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# Chapter 5 Elasticity: A Measure of Response

## Start Up: Raise Fares? Lower Fares? What’s a Public Transit Manager To Do?

Imagine that you are the manager of the public transportation system for a large metropolitan area. Operating costs for the system have soared in the last few years, and you are under pressure to boost revenues. What do you do?

An obvious choice would be to raise fares. That will make your customers angry, but at least it will generate the extra revenue you need—or will it? The law of demand says that raising fares will reduce the number of passengers riding on your system. If the number of passengers falls only a little, then the higher fares that your remaining passengers are paying might produce the higher revenues you need. But what if the number of passengers falls by so much that your higher fares actually reduce your revenues? If that happens, you will have made your customers mad and your financial problem worse!

Maybe you should recommend lower fares. After all, the law of demand also says that lower fares will increase the number of passengers. Having more people use the public transportation system could more than offset a lower fare you collect from each person. But it might not. What will you do?

Your job and the fiscal health of the public transit system are riding on your making the correct decision. To do so, you need to know just how responsive the quantity demanded is to a price change. You need a measure of responsiveness.

Economists use a measure of responsiveness called elasticity. ElasticityThe ratio of the percentage change in a dependent variable to a percentage change in an independent variable. is the ratio of the percentage change in a dependent variable to a percentage change in an independent variable. If the dependent variable is y, and the independent variable is x, then the elasticity of y with respect to a change in x is given by:

Equation 5.1

A variable such as y is said to be more elastic (responsive) if the percentage change in y is large relative to the percentage change in x. It is less elastic if the reverse is true.

As manager of the public transit system, for example, you will want to know how responsive the number of passengers on your system (the dependent variable) will be to a change in fares (the independent variable). The concept of elasticity will help you solve your public transit pricing problem and a great many other issues in economics. We will examine several elasticities in this chapter—all will tell us how responsive one variable is to a change in another.

## 5.1 The Price Elasticity of Demand

### Learning Objectives

1. Explain the concept of price elasticity of demand and its calculation.
2. Explain what it means for demand to be price inelastic, unit price elastic, price elastic, perfectly price inelastic, and perfectly price elastic.
3. Explain how and why the value of the price elasticity of demand changes along a linear demand curve.
4. Understand the relationship between total revenue and price elasticity of demand.
5. Discuss the determinants of price elasticity of demand.

We know from the law of demand how the quantity demanded will respond to a price change: it will change in the opposite direction. But how much will it change? It seems reasonable to expect, for example, that a 10% change in the price charged for a visit to the doctor would yield a different percentage change in quantity demanded than a 10% change in the price of a Ford Mustang. But how much is this difference?

To show how responsive quantity demanded is to a change in price, we apply the concept of elasticity. The price elasticity of demandThe percentage change in quantity demanded of a particular good or service divided by the percentage change in the price of that good or service, all other things unchanged. for a good or service, eD, is the percentage change in quantity demanded of a particular good or service divided by the percentage change in the price of that good or service, all other things unchanged. Thus we can write

Equation 5.2

Because the price elasticity of demand shows the responsiveness of quantity demanded to a price change, assuming that other factors that influence demand are unchanged, it reflects movements along a demand curve. With a downward-sloping demand curve, price and quantity demanded move in opposite directions, so the price elasticity of demand is always negative. A positive percentage change in price implies a negative percentage change in quantity demanded, and vice versa. Sometimes you will see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored because it is expected that there will be a negative (inverse) relationship between quantity demanded and price. In this text, however, we will retain the minus sign in reporting price elasticity of demand and will say “the absolute value of the price elasticity of demand” when that is what we are describing.

Be careful not to confuse elasticity with slope. The slope of a line is the change in the value of the variable on the vertical axis divided by the change in the value of the variable on the horizontal axis between two points. Elasticity is the ratio of the percentage changes. The slope of a demand curve, for example, is the ratio of the change in price to the change in quantity between two points on the curve. The price elasticity of demand is the ratio of the percentage change in quantity to the percentage change in price. As we will see, when computing elasticity at different points on a linear demand curve, the slope is constant—that is, it does not change—but the value for elasticity will change.

## Computing the Price Elasticity of Demand

Finding the price elasticity of demand requires that we first compute percentage changes in price and in quantity demanded. We calculate those changes between two points on a demand curve.

Figure 5.1 "Responsiveness and Demand" shows a particular demand curve, a linear demand curve for public transit rides. Suppose the initial price is $0.80, and the quantity demanded is 40,000 rides per day; we are at point A on the curve. Now suppose the price falls to$0.70, and we want to report the responsiveness of the quantity demanded. We see that at the new price, the quantity demanded rises to 60,000 rides per day (point B). To compute the elasticity, we need to compute the percentage changes in price and in quantity demanded between points A and B.

Figure 5.1 Responsiveness and Demand

The demand curve shows how changes in price lead to changes in the quantity demanded. A movement from point A to point B shows that a $0.10 reduction in price increases the number of rides per day by 20,000. A movement from B to A is a$0.10 increase in price, which reduces quantity demanded by 20,000 rides per day.

We measure the percentage change between two points as the change in the variable divided by the average value of the variable between the two points. Thus, the percentage change in quantity between points A and B in Figure 5.1 "Responsiveness and Demand" is computed relative to the average of the quantity values at points A and B: (60,000 + 40,000)/2 = 50,000. The percentage change in quantity, then, is 20,000/50,000, or 40%. Likewise, the percentage change in price between points A and B is based on the average of the two prices: ($0.80 +$0.70)/2 = $0.75, and so we have a percentage change of −0.10/0.75, or −13.33%. The price elasticity of demand between points A and B is thus 40%/(−13.33%) = −3.00. This measure of elasticity, which is based on percentage changes relative to the average value of each variable between two points, is called arc elasticityMeasure of elasticity based on percentage changes relative to the average value of each variable between two points.. The arc elasticity method has the advantage that it yields the same elasticity whether we go from point A to point B or from point B to point A. It is the method we shall use to compute elasticity. For the arc elasticity method, we calculate the price elasticity of demand using the average value of price, $P¯$, and the average value of quantity demanded, $Q¯$. We shall use the Greek letter Δ to mean “change in,” so the change in quantity between two points is ΔQ and the change in price is ΔP. Now we can write the formula for the price elasticity of demand as Equation 5.3 The price elasticity of demand between points A and B is thus: With the arc elasticity formula, the elasticity is the same whether we move from point A to point B or from point B to point A. If we start at point B and move to point A, we have: The arc elasticity method gives us an estimate of elasticity. It gives the value of elasticity at the midpoint over a range of change, such as the movement between points A and B. For a precise computation of elasticity, we would need to consider the response of a dependent variable to an extremely small change in an independent variable. The fact that arc elasticities are approximate suggests an important practical rule in calculating arc elasticities: we should consider only small changes in independent variables. We cannot apply the concept of arc elasticity to large changes. Another argument for considering only small changes in computing price elasticities of demand will become evident in the next section. We will investigate what happens to price elasticities as we move from one point to another along a linear demand curve. ### Heads Up! Notice that in the arc elasticity formula, the method for computing a percentage change differs from the standard method with which you may be familiar. That method measures the percentage change in a variable relative to its original value. For example, using the standard method, when we go from point A to point B, we would compute the percentage change in quantity as 20,000/40,000 = 50%. The percentage change in price would be −$0.10/$0.80 = −12.5%. The price elasticity of demand would then be 50%/(−12.5%) = −4.00. Going from point B to point A, however, would yield a different elasticity. The percentage change in quantity would be −20,000/60,000, or −33.33%. The percentage change in price would be$0.10/$0.70 = 14.29%. The price elasticity of demand would thus be −33.33%/14.29% = −2.33. By using the average quantity and average price to calculate percentage changes, the arc elasticity approach avoids the necessity to specify the direction of the change and, thereby, gives us the same answer whether we go from A to B or from B to A. ## Price Elasticities Along a Linear Demand Curve What happens to the price elasticity of demand when we travel along the demand curve? The answer depends on the nature of the demand curve itself. On a linear demand curve, such as the one in Figure 5.2 "Price Elasticities of Demand for a Linear Demand Curve", elasticity becomes smaller (in absolute value) as we travel downward and to the right. Figure 5.2 Price Elasticities of Demand for a Linear Demand Curve The price elasticity of demand varies between different pairs of points along a linear demand curve. The lower the price and the greater the quantity demanded, the lower the absolute value of the price elasticity of demand. Figure 5.2 "Price Elasticities of Demand for a Linear Demand Curve" shows the same demand curve we saw in Figure 5.1 "Responsiveness and Demand". We have already calculated the price elasticity of demand between points A and B; it equals −3.00. Notice, however, that when we use the same method to compute the price elasticity of demand between other sets of points, our answer varies. For each of the pairs of points shown, the changes in price and quantity demanded are the same (a$0.10 decrease in price and 20,000 additional rides per day, respectively). But at the high prices and low quantities on the upper part of the demand curve, the percentage change in quantity is relatively large, whereas the percentage change in price is relatively small. The absolute value of the price elasticity of demand is thus relatively large. As we move down the demand curve, equal changes in quantity represent smaller and smaller percentage changes, whereas equal changes in price represent larger and larger percentage changes, and the absolute value of the elasticity measure declines. Between points C and D, for example, the price elasticity of demand is −1.00, and between points E and F the price elasticity of demand is −0.33.

On a linear demand curve, the price elasticity of demand varies depending on the interval over which we are measuring it. For any linear demand curve, the absolute value of the price elasticity of demand will fall as we move down and to the right along the curve.

## The Price Elasticity of Demand and Changes in Total Revenue

Suppose the public transit authority is considering raising fares. Will its total revenues go up or down? Total revenueA firm’s output multiplied by the price at which it sells that output. is the price per unit times the number of units sold.Notice that since the number of units sold of a good is the same as the number of units bought, the definition for total revenue could also be used to define total spending. Which term we use depends on the question at hand. If we are trying to determine what happens to revenues of sellers, then we are asking about total revenue. If we are trying to determine how much consumers spend, then we are asking about total spending. In this case, it is the fare times the number of riders. The transit authority will certainly want to know whether a price increase will cause its total revenue to rise or fall. In fact, determining the impact of a price change on total revenue is crucial to the analysis of many problems in economics.

We will do two quick calculations before generalizing the principle involved. Given the demand curve shown in Figure 5.2 "Price Elasticities of Demand for a Linear Demand Curve", we see that at a price of $0.80, the transit authority will sell 40,000 rides per day. Total revenue would be$32,000 per day ($0.80 times 40,000). If the price were lowered by$0.10 to $0.70, quantity demanded would increase to 60,000 rides and total revenue would increase to$42,000 ($0.70 times 60,000). The reduction in fare increases total revenue. However, if the initial price had been$0.30 and the transit authority reduced it by $0.10 to$0.20, total revenue would decrease from $42,000 ($0.30 times 140,000) to $32,000 ($0.20 times 160,000). So it appears that the impact of a price change on total revenue depends on the initial price and, by implication, the original elasticity. We generalize this point in the remainder of this section.

The problem in assessing the impact of a price change on total revenue of a good or service is that a change in price always changes the quantity demanded in the opposite direction. An increase in price reduces the quantity demanded, and a reduction in price increases the quantity demanded. The question is how much. Because total revenue is found by multiplying the price per unit times the quantity demanded, it is not clear whether a change in price will cause total revenue to rise or fall.

We have already made this point in the context of the transit authority. Consider the following three examples of price increases for gasoline, pizza, and diet cola.

Suppose that 1,000 gallons of gasoline per day are demanded at a price of $4.00 per gallon. Total revenue for gasoline thus equals$4,000 per day (=1,000 gallons per day times $4.00 per gallon). If an increase in the price of gasoline to$4.25 reduces the quantity demanded to 950 gallons per day, total revenue rises to $4,037.50 per day (=950 gallons per day times$4.25 per gallon). Even though people consume less gasoline at $4.25 than at$4.00, total revenue rises because the higher price more than makes up for the drop in consumption.

Next consider pizza. Suppose 1,000 pizzas per week are demanded at a price of $9 per pizza. Total revenue for pizza equals$9,000 per week (=1,000 pizzas per week times $9 per pizza). If an increase in the price of pizza to$10 per pizza reduces quantity demanded to 900 pizzas per week, total revenue will still be $9,000 per week (=900 pizzas per week times$10 per pizza). Again, when price goes up, consumers buy less, but this time there is no change in total revenue.

Now consider diet cola. Suppose 1,000 cans of diet cola per day are demanded at a price of $0.50 per can. Total revenue for diet cola equals$500 per day (=1,000 cans per day times $0.50 per can). If an increase in the price of diet cola to$0.55 per can reduces quantity demanded to 880 cans per month, total revenue for diet cola falls to $484 per day (=880 cans per day times$0.55 per can). As in the case of gasoline, people will buy less diet cola when the price rises from $0.50 to$0.55, but in this example total revenue drops.

In our first example, an increase in price increased total revenue. In the second, a price increase left total revenue unchanged. In the third example, the price rise reduced total revenue. Is there a way to predict how a price change will affect total revenue? There is; the effect depends on the price elasticity of demand.

## Elastic, Unit Elastic, and Inelastic Demand

To determine how a price change will affect total revenue, economists place price elasticities of demand in three categories, based on their absolute value. If the absolute value of the price elasticity of demand is greater than 1, demand is termed price elasticSituation in which the absolute value of the price elasticity of demand is greater than 1.. If it is equal to 1, demand is unit price elasticSituation in which the absolute value of the price elasticity of demand is equal to 1.. And if it is less than 1, demand is price inelasticSituation in which the absolute value of the price of elasticity of demand is less than 1..

## Relating Elasticity to Changes in Total Revenue

When the price of a good or service changes, the quantity demanded changes in the opposite direction. Total revenue will move in the direction of the variable that changes by the larger percentage. If the variables move by the same percentage, total revenue stays the same. If quantity demanded changes by a larger percentage than price (i.e., if demand is price elastic), total revenue will change in the direction of the quantity change. If price changes by a larger percentage than quantity demanded (i.e., if demand is price inelastic), total revenue will move in the direction of the price change. If price and quantity demanded change by the same percentage (i.e., if demand is unit price elastic), then total revenue does not change.

When demand is price inelastic, a given percentage change in price results in a smaller percentage change in quantity demanded. That implies that total revenue will move in the direction of the price change: a reduction in price will reduce total revenue, and an increase in price will increase it.

Consider the price elasticity of demand for gasoline. In the example above, 1,000 gallons of gasoline were purchased each day at a price of $4.00 per gallon; an increase in price to$4.25 per gallon reduced the quantity demanded to 950 gallons per day. We thus had an average quantity of 975 gallons per day and an average price of $4.125. We can thus calculate the arc price elasticity of demand for gasoline: The demand for gasoline is price inelastic, and total revenue moves in the direction of the price change. When price rises, total revenue rises. Recall that in our example above, total spending on gasoline (which equals total revenues to sellers) rose from$4,000 per day (=1,000 gallons per day times $4.00) to$4037.50 per day (=950 gallons per day times $4.25 per gallon). When demand is price inelastic, a given percentage change in price results in a smaller percentage change in quantity demanded. That implies that total revenue will move in the direction of the price change: an increase in price will increase total revenue, and a reduction in price will reduce it. Consider again the example of pizza that we examined above. At a price of$9 per pizza, 1,000 pizzas per week were demanded. Total revenue was $9,000 per week (=1,000 pizzas per week times$9 per pizza). When the price rose to $10, the quantity demanded fell to 900 pizzas per week. Total revenue remained$9,000 per week (=900 pizzas per week times $10 per pizza). Again, we have an average quantity of 950 pizzas per week and an average price of$9.50. Using the arc elasticity method, we can compute:

Demand is unit price elastic, and total revenue remains unchanged. Quantity demanded falls by the same percentage by which price increases.

The MSA also required that states use some of the money they receive from tobacco firms to carry out antismoking programs. The nature and scope of these programs vary widely. State excise taxes, also varying widely, range from 2.5¢ per pack in Virginia (a tobacco-producing state) to $1.51 in Massachusetts. Given the greater responsiveness of teenagers to the price of cigarettes, excise taxes should prove an effective device. One caveat, however, in evaluating the impact of a tax hike on teen smoking is that some teens might switch from cigarettes to smokeless tobacco, which is associated with a higher risk of oral cancer. It is estimated that for young males the cross price elasticity of smokeless tobacco with respect to the price of cigarettes is 1.2—a 10% increase in cigarette prices leads to a 12% increase in young males using smokeless tobacco. ### Answer to Try It! Problem Using the formula for cross price elasticity of demand, we find that eAB = (−3%)/(10%) = −0.3. Since the eAB is negative, bagels and cream cheese are complements. Using the formula for income elasticity of demand, we find that eY = (+1%)/(10%) = +0.1. Since eY is positive, bagels are a normal good. ## 5.3 Price Elasticity of Supply ### Learning Objectives 1. Explain the concept of elasticity of supply and its calculation. 2. Explain what it means for supply to be price inelastic, unit price elastic, price elastic, perfectly price inelastic, and perfectly price elastic. 3. Explain why time is an important determinant of price elasticity of supply. 4. Apply the concept of price elasticity of supply to the labor supply curve. The elasticity measures encountered so far in this chapter all relate to the demand side of the market. It is also useful to know how responsive quantity supplied is to a change in price. Suppose the demand for apartments rises. There will be a shortage of apartments at the old level of apartment rents and pressure on rents to rise. All other things unchanged, the more responsive the quantity of apartments supplied is to changes in monthly rents, the lower the increase in rent required to eliminate the shortage and to bring the market back to equilibrium. Conversely, if quantity supplied is less responsive to price changes, price will have to rise more to eliminate a shortage caused by an increase in demand. This is illustrated in Figure 5.10 "Increase in Apartment Rents Depends on How Responsive Supply Is". Suppose the rent for a typical apartment had been R0 and the quantity Q0 when the demand curve was D1 and the supply curve was either S1 (a supply curve in which quantity supplied is less responsive to price changes) or S2 (a supply curve in which quantity supplied is more responsive to price changes). Note that with either supply curve, equilibrium price and quantity are initially the same. Now suppose that demand increases to D2, perhaps due to population growth. With supply curve S1, the price (rent in this case) will rise to R1 and the quantity of apartments will rise to Q1. If, however, the supply curve had been S2, the rent would only have to rise to R2 to bring the market back to equilibrium. In addition, the new equilibrium number of apartments would be higher at Q2. Supply curve S2 shows greater responsiveness of quantity supplied to price change than does supply curve S1. Figure 5.10 Increase in Apartment Rents Depends on How Responsive Supply Is The more responsive the supply of apartments is to changes in price (rent in this case), the less rents rise when the demand for apartments increases. We measure the price elasticity of supplyThe ratio of the percentage change in quantity supplied of a good or service to the percentage change in its price, all other things unchanged. (eS) as the ratio of the percentage change in quantity supplied of a good or service to the percentage change in its price, all other things unchanged: Equation 5.6 Because price and quantity supplied usually move in the same direction, the price elasticity of supply is usually positive. The larger the price elasticity of supply, the more responsive the firms that supply the good or service are to a price change. Supply is price elastic if the price elasticity of supply is greater than 1, unit price elastic if it is equal to 1, and price inelastic if it is less than 1. A vertical supply curve, as shown in Panel (a) of Figure 5.11 "Supply Curves and Their Price Elasticities", is perfectly inelastic; its price elasticity of supply is zero. The supply of Beatles’ songs is perfectly inelastic because the band no longer exists. A horizontal supply curve, as shown in Panel (b) of Figure 5.11 "Supply Curves and Their Price Elasticities", is perfectly elastic; its price elasticity of supply is infinite. It means that suppliers are willing to supply any amount at a certain price. Figure 5.11 Supply Curves and Their Price Elasticities The supply curve in Panel (a) is perfectly inelastic. In Panel (b), the supply curve is perfectly elastic. ## Time: An Important Determinant of the Elasticity of Supply Time plays a very important role in the determination of the price elasticity of supply. Look again at the effect of rent increases on the supply of apartments. Suppose apartment rents in a city rise. If we are looking at a supply curve of apartments over a period of a few months, the rent increase is likely to induce apartment owners to rent out a relatively small number of additional apartments. With the higher rents, apartment owners may be more vigorous in reducing their vacancy rates, and, indeed, with more people looking for apartments to rent, this should be fairly easy to accomplish. Attics and basements are easy to renovate and rent out as additional units. In a short period of time, however, the supply response is likely to be fairly modest, implying that the price elasticity of supply is fairly low. A supply curve corresponding to a short period of time would look like S1 in Figure 5.10 "Increase in Apartment Rents Depends on How Responsive Supply Is". It is during such periods that there may be calls for rent controls. If the period of time under consideration is a few years rather than a few months, the supply curve is likely to be much more price elastic. Over time, buildings can be converted from other uses and new apartment complexes can be built. A supply curve corresponding to a longer period of time would look like S2 in Figure 5.10 "Increase in Apartment Rents Depends on How Responsive Supply Is". ## Elasticity of Labor Supply: A Special Application The concept of price elasticity of supply can be applied to labor to show how the quantity of labor supplied responds to changes in wages or salaries. What makes this case interesting is that it has sometimes been found that the measured elasticity is negative, that is, that an increase in the wage rate is associated with a reduction in the quantity of labor supplied. In most cases, labor supply curves have their normal upward slope: higher wages induce people to work more. For them, having the additional income from working more is preferable to having more leisure time. However, wage increases may lead some people in very highly paid jobs to cut back on the number of hours they work because their incomes are already high and they would rather have more time for leisure activities. In this case, the labor supply curve would have a negative slope. The reasons for this phenomenon are explained more fully in a later chapter. This chapter has covered a variety of elasticity measures. All report the degree to which a dependent variable responds to a change in an independent variable. As we have seen, the degree of this response can play a critically important role in determining the outcomes of a wide range of economic events. Table 5.2 "Selected Elasticity Estimates"Although close to zero in all cases, the significant and positive signs of income elasticity for marijuana, alcohol, and cocaine suggest that they are normal goods, but significant and negative signs, in the case of heroin, suggest that heroin is an inferior good; Saffer and Chaloupka (cited below) suggest the effects of income for all four substances might be affected by education.Sources: John A. Tauras. “Public Policy and Smoking Cessation among Young Adults in the United States,” Health Policy, 68:3 (June 2004): 321–332. 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(Englewood Cliffs: Prentice Hall, , 1995), pp. 1–33; Kenneth G. Elzinga, “Beer,” in Walter Adams and James Brock, eds., The Structure of American Industry, 9th ed. (Englewood Cliffs: Prentice Hall, 1995), pp. 119–151; John A. Rizzo and David Blumenthal, “Physician Labor Supply: Do Income Effects Matter?” Journal of Health Economics 13(4) (December 1994):433–453; Douglas M. Brown, “The Rising Price of Physicians’ Services: A Correction and Extension on Supply,” Review of Economics and Statistics 76(2) (May 1994):389–393; George C. Davis and Michael K. Wohlgenant, “Demand Elasticities from a Discrete Choice Model: The Natural Christmas Tree Market,” Journal of Agricultural Economics 75(3) (August 1993):730–738; David M. Blau, “The Supply of Child Care Labor,” Journal of Labor Economics 2(11) (April 1993):324–347; Richard Blundell et al., “What Do We Learn About Consumer Demand Patterns from Micro Data?”, American Economic Review 83(3) (June 1993):570–597; F. Gasmi, et al., “Econometric Analysis of Collusive Behavior in a Soft-Drink Market,” Journal of Economics and Management Strategy (Summer 1992), pp. 277–311; M.R. Baye, D.W. Jansen, and J.W. Lee, “Advertising Effects in Complete Demand Systems,” Applied Economics 24 (1992):1087–1096; Gary W. Brester and Michael K. Wohlgenant, “Estimating Interrelated Demands for Meats Using New Measures for Ground and Table Cut Beef,” American Journal of Agricultural Economics 73 (November 1991):1182–1194; Adesoji, O. Adelaja, “Price Changes, Supply Elasticities, Industry Organization, and Dairy Output Distribution,” American Journal of Agricultural Economics 73:1 (February 1991):89–102; Mark A. R. Kleinman, Marijuana: Costs of Abuse, Costs of Control (NY:Greenwood Press, 1989); Jules M. Levine, et al., “The Demand for Higher Education in Three Mid-Atlantic States,” New York Economic Review 18 (Fall 1988):3–20; Dale Heien and Cathy Roheim Wessells, “The Demand for Dairy Products: Structure, Prediction, and Decomposition,” American Journal of Agriculture Economics (May 1988):219–228; Michael Grossman and Henry Saffer, “Beer Taxes, the Legal Drinking Age, and Youth Motor Vehicle Fatalities,” Journal of Legal Studies 16(2) (June 1987):351–374; James M. Griffin and Henry B. Steele, Energy Economics and Policy (New York: Academic Press, 1980), p. 232. provides examples of some estimates of elasticities. Table 5.2 Selected Elasticity Estimates Product Elasticity Product Elasticity Product Elasticity Price Elasticity of Demand Cross Price Elasticity of Demand Income Elasticity of Demand Crude oil (U.S.)* −0.06 Alcohol with respect to price of heroin −0.05 Speeding citations −0.26 to −0.33 Gasoline −0.1 Fuel with respect to price of transport −0.48 Urban Public Trust in France and Madrid (respectively) −0.23; −0.26 Speeding citations −0.21 Alcohol with respect to price of food −0.16 Ground beef −0.197 Cabbage −0.25 Marijuana with respect to price of heroin (similar for cocaine) −0.01 Lottery instant game sales in Colorado −0.06 Cocaine (two estimates) −0.28; −1.0 Beer with respect to price of wine distilled liquor (young drinkers) 0.0 Heroin −0.00 Alcohol −0.30 Beer with respect to price of distilled liquor (young drinkers) 0.0 Marijuana, alcohol, cocaine +0.00 Peaches −0.38 Pork with respect to price of poultry 0.06 Potatoes 0.15 Marijuana −0.4 Pork with respect to price of ground beef 0.23 Food** 0.2 Cigarettes (all smokers; two estimates) −0.4; −0.32 Ground beef with respect to price of poultry 0.24 Clothing*** 0.3 Crude oil (U.S.)** −0.45 Ground beef with respect to price of pork 0.35 Beer 0.4 Milk (two estimates) −0.49; −0.63 Coke with respect to price of Pepsi 0.61 Eggs 0.57 Gasoline (intermediate term) −0.5 Pepsi with respect to price of Coke 0.80 Coke 0.60 Soft drinks −0.55 Local television advertising with respect to price of radio advertising 1.0 Shelter** 0.7 Transportation* −0.6 Smokeless tobacco with respect to price of cigarettes (young males) 1.2 Beef (table cuts—not ground) 0.81 Food −0.7 Price Elasticity of Supply Oranges 0.83 Beer −0.7 to −0.9 Physicians (Specialist) −0.3 Apples 1.32 Cigarettes (teenagers; two estimates) −0.9 to −1.5 Physicians (Primary Care) 0.0 Leisure** 1.4 Heroin −0.94 Physicians (Young male) 0.2 Peaches 1.43 Ground beef −1.0 Physicians (Young female) 0.5 Health care** 1.6 Cottage cheese −1.1 Milk* 0.36 Higher education 1.67 Gasoline** −1.5 Milk** 0.5 Coke −1.71 Child care labor 2 Transportation −1.9 Pepsi −2.08 Fresh tomatoes −2.22 Food** −2.3 Lettuce −2.58 Note: *=short-run; **=long-run ### Key Takeaways • The price elasticity of supply measures the responsiveness of quantity supplied to changes in price. It is the percentage change in quantity supplied divided by the percentage change in price. It is usually positive. • Supply is price inelastic if the price elasticity of supply is less than 1; it is unit price elastic if the price elasticity of supply is equal to 1; and it is price elastic if the price elasticity of supply is greater than 1. A vertical supply curve is said to be perfectly inelastic. A horizontal supply curve is said to be perfectly elastic. • The price elasticity of supply is greater when the length of time under consideration is longer because over time producers have more options for adjusting to the change in price. • When applied to labor supply, the price elasticity of supply is usually positive but can be negative. If higher wages induce people to work more, the labor supply curve is upward sloping and the price elasticity of supply is positive. In some very high-paying professions, the labor supply curve may have a negative slope, which leads to a negative price elasticity of supply. ### Try It! In the late 1990s, it was reported on the news that the high-tech industry was worried about being able to find enough workers with computer-related expertise. Job offers for recent college graduates with degrees in computer science went with high salaries. It was also reported that more undergraduates than ever were majoring in computer science. Compare the price elasticity of supply of computer scientists at that point in time to the price elasticity of supply of computer scientists over a longer period of, say, 1999 to 2009. ### Case in Point: A Variety of Labor Supply Elasticities Figure 5.12 Studies support the idea that labor supply is less elastic in high-paying jobs than in lower-paying ones. For example, David M. Blau estimated the labor supply of child-care workers to be very price elastic, with estimated price elasticity of labor supply of about 2.0. This means that a 10% increase in wages leads to a 20% increase in the quantity of labor supplied. John Burkett estimated the labor supply of both nursing assistants and nurses to be price elastic, with that of nursing assistants to be 1.9 (very close to that of child-care workers) and of nurses to be 1.1. Note that the price elasticity of labor supply of the higher-paid nurses is a bit lower than that of lower-paid nursing assistants. In contrast, John Rizzo and David Blumenthal estimated the price elasticity of labor supply for young physicians (under the age of 40) to be about 0.3. This means that a 10% increase in wages leads to an increase in the quantity of labor supplied of only about 3%. In addition, when Rizzo and Blumenthal looked at labor supply elasticities by gender, they found the female physicians’ labor supply price elasticity to be a bit higher (at about 0.5) than that of the males (at about 0.2) in the sample. Because earnings of female physicians in the sample were lower than earnings of the male physicians in the sample, this difference in labor supply elasticities was expected. Moreover, since the sample consisted of physicians in the early phases of their careers, the positive, though small, price elasticities were also expected. Many of the individuals in the sample also had high debt levels, often from educational loans. Thus, the chance to earn more by working more is an opportunity to repay educational and other loans. In another study of physicians’ labor supply that was not restricted to young physicians, Douglas M. Brown found the labor supply price elasticity for primary care physicians to be close to zero and that of specialists to be negative, at about −0.3. Thus, for this sample of physicians, increases in wages have little or no effect on the amount the primary care doctors work, while a 10% increase in wages for specialists reduces their quantity of labor supplied by about 3%. Because the earnings of specialists exceed those of primary care doctors, this elasticity differential also makes sense. ### Answer to Try It! Problem While at a point in time the supply of people with degrees in computer science is very price inelastic, over time the elasticity should rise. That more students were majoring in computer science lends credence to this prediction. As supply becomes more price elastic, salaries in this field should rise more slowly. ## 5.4 Review and Practice ### Summary This chapter introduced a new tool: the concept of elasticity. Elasticity is a measure of the degree to which a dependent variable responds to a change in an independent variable. It is the percentage change in the dependent variable divided by the percentage change in the independent variable, all other things unchanged. The most widely used elasticity measure is the price elasticity of demand, which reflects the responsiveness of quantity demanded to changes in price. Demand is said to be price elastic if the absolute value of the price elasticity of demand is greater than 1, unit price elastic if it is equal to 1, and price inelastic if it is less than 1. The price elasticity of demand is useful in forecasting the response of quantity demanded to price changes; it is also useful for predicting the impact a price change will have on total revenue. Total revenue moves in the direction of the quantity change if demand is price elastic, it moves in the direction of the price change if demand is price inelastic, and it does not change if demand is unit price elastic. The most important determinants of the price elasticity of demand are the availability of substitutes, the importance of the item in household budgets, and time. Two other elasticity measures commonly used in conjunction with demand are income elasticity and cross price elasticity. The signs of these elasticity measures play important roles. A positive income elasticity tells us that a good is normal; a negative income elasticity tells us the good is inferior. A positive cross price elasticity tells us that two goods are substitutes; a negative cross price elasticity tells us they are complements. Elasticity of supply measures the responsiveness of quantity supplied to changes in price. The value of price elasticity of supply is generally positive. Supply is classified as being price elastic, unit price elastic, or price inelastic if price elasticity is greater than 1, equal to 1, or less than 1, respectively. The length of time over which supply is being considered is an important determinant of the price elasticity of supply. ### Concept Problems 1. Explain why the price elasticity of demand is generally a negative number, except in the cases where the demand curve is perfectly elastic or perfectly inelastic. What would be implied by a positive price elasticity of demand? 2. Explain why the sign (positive or negative) of the cross price elasticity of demand is important. 3. Explain why the sign (positive or negative) of the income elasticity of demand is important. 4. Economists Dale Heien and Cathy Roheim Wessells found that the price elasticity of demand for fresh milk is −0.63 and the price elasticity of demand for cottage cheese is −1.1.Dale M. Heien and Cathy Roheim Wessels, “The Demand for Dairy Products: Structure, Prediction, and Decomposition,” American Journal of Agricultural Economics 70:2 (May 1988): 219–228. Why do you think the elasticity estimates differ? 5. The price elasticity of demand for health care has been estimated to be −0.2. Characterize this demand as price elastic, unit price elastic, or price inelastic. The text argues that the greater the importance of an item in consumer budgets, the greater its elasticity. Health-care costs account for a relatively large share of household budgets. How could the price elasticity of demand for health care be such a small number? 6. Suppose you are able to organize an alliance that includes all farmers. They agree to follow the group’s instructions with respect to the quantity of agricultural products they produce. What might the group seek to do? Why? 7. Suppose you are the chief executive officer of a firm, and you have been planning to reduce your prices. Your marketing manager reports that the price elasticity of demand for your product is −0.65. How will this news affect your plans? 8. Suppose the income elasticity of the demand for beans is −0.8. Interpret this number. 9. Transportation economists generally agree that the cross price elasticity of demand for automobile use with respect to the price of bus fares is about 0. Explain what this number means. 10. Suppose the price elasticity of supply of tomatoes as measured on a given day in July is 0. Interpret this number. 11. The price elasticity of supply for child-care workers was reported to be quite high, about 2. What will happen to the wages of child-care workers as demand for them increases, compared to what would happen if the measured price elasticity of supply were lower? 12. The Case in Point on cigarette taxes and teen smoking suggests that a higher tax on cigarettes would reduce teen smoking and premature deaths. Should cigarette taxes therefore be raised? ### Numerical Problems 1. Economist David Romer found that in introductory economics classes a 10% increase in class attendance is associated with a 4% increase in course grade.David Romer, “Do Students Go to Class? Should They?” Journal of Economic Perspectives 7:3 (Summer 1993): 167–174. What is the elasticity of course grade with respect to class attendance? 1. Using the arc elasticity of demand formula, compute the price elasticity of demand between points B and C. 2. Using the arc elasticity of demand formula, compute the price elasticity of demand between points D and E. 3. How do the values of price elasticity of demand compare? Why are they the same or different? 4. Compute the slope of the demand curve between points B and C. 5. Computer the slope of the demand curve between points D and E. 6. How do the slopes compare? Why are they the same or different? 2. Consider the following quote from The Wall Street Journal: “A bumper crop of oranges in Florida last year drove down orange prices. As juice marketers’ costs fell, they cut prices by as much as 15%. That was enough to tempt some value-oriented customers: unit volume of frozen juices actually rose about 6% during the quarter.” 1. Given these numbers, and assuming there were no changes in demand shifters for frozen orange juice, what was the price elasticity of demand for frozen orange juice? 2. What do you think happened to total spending on frozen orange juice? Why? 3. Suppose you are the manager of a restaurant that serves an average of 400 meals per day at an average price per meal of$20. On the basis of a survey, you have determined that reducing the price of an average meal to $18 would increase the quantity demanded to 450 per day. 1. Compute the price elasticity of demand between these two points. 2. Would you expect total revenues to rise or fall? Explain. 3. Suppose you have reduced the average price of a meal to$18 and are considering a further reduction to $16. Another survey shows that the quantity demanded of meals will increase from 450 to 500 per day. Compute the price elasticity of demand between these two points. 4. Would you expect total revenue to rise or fall as a result of this second price reduction? Explain. 5. Compute total revenue at the three meal prices. Do these totals confirm your answers in (b) and (d) above? 4. The text notes that, for any linear demand curve, demand is price elastic in the upper half and price inelastic in the lower half. Consider the following demand curves: Figure 5.13 The table gives the prices and quantities corresponding to each of the points shown on the two demand curves. Demand curve D1 [Panel (a)] Demand curve D2 [Panel (b)] Price Quantity Price Quantity A 80 2 E 8 20 B 70 3 F 7 30 C 30 7 G 3 70 D 20 8 H 2 80 1. Compute the price elasticity of demand between points A and B and between points C and D on demand curve D1 in Panel (a). Are your results consistent with the notion that a linear demand curve is price elastic in its upper half and price inelastic in its lower half? 2. Compute the price elasticity of demand between points E and F and between points G and H on demand curve D2 in Panel (b). Are your results consistent with the notion that a linear demand curve is price elastic in its upper half and price inelastic in its lower half? 3. Compare total spending at points A and B on D1 in Panel (a). Is your result consistent with your finding about the price elasticity of demand between those two points? 4. Compare total spending at points C and D on D1 in Panel (a). Is your result consistent with your finding about the price elasticity of demand between those two points? 5. Compare total spending at points E and F on D2 in Panel (b). Is your result consistent with your finding about the price elasticity of demand between those two points? 6. Compare total spending at points G and H on D2 in Panel (b). Is your result consistent with your finding about the price elasticity of demand between those two points? 5. Suppose Janice buys the following amounts of various food items depending on her weekly income: Weekly Income Hamburgers Pizza Ice Cream Sundaes$500 3 3 2
$750 4 2 2 1. Compute Janice’s income elasticity of demand for hamburgers. 2. Compute Janice’s income elasticity of demand for pizza. 3. Compute Janice’s income elasticity of demand for ice cream sundaes. 4. Classify each good as normal or inferior. 6. Suppose the following table describes Jocelyn’s weekly snack purchases, which vary depending on the price of a bag of chips: Price of bag of chips Bags of chips Containers of salsa Bags of pretzels Cans of soda$1.00 2 3 1 4
$1.50 1 2 2 4 1. Compute the cross price elasticity of salsa with respect to the price of a bag of chips. 2. Compute the cross price elasticity of pretzels with respect to the price of a bag of chips. 3. Compute the cross price elasticity of soda with respect to the price of a bag of chips. 4. Are chips and salsa substitutes or complements? How do you know? 5. Are chips and pretzels substitutes or complements? How do you know? 6. Are chips and soda substitutes or complements? How do you know? 7. The table below describes the supply curve for light bulbs: Price per light bulb Quantity supplied per day$1.00 500
1.50 3,000
2.00 4,000
2.50 4,500
3.00 4,500

Compute the price elasticity of supply and determine whether supply is price elastic, price inelastic, perfectly elastic, perfectly inelastic, or unit elastic:

1. when the price of a light bulb increases from $1.00 to$1.50.
2. when the price of a light bulb increases from $1.50 to$2.00.
3. when the price of a light bulb increases from $2.00 to$2.50.
4. when the price of a light bulb increases from $2.50 to$3.00.