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Unformatted text preview: 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 81 4 Elasticity A fter studying this chapter, y ou will be able to: ■ Define, calculate, and explain the factors that influence the price elasticity of demand ■ Define, calculate, and explain the factors that influence the cross elasticity of demand and the income elasticity of demand ■ Define, calculate, and explain the factors that influence the elasticity of supply What are the effects of a high gas price on buying plans? You can see some of the biggest effects at car dealers’ such a large scale that we end up cutting our expenditure on lots, where SUVs and other gas guzzlers remain unsold while gas? sub-compacts and hybrids sell in greater quantities. But how This chapter introduces you to elasticity: a tool that big are these effects? When the price of gasoline doubles, as it addresses these quantitative questions. At the end of the has done over the past few years, by how much does the quan- chapter, in Reading Between the Lines, we’ll use the concept tity of SUVs sold decrease, and by how much does the quantity of elasticity to explain what was happening in the markets of sub-compacts sold increase? for gasoline and automobiles in 2008. But we’ll explain and And what about gasoline purchases? Do we keep filling our tanks and spending more on gas? Or do we find substitutes on illustrate elasticity by studying another familiar market: the market for pizza. 81 9160335_CH04_p081-102.qxd 8:57 AM Page 82 CHAPTER 4 Elasticity You know that when supply increases, the equilibrium price falls and the equilibrium quantity increases. But does the price fall by a large amount and the quantity increase by a little? Or does the price barely fall and the quantity increase by a large amount? The answer depends on the responsiveness of the quantity demanded to a change in price. You can see why by studying Fig. 4.1, which shows two possible scenarios in a local pizza market. Figure 4.1(a) shows one scenario, and Fig. 4.1(b) shows the other. In both cases, supply is initially S0. In part (a), the demand for pizza is shown by the demand curve DA. In part (b), the demand for pizza is shown by the demand curve DB. Initially, in both cases, the price is $20 a pizza and the equilibrium quantity is 10 pizzas an hour. Now a large pizza franchise opens up, and the supply of pizza increases. The supply curve shifts rightward to S1. In case (a), the price falls by an enormous $15 to $5 a pizza, and the quantity increases by only 3 to 13 pizzas an hour. In contrast, in case (b), the price falls by only $5 to $15 a pizza and the quantity increases by 7 to 17 pizzas an hour. The different outcomes arise from differing degrees of responsiveness of the quantity demanded to a change in price. But what do we mean by responsiveness? One possible answer is slope. The slope of demand curve DA is steeper than the slope of demand curve DB. In this example, we can compare the slopes of the two demand curves, but we can’t always make such a comparison. The reason is that the slope of a demand curve depends on the units in which we measure the price and quantity. And we often must compare the demand for different goods and services that are measured in unrelated units. For example, a pizza producer might want to compare the demand for pizza with the demand for soft drinks. Which quantity demanded is more responsive to a price change? This question can’t be answered by comparing the slopes of two demand curves. The units of measurement of pizza and soft drinks are unrelated. The question can be answered with a measure of responsiveness that is independent of units of measurement. Elasticity is such a measure. 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 buying plans remain the same. FIGURE 4.1 Price (dollars per pizza) ◆ Price Elasticity of Demand How a Change in Supply Changes Price and Quantity 40.00 S0 An increase in supply brings ... S1 30.00 ... a large fall in price ... 20.00 10.00 ... and a small increase in quantity 5.00 DA 0 5 10 13 15 20 25 Quantity (pizzas per hour) (a) Large price change and small quantity change Price (dollars per pizza) 82 6/22/09 40.00 An increase S0 in supply brings ... S1 30.00 20.00 15.00 10.00 0 DB ... a small fall in price ... 5 ... and a large increase in quantity 10 15 17 20 25 Quantity (pizzas per hour) (b) Small price change and large quantity change Initially, the price is $20 a pizza and the quantity sold is 10 pizzas an hour. Then supply increases from S0 to S1. In part (a), the price falls by $15 to $5 a pizza, and the quantity increases by 3 to 13 pizzas an hour. In part (b), the price falls by only $5 to $15 a pizza, and the quantity increases by 7 to 17 pizzas an hour. The price change is smaller and the quantity change is larger in case (b) than in case (a). The quantity demanded is more responsive to the change in the price in case (b) than in case (a). animation 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 83 Price Elasticity of Demand Calculating Price Elasticity of Demand To use this formula, we need to know the quantities demanded at different prices when all other influences on buying plans remain the same. Suppose we have the data on prices and quantities demanded of pizza and we calculate the price elasticity of demand for pizza. Figure 4.2 zooms in on the demand curve for pizza and shows how the quantity demanded responds to a small change in price. Initially, the price is $20.50 a pizza and 9 pizzas an hour are sold—the original point in the figure. The price then falls to $19.50 a pizza, and the quantity demanded increases to 11 pizzas an hour—the new point in the figure. When the price falls by $1 a pizza, the quantity demanded increases by 2 pizzas an hour. To calculate the price elasticity of demand, we express the changes in price and quantity demanded as percentages of the average price and the average quantity. By using the average price and average quantity, we calculate the elasticity at a point on the demand curve midway between the original point and the new point. The original price is $20.50 and the new price is $19.50, so the average price is $20. The $1 price decrease is 5 percent of the average price. That is, ¢ P> Pave = 1$1> $202 * 100 = 5%. The original quantity demanded is 9 pizzas and the new quantity demanded is 11 pizzas, so the average quantity demanded is 10 pizzas. The 2 pizza increase in the quantity demanded is 20 percent of the average quantity. That is, ¢ Q> Qave = 12> 102 * 100 = 20%. So the price elasticity of demand, which is the percentage change in the quantity demanded (20 percent) divided by the percentage change in price (5 percent) is 4. That is, %¢Q Price elasticity of demand = %¢P 20% = = 4. 5% Price (dollars per pizza) Price elasticity of demand Percentage change in quantity demanded . Percentage change in price Calculating the Elasticity of Demand FIGURE 4.2 Original point 20.50 ∇ We calculate the price elasticity of demand by using the formula: 83 P = $1 Elasticity = 4 20.00 Pave = $20 New point 19.50 D ΔQ = 2 Qave = 10 0 9 10 11 Quantity (pizzas per hour) The elasticity of demand is calculated by using the formula:* Price elasticity of demand = Percentage change in quantity demanded Percentage change in price %¢Q = %¢P = ¢ Q> Qave = 2> 10 ¢ P> Pave 1> 20 = 4. This calculation measures the elasticity at an average price of $20 a pizza and an average quantity of 10 pizzas an hour. * In the formula, the Greek letter delta (Δ) stands for “change in” and %Δ stands for “percentage change in.” animation Average Price and Quantity Notice that we use the average price and average quantity. We do this because it gives the most precise measurement of elasticity—at the midpoint between the original price and the new price. If the price falls from $20.50 to $19.50, the $1 price change is 4.9 percent of $20.50. The 2 pizza change in quantity is 22.2 percent of 9 pizzas, the original quantity. So if we use these numbers, the price elasticity of demand is 22.2 divided by 4.9, which equals 4.5. If the price 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 84 CHAPTER 4 Elasticity 84 a negative number. But it is the magnitude, or absolute value, of the price elasticity of demand that tells us how responsive the quantity demanded is. So to compare price elasticities of demand, we use the magnitude of the elasticity and ignore the minus sign. rises from $19.50 to $20.50, the $1 price change is 5.1 percent of $19.50. The 2 pizza change in quantity is 18.2 percent of 11 pizzas, the original quantity. So if we use these numbers, the price elasticity of demand is 18.2 divided by 5.1, which equals 3.6. By using percentages of the average price and average quantity, we get the same value for the elasticity regardless of whether the price falls from $20.50 to $19.50 or rises from $19.50 to $20.50. Inelastic and Elastic Demand Figure 4.3 shows three demand curves that cover the entire range of possible elasticities of demand. In Fig. 4.3(a), the quantity demanded is constant regardless of the price. If the quantity demanded remains constant when the price changes, then the price elasticity of demand is zero and the good is said to have a perfectly inelastic demand. One good that has a very low price elasticity of demand (perhaps zero over some price range) is insulin. Insulin is of such importance to some diabetics that if the price rises or falls, they do not change the quantity they buy. If the percentage change in the quantity demanded equals the percentage change in the price, then the price elasticity equals 1 and the good is said to have a unit elastic demand. The demand in Fig. 4.3(b) is an example of a unit elastic demand. Between the cases shown in Fig. 4.3(a) and Fig. 4.3(b) is the general case in which the percentage change in the quantity demanded is less than the percentage change in the price. In this case, the price elasticity of demand is between zero and 1 and the good is said to have an inelastic demand. Food and shelter are examples of goods with inelastic demand. Percentages and Proportions Elasticity is the ratio of two percentage changes. So when we divide one percentage change by another, the 100s cancel. A percentage change is a proportionate change multiplied by 100. The proportionate change in price is ΔP/Pave, and the proportionate change in quantity demanded is ΔQ/Qave. So if we divide ΔQ/Qave by ΔP/Pave we get the same answer as we get by using percentage changes. A Units-Free Measure Now that you’ve calculated a price elasticity of demand, you can see why it is a units-free measure. Elasticity is a units-free measure because the percentage change in each variable is independent of the units in which the variable is measured. And the ratio of the two percentages is a number without units. Minus Sign and Elasticity When the price of a good rises, the quantity demanded decreases. Because a positive change in price brings a negative change in the quantity demanded, the price elasticity of demand is D1 Price Price Price Inelastic and Elastic Demand FIGURE 4.3 Elasticity = 0 Elasticity = ∞ Elasticity = 1 12 12 12 6 6 6 D3 D2 0 Quantity (a) Perfectly inelastic demand 0 1 (b) Unit elastic demand Each demand illustrated here has a constant elasticity. The demand curve in part (a) illustrates the demand for a good that has a zero elasticity of demand. The demand curve in animation 2 3 Quantity 0 Quantity (c) Perfectly elastic demand part (b) illustrates the demand for a good with a unit elasticity of demand. And the demand curve in part (c) illustrates the demand for a good with an infinite elasticity of demand. 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 85 Price Elasticity of Demand If the quantity demanded changes by an infinitely large percentage in response to a tiny price change, then the price elasticity of demand is infinity and the good is said to have a perfectly elastic demand. Figure 4.3(c) shows a perfectly elastic demand. An example of a good that has a very high elasticity of demand (almost infinite) is a soft drink from two campus machines located side by side. If the two machines offer the same soft drinks for the same price, some people buy from one machine and some from the other. But if one machine’s price is higher than the other’s, by even a small amount, no one will buy from the machine with the higher price. Soft drinks from the two machines are perfect substitutes. The demand for a good that has a perfect substitute is perfectly elastic. Between the cases in Fig. 4.3(b) and Fig. 4.3(c) is the general case in which the percentage change in the quantity demanded exceeds the percentage change in price. In this case, the price elasticity of demand is greater than 1 and the good is said to have an elastic demand. Automobiles and furniture are examples of goods that have elastic demand. = Price elasticity of demand = ¢ Q> Qave ¢ P> Pave 20> 10 10> 20 = 4. That is, the price elasticity of demand at an average price of $20 a pizza is 4. Next, suppose that the price falls from $15 to $10 a pizza. The quantity demanded increases from 20 to 30 pizzas an hour. The average price is now $12.50 a pizza, and the average quantity is 25 pizzas an hour. So 5> 12.50 20> 40 10> 5 = 1> 4. That is, the price elasticity of demand at an average price of $5 a pizza is 1/4. You’ve now seen how elasticity changes along a straight-line demand curve. At the midpoint of the curve, demand is unit elastic. Above the midpoint, demand is elastic. Below the midpoint, demand is inelastic. Price (dollars per pizza) Elasticity and slope are not the same, but they are related. To understand how they are related, let’s look at elasticity along a straight-line demand curve—a demand curve that has a constant slope. Figure 4.4 illustrates the calculation of elasticity along a straight-line demand curve. First, suppose the price falls from $25 to $15 a pizza. The quantity demanded increases from zero to 20 pizzas an hour. The average price is $20 a pizza, and the average quantity is 10 pizzas. So 10> 25 = 1. That is, the price elasticity of demand at an average price of $12.50 a pizza is 1. Finally, suppose that the price falls from $10 to zero. The quantity demanded increases from 30 to 50 pizzas an hour. The average price is now $5 a pizza, and the average quantity is 40 pizzas an hour. So Elasticity Along a StraightLine Demand Curve FIGURE 4.4 Elasticity Along a Straight-Line Demand Curve Price elasticity of demand = Price elasticity of demand = 85 25.00 Elasticity = 4 20.00 Elastic 15.00 Elasticity = 1 12.50 Inelastic 10.00 / Elasticity =14 5.00 0 10 20 25 30 40 50 Quantity (pizzas per hour) On a straight-line demand curve, elasticity decreases as the price falls and the quantity demanded increases. Demand is unit elastic at the midpoint of the demand curve (elasticity is 1). Above the midpoint, demand is elastic; below the midpoint, demand is inelastic. animation 9160335_CH04_p081-102.qxd 8:57 AM Page 86 CHAPTER 4 Elasticity The total revenue from the sale of a good equals the price of the good multiplied by the quantity sold. When a price changes, total revenue also changes. But a cut in the price does not always decrease total revenue. The change in total revenue depends on the elasticity of demand in the following way: ■ ■ ■ If demand is elastic, a 1 percent price cut increases the quantity sold by more than 1 percent and total revenue increases. ■ ■ ■ If a price cut increases total revenue, demand is elastic. If a price cut decreases total revenue, demand is inelastic. If a price cut leaves total revenue unchanged, demand is unit elastic. 25.00 Elastic demand 20.00 Unit elastic 15.00 12.50 10.00 If demand is inelastic, a 1 percent price cut increases the quantity sold by less than 1 percent and total revenue decreases. If demand is unit elastic, a 1 percent price cut increases the quantity sold by 1 percent and total revenue does not change. In Fig. 4.5(a), over the price range from $25 to $12.50, demand is elastic. Over the price range from $12.50 to zero, demand is inelastic. At a price of $12.50, demand is unit elastic. Figure 4.5(b) shows total revenue. At a price of $25, the quantity sold is zero, so total revenue is zero. At a price of zero, the quantity demanded is 50 pizzas an hour and total revenue is again zero. A price cut in the elastic range brings an increase in total revenue—the percentage increase in the quantity demanded is greater than the percentage decrease in price. A price cut in the inelastic range brings a decrease in total revenue—the percentage increase in the quantity demanded is less than the percentage decrease in price. At unit elasticity, total revenue is at a maximum. Figure 4.5 shows how we can use this relationship between elasticity and total revenue to estimate elasticity using the total revenue test. 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 change in the price, when all other influences on the quantity sold remain the same. Elasticity and Total Revenue FIGURE 4.5 Price (dollars per pizza) Total Revenue and Elasticity Inelastic demand 5.00 25 0 50 Quantity (pizzas per hour) (a) Demand Total revenue (dollars) 86 6/22/09 350.00 Maximum total revenue 312.50 250.00 200.00 150.00 100.00 50.00 When demand is elastic, a price cut increases total revenue 0 When demand is inelastic, a price cut decreases total revenue 25 50 Quantity (pizzas per hour) (b) Total revenue When demand is elastic, in the price range from $25 to $12.50, a decrease in price (part a) brings an increase in total revenue (part b). When demand is inelastic, in the price range from $12.50 to zero, a decrease in price (part a) brings a decrease in total revenue (part b). When demand is unit elastic, at a price of $12.50 (part a), total revenue is at a maximum (part b). animation 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 87 Price Elasticity of Demand Your Expenditure and Your Elasticity When a price changes, the change in your expenditure on the good depends on your elasticity of demand. ■ If your demand is elastic, a 1 percent price cut increases the quantity you buy by more than 1 percent and your expenditure on the item increases. ■ If your demand is inelastic, a 1 percent price cut increases the quantity you buy by less than 1 percent and your expenditure on the item decreases. ■ If your demand is unit elastic, a 1 percent price cut increases the quantity you buy by 1 percent and your expenditure on the item does not change. So if you spend more on an item when its price falls, your demand for that item is elastic; if you spend the same amount, your demand is unit elastic; and if you spend less, your demand is inelastic. The Factors That Influence the Elasticity of Demand Some Real-World Elasticities of Demand Elastic and Inelastic Demand The real-world elasticities of demand in the table range from 1.52 for metals, the item with the most elastic demand in the table, to 0.05 for oil, the item with the most inelastic demand in the table. Oil and food, which have poor substitutes and inelastic demand, might be classified as necessities. Furniture and motor vehicles, which have good substitutes and elastic demand, might be classified as luxuries. Price Elasticities of Demand Good or Service Elasticity Elastic Demand Metals 1.52 What makes the demand for some goods elastic and the demand for others inelastic? The elasticity of demand for a good depends on ■ The closeness of substitutes ■ The proportion of income spent on the good ■ The time elapsed since the price change Electrical engineering products 1.39 Professional services 1.09 Closeness of Substitutes The closer the substitutes for a Transportation services 1.03 good or service, the more elastic is the demand for it. For example, oil from which we make gasoline has substitutes but none that are currently very close (imagine a steam-driven, coal-fueled car). So the demand for oil is inelastic. Plastics are close substitutes for metals, so the demand for metals is elastic. The degree of substitutability between two goods also depends on how narrowly (or broadly) we define them. For example, a personal computer has no really close substitutes, but a Dell PC is a close substitute for a Hewlett-Packard PC. So the elasticity of demand for personal computers is lower than the elasticity of demand for a Dell or a Hewlett-Packard. In everyday language we call goods such as food and shelter necessities and goods such as exotic vacations luxuries. A necessity is a good that has poor substitutes and that is crucial for our well-being. So generally, a necessity has an inelastic demand. A luxury is a good that usually has many substitutes, one of which is not buying it. So a luxury generally has an elastic demand. 87 Mechanical engineering products 1.30 Furniture 1.26 Motor vehicles 1.14 Instrument engineering products 1.10 Inelastic Demand Gas, electricity, and water 0.92 Chemicals 0.89 Drinks (all types) 0.78 Clothing 0.64 Tobacco 0.61 Banking and insurance services 0.56 Housing services 0.55 Agricultural and fish products 0.42 Books, magazines, and newspapers 0.34 Food 0.12 Oil 0.05 Sources of data: Ahsan Mansur and John Whalley, “Numerical Specification of Applied General Equilibrium Models: Estimation, Calibration, and Data,” in Applied General Equilibrium Analysis, eds. Herbert E. Scarf and John B. Shoven (New York: Cambridge University Press, 1984), 109, and Henri Theil, Ching-Fan Chung, and James L. Seale, Jr., Advances in Econometrics, Supplement I, 1989, International Evidence on Consumption Patterns (Greenwich, Conn.: JAI Press Inc., 1989), and Geoffrey Heal, Columbia University, Web site. 9160335_CH04_p081-102.qxd 88 6/22/09 8:57 AM Page 88 CHAPTER 4 Elasticity Proportion of Income Spent on the Good Other things remaining the same, the greater the proportion of income spent on a good, the more elastic is the demand for it. Think about your own elasticity of demand for chewing gum and housing. If the price of chewing gum doubles, you consume almost as much gum as before. Your demand for gum is inelastic. If apartment rents double, you shriek and look for more students Price Elasticities of Demand for Food How Inelastic? As the average income in a country increases and the proportion of income spent on food decreases, the demand for food becomes more inelastic. The figure shows that the price elasticity of demand for food (green bars) is greatest in the poorest countries. The larger the proportion of income spent on food, the larger is the price elasticity of demand for food. In Tanzania, a nation where the average income is onethirtieth that of the United States and where 62 percent of income is spent on food, the price elasticity of demand for food is 0.77. In contrast, in the United States, where 12 percent of income is spent on food, the price elasticity of demand for food is 0.12. Food budget (percentage of income) Country Tanzania 62 India to share accommodation with you. Your demand for housing is not as inelastic as your demand for gum. Why the difference? Housing takes a large proportion of your budget, and gum takes only a tiny proportion. You don’t like either price increase, but you hardly notice the higher price of gum, while the higher rent puts your budget under severe strain. Time Elapsed Since Price Change The longer the time that has elapsed since a price change, the more elastic is demand. When the price of oil increased by 400 percent during the 1970s, people barely changed the quantity of oil and gasoline they bought. But gradually, as more efficient auto and airplane engines were developed, the quantity bought decreased. The demand for oil has become more elastic as more time has elapsed since the huge price hike. Similarly, when the price of a PC fell, the quantity of PCs demanded increased only slightly at first. But as more people have become better informed about the variety of ways of using a PC, the quantity of PCs bought has increased sharply. The demand for PCs has become more elastic. Review Quiz ◆ 1 2 56 Korea 40 Brazil 35 Greece 31 3 Spain 28 France 17 Germany 15 Canada 14 United States 12 4 0 0.2 0.4 0.6 0.8 1.0 Price elasticity of demand Price Elasticities in 10 Countries Source of data: Henri Theil, Ching-Fan Chung, and James L. Seale, Jr., Advances in Econometrics, Supplement 1, 1989, International Evidence on Consumption Patterns (Greenwich, Conn.: JAI Press, Inc., 1989). 5 6 Why do we need a units-free measure of the responsiveness of the quantity demanded of a good or service to a change in its price? Define the price elasticity of demand and show how it is calculated. Why, when we calculate the price elasticity of demand, do we express the change in price as a percentage of the average price and the change in quantity as a percentage of the average quantity? What is the total revenue test? Explain how it works. What are the main influences on the elasticity of demand that make the demand for some goods elastic and the demand for other goods inelastic? Why is the demand for a luxury generally more elastic than the demand for a necessity? Work Study Plan 4.1 and get instant feedback. You’ve now completed your study of the price elasticity of demand. Two other elasticity concepts tell us about the effects of other influences on demand. Let’s look at these other elasticities of demand. 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 89 More Elasticities of Demand Back at the pizzeria, you are trying to work out how a price rise by the burger shop next door will affect the demand for your pizza. You know that pizzas and burgers are substitutes. And you know that when the price of a substitute for pizza rises, the demand for pizza increases. But by how much? You also know that pizza and soft drinks are complements. And you know that if the price of a complement of pizza rises, the demand for pizza decreases. So you wonder, by how much will a rise in the price of a soft drink decrease the demand for your pizza? To answer these questions, you need to calculate the cross elasticity of demand. Let’s examine this elasticity measure. Cross Elasticity of Demand We measure the influence of a change in the price of a substitute or complement by using the concept of the cross elasticity of demand. The cross elasticity of demand is a measure of the responsiveness of the demand for a good to a change in the price of a substitute or complement, other things remaining the same. We calculate the cross elasticity of demand by using the formula: Cross elasticity of demand The change in the price of a burger, a substitute for pizza, is +$1—the new price, $2.50, minus the original price, $1.50. The average price is $2 a burger. So the price of a burger rises by 50 percent. That is, ¢ P> Pave = 1 + 1> 22 * 100 = + 50%. So the cross elasticity of demand for pizza with respect to the price of a burger is + 20% = 0.4. + 50% Figure 4.6 illustrates the cross elasticity of demand. Pizza and burgers are substitutes. Because they are substitutes, when the price of a burger rises, the demand for pizza increases. The demand curve for pizza shifts rightward from D0 to D1. Because a rise in the price of a burger brings an increase in the demand for pizza, the cross elasticity of demand for pizza with respect to the price of a burger is positive. Both the price and the quantity change in the same direction. FIGURE 4.6 Cross Elasticity of Demand Price of pizza ◆ More Elasticities of Demand Price of a burger, a substitute, rises. Positive cross elasticity Percentage change in quantity demanded . Percentage change in price of a substitute or complement The cross elasticity of demand can be positive or negative. It is positive for a substitute and negative for a complement. Substitutes Suppose that the price of pizza is constant and people buy 9 pizzas an hour. Then the price of a burger rises from $1.50 to $2.50. No other influence on buying plans changes and the quantity of pizzas bought increases to 11 an hour. The change in the quantity demanded is +2 pizzas—the new quantity, 11 pizzas, minus the original quantity, 9 pizzas. The average quantity is 10 pizzas. So the quantity of pizzas demanded increases by 20 percent. That is, ¢ Q> Qave = 1 + 2> 102 * 100 = + 20%. 89 Price of a soft drink, a complement, rises. Negative cross elasticity 0 D1 D0 D2 Quantity of pizza A burger is a substitute for pizza. When the price of a burger rises, the demand for pizza increases and the demand curve for pizza shifts rightward from D0 to D1. The cross elasticity of demand is positive. A soft drink is a complement of pizza. When the price of a soft drink rises, the demand for pizza decreases and the demand curve for pizza shifts leftward from D0 to D2. The cross elasticity of demand is negative. animation 9160335_CH04_p081-102.qxd 90 6/22/09 8:57 AM Page 90 CHAPTER 4 Elasticity Complements Now suppose that the price of pizza is constant and 11 pizzas an hour are bought. Then the price of a soft drink rises from $1.50 to $2.50. No other influence on buying plans changes and the quantity of pizzas bought falls to 9 an hour. The change in the quantity demanded is the opposite of what we’ve just calculated: The quantity of pizzas demanded decreases by 20 percent (–20%). The change in the price of a soft drink, a complement of pizza, is the same as the percentage change in the price of a burger that we’ve just calculated. The price rises by 50 percent (+50%). So the cross elasticity of demand for pizza with respect to the price of a soft drink is - 20% = - 0.4. + 50% Because pizza and soft drinks are complements, when the price of a soft drink rises, the demand for pizza decreases. The demand curve for pizza shifts leftward from D0 to D2. Because a rise in the price of a soft drink brings a decrease in the demand for pizza, the cross elasticity of demand for pizza with respect to the price of a soft drink is negative. The price and quantity change in opposite directions. The magnitude of the cross elasticity of demand determines how far the demand curve shifts. The larger the cross elasticity (absolute value), the greater is the change in demand and the larger is the shift in the demand curve. If two items are close substitutes, such as two brands of spring water, the cross elasticity is large. If two items are close complements, such as movies and popcorn, the cross elasticity is large. If two items are somewhat unrelated to each other, such as newspapers and orange juice, the cross elasticity is small—perhaps even zero. The income elasticity of demand is calculated by using the formula: Income elasticity of demand Percentage change in quantity demanded . Percentage change in income Income elasticities of demand can be positive or negative and they fall into three interesting ranges: ■ ■ ■ Greater than 1 (normal good, income elastic) Positive and less than 1 (normal good, income inelastic) Negative (inferior good) Income Elastic Demand Suppose that the price of pizza is constant and 9 pizzas an hour are bought. Then incomes rise from $975 to $1,025 a week. No other influence on buying plans changes and the quantity of pizzas sold increases to 11 an hour. The change in the quantity demanded is +2 pizzas. The average quantity is 10 pizzas, so the quantity demanded increases by 20 percent. The change in income is +$50 and the average income is $1,000, so incomes increase by 5 percent. The income elasticity of demand for pizza is 20% = 4. 5% The demand for pizza is income elastic. The percentage increase in the quantity of pizza demanded exceeds the percentage increase in income. When the demand for a good is income elastic, the percentage of income spent on that good increases as income increases. Income Elasticity of Demand Income Inelastic Demand If the income elasticity of demand is positive but less than 1, demand is income inelastic. The percentage increase in the quantity demanded is positive but less than the percentage increase in income. When the demand for a good is income inelastic, the percentage of income spent on that good decreases as income increases. Suppose the economy is expanding and people are enjoying rising incomes. This prosperity brings an increase in the demand for most types of goods and services. But by how much will the demand for pizza increase? The answer depends on the income elasticity of demand, which is a measure of the responsiveness of the demand for a good or service to a change in income, other things remaining the same. Inferior Goods If the income elasticity of demand is negative, the good is an inferior good. The quantity demanded of an inferior good and the amount spent on it decrease when income increases. Goods in this category include small motorcycles, potatoes, and rice. Low-income consumers buy most of these goods. 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 91 More Elasticities of Demand Income Elasticities of Demand Necessities and Luxuries The table shows estimates of some real-world income elasticities of demand. The demand for a necessity such as food or clothing is income inelastic, while the demand for a luxury such as transportation, which includes airline and foreign travel, is income elastic. But what is a necessity and what is a luxury depends on the level of income. For people with a low income, food and clothing can be luxuries. So the level of income has a big effect on income elasticities of demand. The figure shows this effect on the income elasticity of demand for food in 10 countries. In countries with low incomes, such as Tanzania and India, the income elasticity of demand for food is high. In countries with high incomes, such as the United States, the income elasticity of 91 demand for food is low. That is as income increases, the income elasticity of demand for food decreases. Low-income consumers spend a larger percentage of any increase in income on food than do highincome consumers. Country Income (percentage of U.S. income) Tanzania 3.3 India 5.2 Korea 20.4 Brazil 36.8 Greece 41.3 Spain 55.9 Japan 61.6 France 81.1 Canada 99.2 United States 100.0 Some Real-World Income Elasticities of Demand 0 0.2 0.4 0.6 0.8 1.0 Income elasticity of demand Income Elastic Demand Airline travel 5.82 Movies 3.41 Foreign travel 3.08 Electricity 1.94 Restaurant meals 1.61 Income Elasticities in 10 Countries Review Quiz ◆ Local buses and trains 1.38 1 Haircuts 1.36 2 Automobiles 1.07 3 Income Inelastic Demand Tobacco 0.86 Alcoholic drinks 0.62 Furniture 0.53 Clothing 0.51 Newspapers and magazines 0.38 Telephone 0.32 Food 0.14 Sources of data: H.S. Houthakker and Lester D. Taylor, Consumer Demand in the United States (Cambridge, Mass.: Harvard University Press, 1970), and Henri Theil, Ching-Fan Chung, and James L. Seale, Jr., Advances in Econometrics, Supplement 1, 1989, International Evidence on Consumption Patterns (Greenwich, Conn.: JAI Press, Inc., 1989). 4 5 What does the cross elasticity of demand measure? What does the sign (positive versus negative) of the cross elasticity of demand tell us about the relationship between two goods? What does the income elasticity of demand measure? What does the sign (positive versus negative) of the income elasticity of demand tell us about a good? Why does the level of income influence the magnitude of the income elasticity of demand? Work Study Plan 4.2 and get instant feedback. You’ve now completed your study of the cross elasticity of demand and the income elasticity of demand. Let’s look at the other side of the market and examine the elasticity of supply. 9160335_CH04_p081-102.qxd 8:57 AM Page 92 CHAPTER 4 Elasticity You know that when demand increases, the equilibrium price rises and the equilibrium quantity increases. But does the price rise by a large amount and the quantity increase by a little? Or does the price barely rise and the quantity increase by a large amount? The answer depends on the responsiveness of the quantity supplied to a change in price. You can see why by studying Fig. 4.7, which shows two possible scenarios in a local pizza market. Figure 4.7(a) shows one scenario, and Fig. 4.7(b) shows the other. In both cases, demand is initially D0. In part (a), supply is shown by the supply curve SA. In part (b), supply is shown by the supply curve SB. Initially, in both cases, the price is $20 a pizza and the equilibrium quantity is 10 pizzas an hour. Now increases in incomes and population increase the demand for pizza. The demand curve shifts rightward to D1. In case (a), the price rises by $10 to $30 a pizza, and the quantity increases by only 3 to 13 pizzas an hour. In contrast, in case (b), the price rises by only $1 to $21 a pizza, and the quantity increases by 10 to 20 pizzas an hour. The different outcomes arise from differing degrees of responsiveness of the quantity supplied to a change in price. We measure the degree of responsiveness by using the concept of the elasticity of supply. FIGURE 4.7 Price (dollars per pizza) ◆ Elasticity of Supply 40.00 How a Change in Demand Changes Price and Quantity An increase in demand brings ... SA 30.00 20.00 ... a large price rise ... D1 10.00 D0 ... and a small quantity increase 0 5 10 13 15 20 25 Quantity (pizzas per hour) (a) Large price change and small quantity change Price (dollars per pizza) 92 6/22/09 40.00 An increase in demand brings ... 30.00 21.00 20.00 SB D1 ... a small price rise ... Calculating the Elasticity of Supply 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. It is calculated by using the formula: Elasticity of supply Percentage change in quantity supplied . Percentage change in price We use the same method that you learned when you studied the elasticity of demand. (Refer back to p. 87 to check this method.) Let’s calculate the elasticity of supply along the supply curves in Fig. 4.7. In Fig. 4.7(a), when the price rises from $20 to $30, the price rise is $10 and the average price is $25, so the price rises by 40 percent of the average price. The quantity increases from 10 to 13 pizzas an hour, 10.00 D0 ... and a large quantity increase 0 5 10 15 20 25 Quantity (pizzas per hour) (b) Small price change and large quantity change Initially, the price is $20 a pizza, and the quantity sold is 10 pizzas an hour. Then the demand for pizza increases. The demand curve shifts rightward to D1. In part (a), the price rises by $10 to $30 a pizza, and the quantity increases by 3 to 13 pizzas an hour. In part (b), the price rises by only $1 to $21 a pizza, and the quantity increases by 10 to 20 pizzas an hour. The price change is smaller and the quantity change is larger in case (b) than in case (a). The quantity supplied is more responsive to a change in the price in case (b) than in case (a). animation 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 93 Elasticity of Supply The Factors That Influence the Elasticity of Supply so the increase is 3 pizzas, the average quantity is 11.5 pizzas an hour, and the quantity increases by 26 percent. The elasticity of supply is equal to 26 percent divided by 40 percent, which equals 0.65. In Fig. 4.7(b), when the price rises from $20 to $21, the price rise is $1 and the average price is $20.50, so the price rises by 4.9 percent of the average price. The quantity increases from 10 to 20 pizzas an hour, so the increase is 10 pizzas, the average quantity is 15 pizzas, and the quantity increases by 67 percent. The elasticity of supply is equal to 67 percent divided by 4.9 percent, which equals 13.67. Figure 4.8 shows the range of elasticities of supply. If the quantity supplied is fixed regardless of the price, the supply curve is vertical and the elasticity of supply is zero. Supply is perfectly inelastic. This case is shown in Fig. 4.8(a). A special intermediate case occurs when the percentage change in price equals the percentage change in quantity. Supply is then unit elastic. This case is shown in Fig. 4.8(b). No matter how steep the supply curve is, if it is linear and passes through the origin, supply is unit elastic. If there is a price at which sellers are willing to offer any quantity for sale, the supply curve is horizontal and the elasticity of supply is infinite. Supply is perfectly elastic. This case is shown in Fig. 4.8(c). The elasticity of supply of a good depends on Resource substitution possibilities Time frame for the supply decision ■ ■ Resource Substitution Possibilities Some goods and services can be produced only by using unique or rare productive resources. These items have a low, perhaps even a zero, elasticity of supply. Other goods and services can be produced by using commonly available resources that could be allocated to a wide variety of alternative tasks. Such items have a high elasticity of supply. A Van Gogh painting is an example of a good with a vertical supply curve and a zero elasticity of supply. At the other extreme, wheat can be grown on land that is almost equally good for growing corn, so it is just as easy to grow wheat as corn. The opportunity cost of wheat in terms of forgone corn is almost constant. As a result, the supply curve of wheat is almost horizontal and its elasticity of supply is very large. Similarly, when a good is produced in many different countries (for example, sugar and beef ), the supply of the good is highly elastic. S1 Price Inelastic and Elastic Supply Price Price FIGURE 4.8 93 S 2A Elasticity of supply = ∞ Elasticity of supply = 0 Elasticity of supply = 1 S3 S 2B 0 Quantity (a) Perfectly inelastic supply 0 (b) Unit elastic supply Each supply illustrated here has a constant elasticity. The supply curve in part (a) illustrates the supply of a good that has a zero elasticity of supply. The supply curve in part (b) illustrates the supply of a good with a unit elasticity of animation Quantity 0 Quantity (c) Perfectly elastic supply supply. All linear supply curves that pass through the origin illustrate supplies that are unit elastic. The supply curve in part (c) illustrates the supply of a good with an infinite elasticity of supply. 9160335_CH04_p081-102.qxd 94 6/22/09 8:57 AM Page 94 CHAPTER 4 Elasticity The supply of most goods and services lies between these two extremes. The quantity produced can be increased but only by incurring a higher cost. If a higher price is offered, the quantity supplied increases. Such goods and services have an elasticity of supply between zero and infinity. Time Frame for the Supply Decision To study the influence of the amount of time elapsed since a price change, we distinguish three time frames of supply: 1. Momentary supply 2. Long-run supply 3. Short-run supply When the price of a good rises or falls, the momentary supply curve shows the response of the quantity supplied immediately following the price change. Some goods, such as fruits and vegetables, have a perfectly inelastic momentary supply—a vertical supply curve. The quantities supplied depend on cropplanting decisions made earlier. In the case of oranges, for example, planting decisions have to be made many years in advance of the crop being available. The momentary supply curve is vertical because, on a given day, no matter what the price of oranges, producers cannot change their output. They have picked, packed, and shipped their crop to market, and the quantity available for that day is fixed. In contrast, some goods have a perfectly elastic momentary supply. Long-distance phone calls are an example. When many people simultaneously make a call, there is a big surge in the demand for telephone cables, computer switching, and satellite time, and the quantity supplied increases. But the price remains constant. Long-distance carriers monitor fluctuations in demand and reroute calls to ensure that the quantity supplied equals the quantity demanded without changing the price. The long-run supply curve shows the response of the quantity supplied to a price change after all the technologically possible ways of adjusting supply have been exploited. In the case of oranges, the long run is the time it takes new plantings to grow to full maturity—about 15 years. In some cases, the longrun adjustment occurs only after a completely new production plant has been built and workers have been trained to operate it—typically a process that might take several years. The short-run supply curve shows how the quantity supplied responds to a price change when only some of the technologically possible adjustments to production have been made. The short-run response to a price change is a sequence of adjustments. The first adjustment that is usually made is in the amount of labor employed. To increase output in the short run, firms work their labor force overtime and perhaps hire additional workers. To decrease their output in the short run, firms either lay off workers or reduce their hours of work. With the passage of time, firms can make additional adjustments, perhaps training additional workers or buying additional tools and other equipment. The short-run supply curve slopes upward because producers can take actions quite quickly to change the quantity supplied in response to a price change. For example, if the price of oranges falls, growers can stop picking and leave oranges to rot on the trees. Or if the price rises, they can use more fertilizer and improved irrigation to increase the yields of their existing trees. In the long run, they can plant more trees and increase the quantity supplied even more in response to a given price rise. Review Quiz ◆ 1 2 3 4 5 Why do we need a units-free measure of the responsiveness of the quantity supplied of a good or service to a change in its price? Define the elasticity of supply and show how it is calculated. What are the main influences on the elasticity of supply that make the supply of some goods elastic and the supply of other goods inelastic? Provide examples of goods or services whose elasticities of supply are (a) zero, (b) greater than zero but less than infinity, and (c) infinity. How does the time frame over which a supply decision is made influence the elasticity of supply? Explain your answer. Work Study Plan 4.3 and get instant feedback. ◆ You have now learned about the elasticities of demand and supply. Table 4.1 summarizes all the elasticities that you’ve met in this chapter. In the next chapter, we study the efficiency of competitive markets. But first study Reading Between the Lines on pp. 96–97, which puts the elasticity of demand to work and looks at the markets for gasoline and automobiles. 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 95 Elasticity of Supply TABLE 4.1 95 A Compact Glossary of Elasticities P rice Elasticities of Demand A relationship is described as When its magnitude is Which means that Perfectly elastic Infinity Elastic Less than infinity Unit elastic 1 Inelastic Greater than zero but less than 1 Zero The smallest possible increase in price causes an infinitely large decrease in the quantity demanded* The percentage decrease in the quantity demanded but greater than 1 exceeds the percentage increase in price The percentage decrease in the quantity demanded equals the percentage increase in price The percentage decrease in the quantity demanded is less than the percentage increase in price The quantity demanded is the same at all prices A relationship is described as When its value is Which means that Close substitutes Large Substitutes Positive Unrelated goods Zero Complements Negative The smallest possible increase in the price of one good causes an infinitely large increase in the quantity demanded of the other good If the price of one good increases, the quantity demanded of the other good also increases If the price of one good increases, the quantity demanded of the other good remains the same If the price of one good increases, the quantity demanded of the other good decreases Perfectly inelastic Cross Elasticities of Demand Income Elasticities of Demand A relationship is described as When its value is Which means that Income elastic (normal good) Income inelastic (normal good) Greater than 1 Negative (inferior good) Less than zero The percentage increase in the quantity demanded is greater than the percentage increase in income The percentage increase in the quantity demanded is greater than zero less than the percentage increase in income When income increases, quantity demanded decreases Less than 1 but Elasticities of Supply A relationship is described as When its magnitude is Which means that Perfectly elastic Infinity Elastic Less than infinity but greater than 1 Greater than zero but less than 1 Zero The smallest possible increase in price causes an infinitely large increase in the quantity supplied The percentage increase in the quantity supplied exceeds the percentage increase in the price The percentage increase in the quantity supplied is less than the percentage increase in the price The quantity supplied is the same at all prices Inelastic Perfectly inelastic * In each description, the directions of change may be reversed. For example, in this case, the smallest possible decrease in price causes an infinitely large increase in the quantity demanded. 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 96 READING BETWEEN THE LINES The Elasticities of Demand for Gasoline, SUVs, and Subcompacts As Gas Costs Soar, Buyers Are Flocking to Small Cars Soaring gas prices have turned the steady migration by Americans to smaller cars into a stampede. … http://www.nytimes.com May 2, 2008 Sales of Toyota’s subcompact Yaris increased 46 percent, and Honda’s tiny Fit had a record month. Ford’s compact Focus model jumped 32 percent in April from a year earlier. All those models are rated at more than 30 miles per gallon for highway driving. ... Sales of traditional SUV’s are down more than 25 percent this year. In April, for example, sales of G.M.’s Chevrolet Tahoe fell 35 percent. Full-size pickup sales have fallen more than 15 percent this year, with Ford’s industry-leading F-Series pickup dropping 27 percent in April alone. Sales of pickups, though, are expected to strengthen with the economy, because of their use as commercial vehicles. … How the downsizing of America’s vehicle fleet will affect fuel consumption is still largely unknown. When gas prices rise, as they are now, many drivers simply drive less to save money. But there are some indications that the trend toward smaller vehicles will reduce the nation’s fuel use. In California, motorists bought 4 percent less gasoline in January than they did the year before, a drop of more than 58 million gallons, according to the Oil Price Information Service. “That is an incredible year-over-year drop,’’ said Tom Kloza, the organization’s chief oil analyst. “Some of it clearly has to do with changes in the vehicle fleet.’’… Copyright 2008 The New York Times Company. Reprinted with permission. Further reproduction prohibited. Essence of the Story ■ Faced with high gas prices, Americans are substituting smaller cars for SUVs. ■ Toyota Yaris sales increased 46 percent and Ford Focus sales increased 32 percent in April 2008 from a year earlier. ■ 96 Sales of SUVs decreased by more than 25 percent in 2008 and Chevrolet Tahoe sales fell 35 percent. ■ Full-size pickup sales decreased more than 15 percent in 2008 and Ford F-Series pickup sales decreased by 27 percent in April 2008. ■ The effect of a downsized vehicle fleet on fuel consumption is unknown. ■ In California, gasoline consumption decreased by 4 percent in January 2008 from a year earlier. 6/22/09 8:57 AM Page 97 Economic Analysis ■ ■ Using data provided in this news article and by the Energy Information Administration, and assuming that no other influences on buying plans changed, we can estimate the price elasticity of demand for gasoline in California. Price (dollars per gallon) 9160335_CH04_p081-102.qxd Table 1 summarizes the gasoline price and quantity data and, using the midpoint method, calculates the price elasticity of demand. 3.50 New point 3.09 Elasticity = 0.14 P = 0.80 2.69 Original point Pave 2.29 Q = 58 Table 1 Price Elasticity of Demand for Gasoline in California January-07 January-08 Change Average % change Elasticity ■ ■ 1450 1392 –58 1421 –4.1 2.29 3.09 0.80 2.69 29.7 0.14 Figure 1 illustrates the changes in price and quantity and the elasticity calculation. Table 2 Cross Elasticities of Demand for Vehicles in the United States Vehicle Toyota Yaris Ford Focus Chevrolet Tahoe Ford F-Series Price of gasoline Apr-07 Apr-08 % Cross elasticity Number change of demand 7,323 16,626 10,980 56,692 2.89 11,434 23,850 8,139 44,813 3.51 43.8 35.7 –29.7 –23.4 19.4 2.3 1.8 –1.5 –1.2 ■ The cross elasticities of demand are calculated using the formula on p. 93. The cross elasticities of demand for the Yaris and Focus are positive and large. A rise in the price of gasoline increases the demand for these vehicles. A small car and gasoline are substitutes—a smaller car is used in place of a large gas bill. Figure 2 illustrates the cross elasticity of demand for small vehicles. Positive cross elasticity: price of gasoline rises and demand for small cars increases 14,000 D0 0 7,323 11,434 Quantity (cars per month) Figure 2 Cross elasticity: Yaris and price of gasoline 55,000 Negative cross elasticity: price of gasoline rises and demand for large vehicles decreases 35,000 D0 D1 (dollars per gallon) ■ 24,000 D1 The estimated price elasticity of demand for gasoline in California is 0.14, which means that the demand is inelastic. A large percentage change in price brings a small percentage change in the quantity of gasoline demanded. Table 2 shows the quantities sold of four vehicles and the price of gasoline in April 2007 and April 2008 and calculates some cross elasticities of demand. 1,392 1,421 1,450 Quantity (millions of gallons per month) Figure 1 Price elasticity of demand for gasoline Price (dollars per vehicle) ■ 0 Price (dollars per gallon) Price (dollars per car) Quantity (millions of gallons) D Qave 0 8,139 10,980 Quantity (vehicles per month) Figure 3 Cross elasticity: Tahoe and price of gasoline ■ The cross elasticity of demand for the Tahoe and F-Series are negative and large. A rise in the price of gasoline decreases the demand for these vehicles. A large vehicle and gasoline are complements. Figure 3 illustrates the cross elasticity of demand for large vehicles. 97 9160335_CH04_p081-102.qxd 98 6/22/09 8:57 AM Page 98 CHAPTER 4 Elasticity SUMMARY ◆ Key Points Price Elasticity of Demand (pp. 82–88) ■ ■ ■ ■ ■ Elasticity is a measure of the responsiveness of the quantity demanded of a good to a change in its price, other things remaining the same. Price elasticity of demand equals the percentage change in the quantity demanded divided by the percentage change in the price. The larger the magnitude of the price elasticity of demand, the greater is the responsiveness of the quantity demanded to a given price change. If demand is elastic, a cut in price leads to an increase in total revenue. If demand is unit elastic, a cut in price leaves total revenue unchanged. And if demand is inelastic, a cut in price leads to a decrease in total revenue. Price elasticity of demand depends on how easily one good serves as a substitute for another, the proportion of income spent on the good, and the length of time elapsed since the price change. More Elasticities of Demand (pp. 89–91) ■ ■ ■ ■ ■ Elasticity of Supply (pp. 92–95) ■ ■ ■ ■ Cross elasticity of demand measures the responsiveness of the demand for one good to a change in the price of a substitute or a complement, other things remaining the same. The cross elasticity of demand with respect to the price of a substitute is positive. The cross elasticity of demand with respect to the price of a complement is negative. Income elasticity of demand measures the responsiveness of demand to a change in income, other things remaining the same. For a normal good, the income elasticity of demand is positive. For an inferior good, the income elasticity of demand is negative. When the income elasticity of demand is greater than 1 (income elastic), the percentage of income spent on the good increases as income increases. When the income elasticity of demand is less than 1 (income inelastic and inferior), the percentage of income spent on the good decreases as income increases. ■ ■ Elasticity of supply measures the responsiveness of the quantity supplied of a good to a change in its price, other things remaining the same. The elasticity of supply is usually positive and ranges between zero (vertical supply curve) and infinity (horizontal supply curve). Supply decisions have three time frames: momentary, long run, and short run. Momentary supply refers to the response of the quantity supplied to a price change at the instant that the price changes. Long-run supply refers to the response of the quantity supplied to a price change when all the technologically feasible adjustments in production have been made. Short-run supply refers to the response of the quantity supplied to a price change after some of the technologically feasible adjustments in production have been made. Key Figures and Table Figure 4.2 Calculating the Elasticity of Demand, 83 Figure 4.3 Inelastic and Elastic Demand, 84 Figure 4.4 Elasticity Along a Straight-Line Demand Curve, 85 Figure 4.5 Elasticity and Total Revenue, 86 Figure 4.6 Cross Elasticity of Demand, 89 Table 4.1 A Compact Glossary of Elasticities, 95 Key Terms Cross elasticity of demand, 89 Elastic demand, 85 Elasticity of supply, 92 Income elasticity of demand, 90 Inelastic demand, 84 Perfectly elastic demand, 85 Perfectly inelastic demand, 84 Price elasticity of demand, 82 Total revenue, 86 Total revenue test, 86 Unit elastic demand, 84 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 99 Problems and Applications PROBLEMS and APPLICATIONS 99 ◆ Work problems 1–12 in Chapter 4 Study Plan and get instant feedback. Work problems 14–26 as Homework, a Quiz, or a Test if assigned by your instructor. 1. Rain spoils the strawberry crop. As a result, the price rises from $4 to $6 a box and the quantity demanded decreases from 1,000 to 600 boxes a week. Over this price range, a. What is the price elasticity of demand? b. Describe the demand for strawberries. 2. If the quantity of dental services demanded increases by 10 percent when the price of dental services falls by 10 percent, is the demand for dental services inelastic, elastic, or unit elastic? 3. The demand schedule for hotel rooms is Price Quantity demanded (dollars per night) (millions of rooms per night) 200 100 250 80 400 50 500 40 800 25 1,000 20 a. What happens to total revenue if the price falls from $400 to $250 a night? b. What happens to total revenue if the price falls from $250 to $200 a night? c. At what price is total revenue at a maximum? Explain and interpret your answer. d. Is the demand for hotel rooms elastic, unit elastic, or inelastic? 4. The Grip of Gas: Why You’ll Pay Through the Nose to Keep Driving Drivers in the United States consistently rank as the least sensitive to changes in gas prices. ... If prices rose from $3 per gallon to $4 per gallon and stayed there for a year … purchases of gasoline in the United States would fall only about 5 percent. Slate, September 27, 2005 a. Using the information provided, calculate the price elasticity of demand for gasoline. b. Does this measurement indicate that the demand for gasoline is elastic, unit elastic, or inelastic? c. If the price of gasoline rises, will total revenue from gasoline sales increase or decrease? Explain. 5. In 2003, when music downloading first took off, Universal Music slashed the price of a CD from an average of $21 to an average of $15. The company said that it expected the price cut to boost the quantity of CDs sold by 30 percent, other things remaining the same. a. What was Universal Music’s estimate of the price elasticity of demand for CDs? b. Given your answer in a, if you were making the pricing decision at Universal Music, would you cut the price, raise the price, or not change the price? Explain your decision. 6. Why the Tepid Response to Rising Gasoline Prices? Estimates of the long-run response to past movements in [gasoline] prices imply that a 10 percent price rise causes 5 to 10 percent less consumption, other things being equal. ... The nationwide average price of gasoline surged 53 percent from 1998 to 2004, after adjusting for inflation. Yet consumption was up 10 percent in this period. Of course, many other things changed in this period. Perhaps most important, [incomes] grew by 19 percent. ... This would ordinarily be expected to push gasoline sales up about 20 percent ... The New York Times, October 13, 2005 a. What does the above information tell us about the responsiveness of the quantity of gasoline demanded to a change in the price a long time after the price change occurs? b. Calculate the income elasticity of demand for gasoline implied by the above information. c. If other things remained the same except for the increase in income and the rise in price, what would the data for 1998 to 2004 imply about the price elasticity of demand for gasoline? d. List all the factors you can think of that might bias the estimate of the price elasticity of demand for gasoline, using just the data for 1998 to 2004. 7. If a 12 percent rise in the price of orange juice decreases the quantity of orange juice demanded by 22 percent and increases the quantity of apple juice demanded by 14 percent, calculate the 9160335_CH04_p081-102.qxd 100 6/22/09 8:57 AM Page 100 CHAPTER 4 Elasticity a. Price elasticity of demand for orange juice. b. Cross elasticity of demand for apple juice with respect to the price of orange juice. 8. Swelling Textbook Costs Have College Students Saying ‘Pass’ Textbook prices have been rising at double the rate of inflation for the past two decades … [and] nearly 60 percent of students nationwide choose not to buy all the course materials. … For students working to pay for school or for those whose parents sweat every increase in tuition, book prices can be a nasty surprise. … And plenty of students come up with their own strategies: Hunting down used copies and selling books back at the end of the semester; buying online, which is sometimes cheaper than the campus store; asking professors to put a copy in the library and waiting around till it’s free. Or borrowing, copying, taking careful notes in class—and gambling that the exam questions don’t come from the text. … Washington Post, January 23, 2006 Explain what this news clip implies about a. The price elasticity of demand for college textbooks. b. The income elasticity of demand for college textbooks. c. The cross elasticity of demand for college textbooks from the campus bookstore with respect to the online price of a textbook. 9. Home Depot Earnings Hammered As home prices slump across the country, fewer people are spending money to renovate their homes, and the improvements that they are making are not as expensive. … People are spending on small ticket types of repairs, … not big ticket renovations. … With gas and food prices increasing … people have less extra income to spend on major home improvements. CNN, May 20, 2008 a. What does this news clip imply about the income elasticity of demand for big-ticket home-improvement items? b. Would the income elasticity of demand be greater or less than 1? Explain. 10. Spam Sales Rise as Food Costs Soar Sales of Spam—that much maligned meat—are rising as consumers are turning more to lunch meats and other lower-cost foods to extend their already stretched food budgets. … Consumers are quick to realize that meats like Spam and other processed foods can be substituted for costlier cuts as a way of controlling costs. AOL Money & Finance, May 28, 2008 a. Is Spam a normal good or inferior good? Explain. b. Would the income elasticity of demand for Spam be negative or positive? Explain. 11. Study Ranks Honolulu Third Highest for ‘Unaffordable Housing’ [Study ranks] Honolulu number 3 in the world for the most unaffordable housing market in urban locations. Honolulu is listed only behind Los Angeles and San Diego and is deemed “severely unaffordable.” … Where there are significant constraints on the supply of land for residential development, housing inflation has occurred. Hawaii Reporter, September 11, 2007 a. Would the supply of housing in Honolulu be elastic or inelastic? b. Explain how the elasticity of supply plays an important role in influencing how rapidly housing prices in Honolulu rise. 12. The demand for illegal drugs is inelastic. Much of the expenditure on illegal drugs comes from crime. Assuming these statements to be correct, a. How will a successful campaign that decreases the supply of drugs influence the price of illegal drugs and the amount spent on them? b. What will happen to the amount of crime? c. What is the most effective way of decreasing the quantity of illegal drugs bought and decreasing the amount of drug-related crime? 13. Use the links on MyEconLab (Textbook Resources, Chapter 4, Web links) to find the number of gallons in a barrel of oil and the prices of crude oil and gasoline in the summer of 2007 and 2008. a. What are the other costs that make up the total cost of a gallon of gasoline? b. If the price of crude oil falls by 10 percent, by what percentage do you expect the price of gasoline to change, other things remaining the same? c. Which demand do you think is more elastic: that for crude oil or gasoline? Why? d. Use the concepts of demand, supply, and elasticity to explain recent changes in the prices of crude oil and gasoline. 9160335_CH04_p081-102.qxd 6/22/09 8:57 AM Page 101 Problems and Applications Price (dollars per DVD) 14. With higher fuel costs, airlines raise their fares. The average fare rises from 75¢ per passenger mile to $1.25 per passenger mile and the number of passenger miles decreases from 2.5 million a day to 1.5 million a day. Over this price range, a. What is the price elasticity of demand for air travel? b. Describe the demand for air travel. 15. The figure shows the demand for DVD rentals. 6 5 4 3 2 1 D 0 25 50 75 100 125 150 DVDs per day a. Calculate the elasticity of demand when the price rises from $3 to $5 a DVD. b. At what price is the elasticity of demand for DVDs equal to 1? 16. The demand schedule for computer chips is Price Quantity demanded (dollars per chip) (millions of chips per year) 200 250 300 350 400 50 45 40 35 30 a. What happens to total revenue if the price falls from $400 to $350 a chip? b. What happens to total revenue if the price falls from $350 to $300 a chip? c. At what price is total revenue at a maximum? d. At an average price of $350, is the demand for chips elastic, inelastic, or unit elastic? Use the total revenue test to answer this question. 17. In problem 16, at $250 a chip, is the demand for chips elastic or inelastic? Use the total revenue test to answer this question. 18. Your price elasticity of demand for bananas is 4. If the price of bananas rises by 5 percent, what is 101 a. The percentage change in the quantity of bananas you buy? b. The change in your expenditure on bananas? 19. Why Gasoline Follows Oil Up but Not Down If it seems like gasoline prices are quick to skyrocket when the price of oil goes up, but then take their sweet ol’ time coming back down when crude prices sink, the answer is simple: They do. “There is a rocket and feather aspect.”… The service stations are still selling the same amount of gasoline when wholesale prices fall … “so there’s no reason to drop. … [Service stations] typically react [to a spike in oil prices] by pushing prices higher, even before they replace their inventories. …” Eventually, the free market steps in and prices begin going down when other nearby stations reduce their price. CNN, January 12, 2007 a. Explain the link between the elasticity of supply of gasoline and gas price fluctuations. b. Explain the connection between the elasticity of demand for gasoline and the “rocket and feather” tendency of price fluctuations. 20. As Gasoline Prices Soar, Americans Slowly Adapt … in March, Americans drove 11 billion fewer miles than in March 2007. … “People have recognized that prices are not going down and are adapting to higher energy cost.” … Americans spend 3.7 percent of their disposable income on transportation fuels. At its lowest point, that share was 1.9 percent in 1998, and at its highest it reached 4.5 percent in 1981. … “We actually have a lot of choices, based on what car we drive, where we live, how much time we choose to drive, and where we choose to go.” For many people, higher energy costs mean fewer restaurant meals, deferred weekend outings with the kids, less air travel and more time closer to home. … International Herald Tribune, May 23, 2008 a. List and explain the elasticities of demand that are implicitly referred to in the news clip. b. Explain the factors identified in the news clip that may make the demand for gasoline inelastic. 21. When Alex’s income increased from $3,000 to $5,000, he increased his consumption of bagels from 4 to 8 a month and decreased his consumption of donuts from 12 to 6 a month. Calculate 9160335_CH04_p081-102.qxd 102 6/22/09 8:57 AM Page 102 CHAPTER 4 Elasticity Alex’s income elasticity of demand for a. Bagels. b. Donuts. 22. Wal-Mart’s Recession-Time Pet Project Wal-Mart … is “redefining” the pets business in its stores, including repositioning pet food and supplies right in front of its other fast-growing business, baby products. There lies the connection, according to retail industry experts, who point out that kids and pets tend to be fairly recession-resistant businesses. Even in a recession, dogs will be fed and kids will get their toys. … CNN, May 13, 2008 a. What does this news clip imply about the income elasticity of demand for pet food and baby products? b. Would the income elasticity of demand be greater or less than 1? Explain. 23. Netflix to Offer Online Movie Viewing Online movie rental service Netflix introduced a new feature Tuesday to allow customers to watch movies and television series on their personal computers. … Netflix has been competing with video rental retailer Blockbuster, which has added an online rental service to the in-store rental service. CNN, January 16, 2007 a. How will the offering of online movie viewing influence the price elasticity of demand for instore movie rentals? b. Would the cross elasticity of demand for online movies and in-store movie rentals be negative or positive? Explain. c. Would the cross elasticity of demand for online movies with respect to high-speed Internet service be negative or positive? Explain. 24. To Love, Honor, and Save Money Nearly half of caterers and event planners surveyed … said they were seeing declines in wedding spending in response to the economic slowdown; 12% even reported wedding cancellations because of financial concerns. Time, June 2, 2008 a. Based upon this news clip, are wedding events a normal good or inferior good? Explain. b. Are wedding events more of a necessity or luxury? Explain. c. Given your answer to b, would that make the income elasticity of demand greater than 1, less than 1, or equal to 1? 25. The table gives the supply schedule of longdistance phone calls. Price Quantity supplied (cents per minute) (millions of minutes per day) 10 20 30 40 200 400 600 800 Calculate the elasticity of supply when a. The price falls from 40 cents to 30 cents a minute. b. The average price is 20 cents a minute. 26. Study Reading Between the Lines on pp. 96–97 and then answer the following questions. a. What factors other than the price of gasoline would you expect to influence California motorists’ planned purchases of gasoline? b. In which directions would the factors that you identified in a change the demand for gasoline in California? c. How would the changes in the demand for gasoline have biased our estimate of the price elasticity of demand for gasoline? d. Given the influence of the price of gasoline on the demand for small vehicles and large vehicles, how would you expect the prices of small vehicles and large vehicles to have changed in 2008? e. What elasticities do you need to know to predict the magnitude of the changes in the prices of small vehicles and large vehicles? f. If the prices of cars did change in 2008 in the directions that you have predicted in d, how would these changes impact our estimates of the cross elasticities of demand for small vehicles and large vehicles with respect to the price of gasoline? g. How would you expect the demand for vehicles to change in the long run in response to a permanent rise in the price of gasoline? ...
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This note was uploaded on 04/04/2012 for the course ECON 251 taught by Professor Blanchard during the Spring '08 term at Purdue University-West Lafayette.

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