Because Coke’s revenue increased following an increase in price, we know that the demand for Coke is price inelastic, holding all other factors constant.
3.10 a. No. If the demand for the publisher’s books is inelastic, then an increase in price will increase total revenue.
b. The author of the article is assuming the demand for the publisher’s books is elastic. If demand for the books is elastic, an increase in price will decrease total revenue.
3.11 Assuming that there was not an increase in demand for the author’s book(s), then a decrease in price that resulted in an increase in income, or revenue, implies that the demand for her books was price elastic.
3.12 a. For the Route 22 bridge:
Revenue in
was
+ 728,022) × $0.50 = $623,679.50. In December total revenue increased to (433,691 + 656,257) × $1 = $1,089,948. The increase occurred because the demand at both bridges is price inelastic.
Learning Objective: Define cross-price elasticity of demand and income
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4.1 Cross-price elasticity of demand equals the percentage change in quantity demanded of one good divided by the percentage change in the price of another good. If the cross-price elasticity is negative, then the goods are complements; if it is positive, then they are substitutes.
4.2 Income elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in income. If the income elasticity is greater than 0, then the good is normal; if it is less than 0, then the good is inferior. Goods with income elasticities between 0 and 1 are often called necessities; goods with income elasticities greater than 1 are often called luxuries.
4.3 a. Lettuce has the higher price elasticity because the percentage change in quantity demanded following a price increase is much larger for lettuce than for bread.
b. Positive. As the price of lettuce rises, the quantity demanded of the other green vegetables rises, so they are substitutes.
4.4 To find the cross-price elasticity, divide the percentage change in the quantity demanded of buns by the percentage change in the price of hot dogs. At the initial price of buns ($1.20), the quantity demanded rises from 10,000 to 12,000, which is the change in quantity demanded that should be used.
Because the cross-price elasticity of demand is negative, we know these two goods are complements.
4.5 (a) and (c) are substitutes, so the cross-price elasticities will be positive; (b) and (d) are complements, so the cross-price elasticities will be negative.
4.6 a. On the basis of the information given, the cross-price elasticity of demand is negative (everything else equal) because the percentage change in ridership on mass transit increased (by 1 percent) at the same time that gasoline prices decreased (by 33 percent). If the crossprice elasticity of demand between two products is negative the products are considered complements.
b. Because during the same period–late 2014–unemployment was falling and more people used private and public transportation to commute to work, it is likely that “everything else” was not equal; in addition to the changes in the price of transportation there was a simultaneous
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elasticity of demand and understand their determinants and how they are measured.
increase in the demand for transportation. So we cannot be sure of the value of the cross-price elasticity of demand between gasoline and rides on mass transit, or even whether the value is positive or negative.
4.7 (a) Bread, (b) Pepsi, (d) laptop computers, (c) Mercedes-Benz automobiles is the most likely order. For normal goods that are considered necessities (such as food and clothing), their income elasticity is positive and less than 1. For normal goods that are considered luxuries (such as laptop computers and Mercedes-Benz automobiles), their income elasticity is positive and greater than 1. The items are ranked from most necessary to most luxurious.
4.8 The more narrowly we define a market, the more price elastic demand will be. So if data for only one brand of beer is used instead of multiple brands, demand for beer will likely be more elastic, which may not be an accurate estimate of the price elasticity for beer as a product
4.9 During recessions, falling consumer incomes can cause firms selling luxury goods (goods with an income elasticity of demand greater than 1) to see their sales decrease the most. During recessions, falling consumer incomes can cause firms selling inferior goods (goods with an income elasticity of demand less than 1) to see their sales increase the most.
5.1 Increasing productivity in agriculture has brought about lower prices for food products as, over time, increases in supply have dramatically outpaced increases in demand. Because the price elasticity of demand for food is low, lower prices have not caused a large increase in quantity demanded. The increase in incomes over time has not increased the demand for food much because the income elasticity for food is low. Farmers, therefore, need to sell larger and larger quantities of food at lower and lower prices to earn the same revenue. As a result, small farms are no longer as profitable as they once were, and many people have abandoned farming to pursue other occupations.
5.2 a. (Percentage change in price) × (price elasticity of demand) = percentage change in quantity: 50% × −0.25 = −12.5%. So, the quantity of cigarettes demanded should decline 12.5% from its current level of 360 billion per year. 12.5% of 360 billion is 45 billion.
b. Raising the tax on cigarettes is a more effective way to reduce smoking if the demand for cigarettes is elastic. With elastic demand, an increase in price resulting from a tax increase would result in a greater reduction in the quantity demanded of cigarettes than if the demand were inelastic.
5.3 a. We can plug into the midpoint formula the values given for the price elasticity, the original price of $3.00, and the new price of $3.70 (= $3.00 + $0.70):
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-0.55 = Percentage change in quantity demanded $3 70 - $3 00 ( ) $3.70 + $3.00
Rearranging and writing out the expression for the percentage change in quantity demanded:
-0 11= Q2 -140billion
Solving for the new quantity demanded: Q2 = 125.4 billion gallons
Because the price elasticity of demand for gasoline is low ( 0.55), a 21 percent increase in price of gasoline leads to only about a 10 percent decline in gasoline consumption per year.
b. The federal government would collect an amount equal to the tax per gallon multiplied by the number of gallons sold: $1 per gallon × 125.40 billion gallons = $125.4 billion.
c. The answers are similar to Solved Problem 6.5 on page 201 Even though demand for gasoline is more elastic in the long run than in the short run, the elasticity is still relatively low, so the decline in the quantity of gasoline demanded is relatively small, and the government collects a relatively large amount of tax revenue.
5.4 For the government policy to be effective, the demand for bribes must be elastic. The more elastic the demand curve, the more effective the policy will be. On the graph, the burden of corruption before the policy is enacted is represented by the area 0Q1AP1. The burden of corruption after the policy is enacted is represented by the area 0Q2BP2 In effect, this problem is applying the result that a price increase will result in an increase in revenue if demand is inelastic but a decrease in revenue if demand is elastic.
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5.5 His reasoning is correct: Because the demand for kumquats is elastic, a price increase resulting from the implementation of a price floor will decrease the revenue received by kumquat producers.
5.6 Imposing a price ceiling causes the market quantity to decline from Q1 to Q2 and the price to decline from P1 to PC We measure the loss of efficiency by the deadweight loss. When demand is elastic D2), the deadweight loss in the figure is A. When demand is inelastic (D1), the deadweight loss is A + B. Therefore, the loss of economic efficiency from a price ceiling is greater when demand is price inelastic.
Learning Objective: Define price elasticity of supply and understand its main determinants and how it is measured.
6.1 The price elasticity of supply = (percentage change in quantity supplied)/(percentage change in price). In this case, the elasticity of supply = 9%/10% = 0.9. The dividing point between elastic and inelastic is 1.0, so the price elasticity of supply for frozen pizzas is inelastic
6.2 The main determinant of the price elasticity of supply is time. The longer the time period, the more firms are able to adjust the quantity they supply to a change in price. So, we would expect that as the time period increases, the price elasticity of supply will increase. An exception to this rule is products that require use of a resource that is in fixed supply, such as wine from a particular region in France.
6.3 Regardless of the number of tickets sold for these games, the quantity supplied of tickets–tickets offered for sale was 49,170 for each game. Assuming that the number of seats does not change throughout the 2015 season the supply of tickets would be perfectly inelastic.
6.4 a. The limitation on the number of taxi medallions implies that the supply of medallions is perfectly inelastic.
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b. The supply of Uber rides is more elastic than the supply of taxis, since the number of Uber rides varies as the demand for rides varies.
6.5 A small increase in the supply of oil would lead to a large decline in price if the demand for oil is relatively inelastic.
6.6 a. The following graph shows that when demand is very inelastic (demand curves D1 and D2), an increase in demand from D1 to D2 results in an increase in the price of oil from $40 to $110. If demand is more elastic (demand curves D3 and D4), then a shift in demand from D3 to D4 results in a much smaller increase in price from $40 only to P1.
b. The graph below shows that an increase in the supply of oil from S1 to S2 will result in a smaller change in price when demand is relatively elastic (D2) than when demand is relatively inelastic (D1). With the more inelastic demand curve (D1), the equilibrium price falls from $110 to $47. With the more elastic demand curve (D2), the price only falls from $110 to P1
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6.7 To find the price elasticity of supply, divide the percentage change in quantity supplied by percentage change in price. In panel (a), the percentage change in quantity supplied = 1,4001,200 10015.4%
, and the percentage change in price = $4$2
. So, the price elasticity of supply = 15.4% 0.23. 66.7%
In panel (b), the percentage change in quantity supplied = 2,1001,200 10054.5% 1,650
, and the percentage change in price = $2.50$2.00 10022.2%.
So, the price elasticity of supply = 54.5% 2.45. 22.2%
6.8 Because it can take years to attract skilled construction workers back to the area or to train new workers, it is likely that the supply of housing in Denver will be considerably more elastic in the long run than in the short run. The following graph illustrates this point by comparing the market for housing in the short run (S2014), when supply is relatively inelastic, and for a longer time period (S 2018), when supply is more elastic. The graph shows that, holding other factors constant, an increase in demand from D1 to D2 increases the price of housing from P1 to P2 when supply is inelastic in the short run, but only from P1 to P3 when supply is more elastic in the long run. The price increase will be lower the longer the period of time the market has to adjust to a given increase in demand.
6.9 a. The increase in demand for roses on Valentine’s Day causes the price to increase from $1 to $2.
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b. Based on this information, we don’t know much about the price elasticity of demand for roses. The demand curve has shifted, so the rise in the quantity of roses demanded is not caused by the rise in their price and we can’t calculate the price elasticity of demand. We have a movement along the supply curve, so we can calculate the price elasticity of supply for roses.
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6.10
The price elasticity of supply elasticity = (percentage change in quantity supplied)/(percentage change in price). So, using the midpoint formula:
Percentage change in the quantity supplied = 30,000 -8,000 19,000 ´100 = 115.8%
Percentage change in the price = $2.00 - $1.00 $1 50 ´100 = 66.7%
Therefore, the price elasticity of supply = 115.8% 66.7% = 1.74.
The fact that the elasticity doesn’t have a negative sign is a reminder that with an upwardsloping supply curve, increases in price to lead to increases in the quantity supplied, so the price elasticity of supply must be positive. The supply of roses is price elastic given the elasticity is greater than one.
a. Price elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in price. In this case, the percentage change in supply is always zero, because the quantity supplied by the university does not change in response to changes in demand, so the price elasticity of supply is 0.
b. As shown in the following graph, when the demand curve for basketball tickets shifts from D1 to D2, the equilibrium price increases from $15 to $20, but there is no change in the equilibrium quantity.
c. One determinant of price elasticity of supply is the period of time. Over a longer period of time, supply is more price elastic. So, although the supply curve for basketball tickets is perfectly inelastic in the short run, it is possible that over time State University could build a larger basketball arena with more seats to accommodate more fans.
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