The Organization of Oil Exporting Countries (OPEC) is a big enoughplayer in the global oil market to influence the price of oil. To raise theprice, OPEC must cut production. If it does so, by how much will theprice rise? Will non-OPEC producers also cut production? Or will theyproduce more to take advantage of the higher price achieved by OPECsactions? To answer questions like these, we need to know the quantita-tive relationship between price and the quantities demanded and sup-plied. All firms are interested in the factors that influence prices andin predicting prices. A pizza producer wants to know if the arrival of anew competitor will lower the price of pizza, whether as peoplesincomes rise they will spend more or less on pizza. A labor union wantsto know whether, if it goes for a large wage rise the number of peopleemployed will fall by a lot or a little.

In this chapter, you will learn about a tool that helps us to answerquestions like the ones weve just considered. You will learn about theelasticity of demand and supply. At the end of the chapter, well returnto the questions the OPEC needs to answer and see how the concept ofelasticity helps us to understand the effects of OPECs actions on theprice of crude oil, a price that has a big impact on the price that you end

up paying for gasoline.

After studying this chapter,you will be able to Define, calculate, and explain the

factors that influence the priceelasticity of demand

Define, calculate, and explain thefactors that influence the cross elasticity of demand and the incomeelasticity of demand

Define, calculate, and explain thefactors that influence the elasticityof supply

Predicting Prices

81

4ELASTICITY C H A P T E R

Price Elasticity of Demand

Y , equilibrium price falls and the equilibrium quantityincreases. But does the price fall by a large amount andthe quantity increase by a little? Or does the pricebarely fall and the quantity increase by a large amount?

The answer depends on the responsiveness of thequantity demanded to a change in price. You can seewhy by studying Fig. 4.1, which shows two possiblescenarios in a local pizza market. Figure 4.1(a) showsone 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 curveDA. In part (b), the demand for pizza is shown by thedemand curve DB. Initially, in both cases, the price is$20 a pizza and the quantity of pizza produced andconsumed is 10 pizzas an hour.

Now a large pizza franchise opens up, and thesupply of pizza increases. The supply curve shiftsrightward to S1. In case (a), the price falls by an enor-mous $15 to $5 a pizza, and the quantity increases byonly 3 to 13 pizzas an hour. In contrast, in case (b),the price falls by only $5 to $15 a pizza and thequantity increases by 7 to 17 pizzas an hour.

The different outcomes arise from differing degreesof responsiveness of the quantity demanded to a changein price. But what do we mean by responsiveness? Onepossible answer is slope. The slope of demand curve DAis steeper than the slope of demand curve DB.

In this example, we can compare the slopes ofthe two demand curves. But we cant always do so.The reason is that the slope of a demand curvedepends on the units in which we measure the priceand quantity. And we often must compare thedemand curves for different goods and services thatare measured in unrelated units. For example, a pizzaproducer might want to compare the demand forpizza with the demand for soft drinks. Which quan-tity demanded is more responsive to a price change?This question cant be answered by comparing theslopes of two demand curves. The units of measure-ment of pizza and soft drinks are unrelated. Thequestion can be answered with a measure of respon-siveness that is independent of units of measurement.Elasticity is such a measure.

The price elasticity of demand is a units-free meas-ure of the responsiveness of the quantity demanded ofa good to a change in its price when all other influ-ences on buyers plans remain the same.

82 CHAPTER 4 E L A S T I C I T Y

FIGURE 4.1 How a Change in SupplyChanges Price and Quantity

An increasein supplybrings ...

... a largefall in price ...

13 2520151050

10.00

20.00

30.00

5.00

40.00

S0 S1

DA

(a) Large price change and small quantity changePr

ice

(dol

lars

per

piz

za)

Quantity (pizzas per hour)

(b) Small price change and large quantity change

... and a smallincrease in quantity

An increasein supplybrings ...

... a smallfall inprice ...

17 2520151050

10.00

20.00

30.00

15.00

40.00

S0 S1

DB

Pric

e (d

olla

rs p

er p

izza

)

Quantity (pizzas per hour)

... and a large increase in quantity

Initially the price is $20 a pizza and the quantity sold is 10pizzas an hour. Then supply increases from S0 to S1. In part(a), the price falls by $15 to $5 a pizza, and the quantityincreases by only 3 to 13 pizzas an hour. In part (b), theprice falls by only $5 to $15 a pizza, and the quantityincreases by 7 to 17 pizzas an hour. This price change issmaller and the quantity change is larger than in case (a).The quantity demanded is more responsive to price in case(b) than in case (a).

Calculating Elasticity

We calculate the price elasticity of demand by usingthe formula:

To use this formula, we need to know the quantitiesdemanded at different prices when all other influ-ences on buyers plans remain the same. Suppose wehave the data on prices and quantities demanded ofpizza and we calculate the price elasticity of demandfor pizza.

Figure 4.2 zooms in on the demand curve forpizza and shows how the quantity demandedresponds to a small change in price. Initially, theprice is $20.50 a pizza and 9 pizzas an hour are sold the original point in the figure. The price thenfalls to $19.50 a pizza, and the quantity demandedincreases to 11 pizzas an hour the new point inthe figure. When the price falls by $1 a pizza, thequantity demanded increases by 2 pizzas an hour.

To calculate the price elasticity of demand, weexpress the changes in price and quantity demanded aspercentages of the average price and the average quan-tity. By using the average price and average quantity,we calculate the elasticity at a point on the demandcurve midway between the original point and the newpoint. The original price is $20.50 and the new price is$19.50, so the average price is $20. The $1 pricedecrease is 5 percent of the average price. That is,

The original quantity demanded is 9 pizzas andthe new quantity demanded is 11 pizzas, so the aver-age quantity demanded is 10 pizzas. The 2 pizzaincrease in the quantity demanded is 20 percent ofthe average quantity. That is,

So the price elasticity of demand, which is thepercentage change in the quantity demanded (20 per-cent) divided by the percentage change in price (5percent) is 4. That is,

20%

5% 4.

Price elasticity of demand %Q%P

Q>Qave 12>102 100 20%.

P>Pave 1$1>$202 100 5%.

Price elasticity ofdemand

Percentage changein quantity demanded

Percentage change in price.

Average Price and Quantity Notice that we usethe average price and average quantity. We do thisbecause it gives the most precise measurement of elas-ticity at the midpoint between the original priceand the new price. If the price falls from $20.50 to$19.50, the $1 price change is 4.8 percent of $20.50.The 2 pizza change in quantity is 22.2 percent of 9,the original quantity. So if we use these numbers, theelasticity of demand is 22.2 divided by 4.8, whichequals 4.5. If the price rises from $19.50 to $20.50,

P R I C E E L A S T I C I T Y O F D E M A N D 83

FIGURE 4.2 Calculating the Elasticityof Demand

10Pr

ice

(dol

lars

per

piz

za)

Quantity (pizzas per hour)

20.50

0 119

19.50

20.00Elasticity = 4

Qave

Pave

P = $1

Originalpoint

Newpoint

D

Q = 2

= $20

= 10

The elasticity of demand is calculated by using theformula:*

4.

2>10

1>20

Q>QaveP>Pave

%Q%P

Price elasticity of demand

Percentage changein quantity demanded

Percentage change in price

This calculation measures the elasticity at an average priceof $20 a pizza and an average quantity of 10 pizzas an hour.

* In the formula, the Greek letter delta () stands for change in and %stands for percentage change in.

the $1 price change is 5.1 percent of $19.50. The 2pizza change in quantity is 18.2 percent of 11, theoriginal quantity. So if we use these numbers, theelasticity of demand is 18.2 divided by 5.1, whichequals 3.6.

By using percentages of the average price andaverage quantity, we get the same value for the elastic-ity regardless of whether the price falls from $20.50to $19.50 or rises from $19.50 to $20.50.

Percentages and Proportions Elasticity is the ratioof two percentage changes. So when we divide onepercentage change by another, the 100s cancel. A per-centage change is a proportionate change multipliedby 100. The proportionate change in price is P/Pave,and the proportionate change in quantity demandedis Q/Qave. So if we divide Q/Qave by P/Pave weget the same answer as we get by using percentagechanges.

A Units-Free Measure Now that youve calculateda price elasticity of demand, you can see why it is aunits-free measure. Elasticity is a units-free measurebecause the percentage change in each variable isindependent of the units in which the variable ismeasured. And the ratio of the two percentages is anumber without units.

Minus Sign and Elasticity When the price of agood rises, the quantity demanded decreases along the

demand curve. Because a positive change in pricebrings a negative change in the quantity demanded,the price elasticity of demand is a negative number.But it is the magnitude, or absolute value, of the priceelasticity of demand that tells us how responsive how elastic demand is. To compare elasticities, weuse the magnitude of the price elasticity of demandand ignore the minus sign.

Inelastic and Elastic Demand

Figure 4.3 shows three demand curves that coverthe entire range of possible elasticities of demand.In Fig. 4.3(a), the quantity demanded is constantregardless of the price. If the quantity demandedremains constant when the price changes, then theprice elasticity of demand is zero and the good is saidto have perfectly inelastic demand. One good that hasa very low price elasticity of demand (perhaps zeroover some price range) is insulin. Insulin is of suchimportance to some diabetics that if the price rises orfalls, they do not change the quantity they buy.

If the percentage change in the quantity demandedequals the percentage change in price, then the priceelasticity equals 1 and the good is said to have unitelastic demand. The demand in Fig. 4.3(b) is anexample of unit elastic demand.

Between the cases shown in Fig. 4.3(a) and Fig.4.3(b) is the general case in which the percentagechange in the quantity demanded is less than the

84 CHAPTER 4 E L A S T I C I T Y

FIGURE 4.3 Inelastic and Elastic Demand

Pric

e

D 2

0 Quantity

(b) Unit elastic demand

Pric

e D1

0 Quantity

(a) Perfectly inelastic demand

Pric

e

D3

0 Quantity

(c) Perfectly elastic demand

12

1 2 3

6

12

6

12

6

Elasticity = 0 Elasticity = 1 Elasticity =

Each demand illustrated here has a constant elasticity. Thedemand curve in part (a) illustrates the demand for a goodthat has a zero elasticity of demand. The demand curve in

part (b) illustrates the demand for a good with a unit elastic-ity of demand. And the demand curve in part (c) illustratesthe demand for a good with an infinite elasticity of demand.

percentage change in price. In this case, the priceelasticity of demand is between zero and 1 and thegood is said to have inelastic demand. Food andhousing are examples of goods with inelastic demand.

If the quantity demanded changes by an infi-nitely large percentage in response to a tiny pricechange, then the price elasticity of demand is infin-ity and the good is said to have perfectly elasticdemand. Figure 4.3(c) shows perfectly elasticdemand. An example of a good that has a veryhigh elasticity of demand (almost infinite) is a softdrink from two campus machines located side byside. If the two machines offer the same soft drinksfor the same price, some people buy from onemachine and some from the other. But if onemachines price is higher than the others, by evena small amount, no one will buy from the machinewith the higher price. Soft drinks from the twomachines are perfect substitutes.

Between the cases in Fig. 4.3(b) and Fig. 4.3(c)is the general case in which the percentage change inthe quantity demanded exceeds the percentage changein price. In this case, the price elasticity is greaterthan 1 and the good is said to have elastic demand.Automobiles and furniture are examples of goods thathave elastic demand.

Elasticity Along a Straight-Line Demand Curve

Along a straight-line demand curve, like the oneshown in Fig. 4.4, the elasticity varies. At high pricesand small quantities, the elasticity is large; and at lowprices and large quantities, the elasticity is small. Toconvince yourself of this fact, calculate the elasticityat three different average prices.

First, suppose the price falls from $25 to $15 apizza. The quantity demanded increases from zero to20 pizzas an hour. The average price is $20, so thepercentage change in price is $10 divided by $20multiplied by 100, which equals 50. The averagequantity is 10 pizzas, so the percentage change inquantity is 20 pizzas divided by 10 pizzas, multipliedby 100, which equals 200. So dividing the percent-age change in the quantity demanded (200) by thepercentage change in price (50), you see that theelasticity of demand at an average price of $20 is 4.

Next, suppose that the price falls from $15 to$10 a pizza. The quantity demanded increases from20 to 30 pizzas an hour. The average price is now$12.50, so the percentage change in price is $5

divided by $12.50 multiplied by 100, which equals40 percent. The average quantity is 25 pizzas an hour,so the percentage change in the quantity demanded is10 pizzas divided by 25 pizzas multiplied by 100,which also equals 40 percent. So dividing the per-centage change in the quantity demanded (40) by thepercentage change in price (40), you see that the elas-ticity of demand at an average price of $12.50 is 1.The elasticity of demand is always equal to 1 at themidpoint of a straight-line demand curve.

Finally, suppose that the price falls from $10 tozero. The quantity demanded increases from 30 to 50pizzas an hour. The average price is now $5, so thepercentage change in price is $10 divided by $5 mul-tiplied by 100, which equals 200 percent. The aver-age quantity is 40 pizzas an hour, so the percentagechange in the quantity demanded is 20 pizzas dividedby 40 pizzas multiplied by 100, which also equals 50percent. So dividing the percentage change in thequantity demanded (50) by the percentage change inprice (200), you see that the elasticity of demand atan average price of $5 is 14.

P R I C E E L A S T I C I T Y O F D E M A N D 85

FIGURE 4.4 Elasticity Along a Straight-Line Demand Curve

10 25

Pric

e (d

olla

rs p

er p

izza

)

Quantity (pizzas per hour)

10.00

0

5.00

50

Inelastic

Elasticity = 4

Elasticity =

Elastic

15.00

12.50

20.00

25.00

Elasticity = 1

20 30 40

1 4/

On a straight-line demand curve, elasticity decreases as theprice falls and the quantity demanded increases. Demand isunit elastic at the midpoint of the demand curve (elasticityis 1). Above the midpoint, demand is elastic; below the mid-point, demand is inelastic.

Total Revenue and Elasticity

The total revenue from the sale of a good equals theprice of the good multiplied by the quantity sold.When a price changes, total revenue also changes.But a rise in price does not always increase total rev-enue. The change in total revenue depends on theelasticity of demand in the following way:

If demand is elastic, a 1 percent price cut increasesthe quantity sold by more than 1 percent and totalrevenue increases.

If demand is inelastic, a 1 percent price cutincreases the quantity sold by less than 1 percentand total revenue decreases.

If demand is unit elastic, a 1 percent price cutincreases the quantity sold by 1 percent and sototal revenue does not change.

Figure 4.5 shows how we can use this relation-ship between elasticity and total revenue to esti-mate elasticity using the total revenue test. Thetotal revenue test is a method of estimating theprice elasticity of demand by observing the changein total revenue that results from a change in theprice, when all other influences on the quantitysold remain the same.

If a price cut increases total revenue, demand iselastic.

If a price cut decreases total revenue, demand isinelastic.

If a price cut leaves total revenue unchanged,demand is unit elastic.

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 isalso zero. At a price of zero, the quantity demandedis 50 pizzas an hour but total revenue is again zero.A price cut in the elastic range brings an increase intotal revenue the percentage increase in the quan-tity demanded is greater than the percentage decreasein price. A price cut in the inelastic range brings adecrease in total revenue the percentage increasein the quantity demanded is less than the percentagedecrease in price. At unit elasticity, total revenue isat a maximum.

86 CHAPTER 4 E L A S T I C I T Y

FIGURE 4.5 Elasticity and Total Revenue

(b) Total revenue

Elasticdemand

Tota

l rev

enue

(dol

lars

)

Quantity (pizzas per hour)

25 500

5.00

10.00

15.00

20.00

25.00

12.50

Unitelastic

Inelasticdemand

25 50

(a) DemandPr

ice

(dol

lars

per

piz

za)

Quantity (pizzas per hour)

0

50.00

100.00

150.00

250.00

312.50

200.00

350.00 Maximumtotal revenue

When demandis elastic, aprice cutincreasestotal revenue

When demandis inelastic, aprice cutdecreasestotal revenue

When demand is elastic, in the price range from $25 to$12.50, a decrease in price (part a) brings an increase intotal revenue (part b).When demand is inelastic, in theprice range from $12.50 to zero, a decrease in price (parta) brings a decrease in total revenue (part b).Whendemand is unit elastic, at a price of $12.50 (part a), totalrevenue is at a maximum (part b).

Your Expenditure and Your Elasticity

When a price changes, the change in your expenditureon the good depends on your elasticity of demand.

If your demand is elastic, a 1 percent price cutincreases the quantity you buy by more than 1 per-cent and your expenditure on the item increases.

If your demand is inelastic, a 1 percent price cutincreases the quantity you buy by less than 1 per-cent and your expenditure on the item decreases.

If your demand is unit elastic, a 1 percent pricecut increases the quantity you buy by 1 percentand your expenditure on the item does not change.

So if when the price of an item falls, you spendmore on it, your demand for that item is elastic; if youspend the same amount, your demand is unit elastic;and if you spend less, your demand is inelastic.

The Factors That Influence theElasticity of Demand

Table 4.1 lists some estimates of actual elasticities inthe real world. You can see that these real-world elas-ticities of demand range from 1.52 for metals, theitem with the most elastic demand in the table, to0.05 for oil, the item with the most inelastic demandin the table. What makes the demand for some goodselastic and the demand for others inelastic?

Elasticity depends on three main factors:

The closeness of substitutes The proportion of income spent on the good The time elapsed since a price change

Closeness of Substitutes The closer the substitutesfor a good or service, the more elastic is the demand forit. For example, oil from which we make gasoline hassubstitutes but none that are currently very close (imag-ine a steam-driven, coal-fueled car). So the demand foroil is inelastic. Plastics are close substitutes for metals,so the demand for metal is an elastic demand.

The degree of substitutability between two goodsalso depends on how narrowly (or broadly) we definethem. For example, the elasticity of demand for meatis low, but the elasticity of demand for beef or pork ishigh. The elasticity of demand for personal comput-ers is low, but the elasticity of demand for a Compaq,Dell, or IBM is high.

In everyday language we call some goods, suchas food and housing, necessities and other goods, suchas exotic vacations, luxuries. A necessity is a good

that has poor substitutes and that is crucial for ourwell-being. So generally, a necessity has an inelasticdemand. In Table 4.1, food and oil might be classifiedas necessities that have inelastic demand.

A luxury is a good that usually has many substi-tutes, one of which is not buying it. So a luxury gen-erally has an elastic demand. In Table 4.1, furnitureand motor vehicles might be classified as luxuries thathave elastic demand.

P R I C E E L A S T I C I T Y O F D E M A N D 87

TABLE 4.1 Some Real-World PriceElasticities of Demand

Good or Service Elasticity

Elastic Demand

Metals 1.52

Electrical engineering products 1.39

Mechanical engineering products 1.30

Furniture 1.26

Motor vehicles 1.14

Instrument engineering products 1.10

Professional services 1.09

Transportation services 1.03

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: Ahsan Mansur and John Whalley,Numerical Specification of AppliedGeneral Equilibrium Models: Estimation, Calibration, and Data, in AppliedGeneral Equilibrium Analysis, eds. Herbert E. Scarf and John B. Shoven (NewYork: Cambridge University Press, 1984), 109, and Henri Theil, Ching-FanChung, and James L. Seale, Jr., Advances in Econometrics, Supplement I, 1989,International Evidence on Consumption Patterns (Greenwich, Conn.: JAI PressInc., 1989), and Geoffrey Heal, Columbia University,Web site.

Youve now completed your study of the priceelasticity of demand. Two other elasticity concepts tellus about the effects of other influences on demand.Lets look at these other elasticities of demand.

88 CHAPTER 4 E L A S T I C I T Y

Proportion of Income Spent on the Good Otherthings remaining the same, the greater the proportionof income spent on a good, the more elastic is thedemand for it.

Think about your own elasticity of demand forchewing gum and housing. If the price of chewinggum doubles, you consume almost as much gum asbefore. Your demand for gum is inelastic. If apartmentrents double, you shriek and look for more studentsto share accommodation with you. Your demand forhousing is more elastic than your demand for gum.Why the difference? Housing takes a large proportionof your budget, and gum takes only a tiny proportion.You dont like either price increase, but you hardlynotice the higher price of gum, while the higher rentputs your budget under severe strain.

Figure 4.6 shows the proportion of income spenton food and the price elasticity of demand for food in10 countries. This figure confirms the general ten-dency we have just described. The larger the propor-tion of income spent on food, the larger is the priceelasticity of demand for food. For example, in Tanzania,

a nation where average incomes are 3.3 percent ofincomes in the United States and where 62 percentof income is spent on food, the price elasticity ofdemand for food is 0.77. In contrast, in the UnitedStates, where 12 percent of income is spent on food,the price elasticity of demand for food is 0.12.

Time Elapsed Since Price Change The longer thetime that has elapsed since a price change, the moreelastic is demand. When the price of oil increased by400 percent during the 1970s, people barely changedthe quantity of oil and gasoline they consumed. Butgradually, as more efficient auto and airplane engineswere developed, the quantity consumed decreased.The demand for oil has become more elastic as moretime has elapsed since the huge price hike. Similarly,when the price of a PC fell, the quantity of PCsdemanded increased only slightly at first. But as morepeople have become better informed about the vari-ety of ways of using a PC, the quantity of PCsbought has increased sharply. The demand for PCshas become more elastic.

1 Why do we need a units-free measure of theresponsiveness of the quantity demanded of agood or service to a change in its price?

2 Can you define and calculate the price elasticityof demand?

3 Why, when we calculate the price elasticity ofdemand, do we express the change in price as apercentage of the average price and the change inquantity as a percentage of the average quantity?

4 What is the total revenue test and why does itwork?

5 What are the main influences on the elasticityof demand that make the demand for somegoods elastic and the demand for other goodsinelastic?

6 Why is the demand for a luxury generally moreelastic than the demand for a necessity?

FIGURE 4.6 Price Elasticities in10 Countries

0 0.2 0.4 0.6 0.8 1.0

Tanzania

India

Korea

Brazil

Greece

Spain

France

Germany

Canada

United States

Price elasticity

Country

62

56

40

35

31

28

17

15

14

12

Food budget(percentage of income)

As income increases and the proportion of income spent onfood decreases, the demand for food becomes less elastic.

Source: Henri Theil, Ching-Fan Chung, and James L. Seale, Jr., Advances inEconometrics, Supplement 1, 1989, International Evidence on Consumption Pat-terns (Greenwich, Conn.: JAI Press, Inc., 1989).

More Elasticit iesof Demand

B , out how a price cut by the burger shop next door willaffect the demand for your pizza. You know that piz-zas and burgers are substitutes. And you know thatwhen the price of a substitute for pizza falls, thedemand for pizza decreases. But by how much?

You also know that pizza and soft drinks are com-plements. And you know that if the price of a comple-ment of pizza falls, the demand for pizza increases. Soyou wonder whether you might keep your customersby cutting the price you charge for soft drinks. Butagain by how much?

To answer these questions, you need to calculatethe cross elasticity of demand. Lets examine this elas-ticity measure.

Cross Elasticity of Demand

We measure the influence of a change in the price ofa substitute or complement by using the concept ofthe cross elasticity of demand. The cross elasticity ofdemand is a measure of the responsiveness of thedemand for a good to a change in the price of a sub-stitute or complement, other things remaining thesame. We calculate the cross elasticity of demand byusing the formula:

The cross elasticity of demand can be positive ornegative. It is positive for a substitute and negative fora complement.

Substitutes Suppose that the price of pizza is con-stant and 9 pizzas an hour are sold. The price of aburger then rises from $1.50 to $2.50. No otherinfluence on buying plans changes and the quantityof pizzas sold increases to 11 an hour.

The change in the quantity demanded is the newquantity, 11 pizzas, minus the original quantity, 9pizzas, which is +2 pizzas. The average quantity is 10pizzas. So the quantity of pizzas demanded increasesby 20 percent (+20). That is,

Q>Qave 12>102 100 20%.

Cross elasticityof demand

Percentage changein quantity demanded

Percentage change in price ofa substitute or complement

.

The change in the price of a burger, a substitutefor pizza, is the new price, $2.50, minus the originalprice, $1.50, which is +$1. The average price is $2.So the price of a burger rises by 50 percent (+50).That is,

So the cross elasticity of demand for pizza withrespect to the price of a burger is

Figure 4.7 illustrates the cross elasticity ofdemand. Pizza and burgers are substitutes. Becausethey are substitutes, when the price of a burger rises,the demand for pizza increases. The demand curve forpizza shifts rightward from D0 to D1. Because a rise inthe price of a burger brings a increase in the demandfor pizza, the cross elasticity of demand for pizza withrespect to the price of a burger is positive. Both theprice and the quantity change in the same direction.

20%

50% 0.4.

P>Pave 11>22 100 50%.

M O R E E L A S T I C I T I E S O F D E M A N D 89

FIGURE 4.7 Cross Elasticity of Demand

Pric

e of

piz

za

Quantity of pizza0

D0

D1

D2

Price of soft drink, a complement,rises. Negativecross elasticity

Price of a burger,a substitute, rises.Positive cross elasticity

A burger is a substitute for pizza.When the price of aburger rises, the demand for pizza increases and thedemand curve for pizza shifts rightward from D0 to D1. Thecross elasticity of the demand is positive.

Soft drinks are a complement of pizza.When the priceof soft drinks rises, the demand for pizza decreases and thedemand curve for pizza shifts leftward from D0 to D2. Thecross elasticity of the demand is negative.

Complements Now suppose that the price of pizzais constant and 11 pizzas an hour are sold. The priceof a soft drink rises from $1.50 to $2.50. No otherinfluence on buying plans changes and the quantityof pizzas sold falls to 9 an hour.

The change in the quantity demanded is theopposite of what weve just calculated: The quantityof pizzas demanded decreases by 20 percent (20).

The change in the price of a soft drink, acomplement of pizza, is the same as the percentagechange in the price of a burger that weve just calcu-lated: The price rises by 50 percent (+50). So thecross elasticity of demand for pizza with respect tothe price of a soft drink is

Because pizza and soft drinks are complements,when the price of a soft drink rises, the demand forpizza decreases. The demand curve for pizza shiftsleftward from D0 to D2. Because a rise in the price ofsoft drinks brings a decrease in the demand for pizza,the cross elasticity of demand for pizza with respectto the price of soft drinks is negative. The price andquantity change in opposite directions.

The magnitude of the cross elasticity of demanddetermines how far the demand curve shifts. Thelarger the cross elasticity (absolute value), the greateris the change in demand and the larger is the shift inthe demand curve.

If two items are very close substitutes, such astwo brands of spring water, the cross elasticity islarge. If two items are close complements, such asmovies and popcorn, the cross elasticity is large.

If two items are somewhat unrelated to eachother, such as newspapers and orange juice, the crosselasticity is small perhaps even zero.

Income Elasticity of Demand

Suppose the economy is expanding and people areenjoying rising incomes. This prosperity is bringingan increase in the demand for most types of goodsand services. But by how much will the demand forpizza increase? The answer depends on the incomeelasticity of demand, which is a measure of theresponsiveness of the demand for a good or serviceto a change in income, other things remainingthe same.

20%50%

0.4.

The income elasticity of demand is calculated byusing the formula:

Income elasticities of demand can be positive ornegative and 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 ofpizza is constant and 9 pizzas an hour are sold. Thenincomes rise from $975 to $1,025 a week. No otherinfluence on buying plans changes and the quantityof pizzas sold increases to 11 an hour.

The change in the quantity demanded is +2pizzas. The average quantity is 10, so the quantitydemanded increases by 20 percent. The change inincome is +$50 and the average income is $1,000, soincomes increase by 5 percent. The income elasticityof demand for pizza is

As income increases, the quantity of pizzademanded increases faster than income. The demandfor pizza is income-elastic. Other goods in this cate-gory include ocean cruises, international travel, jew-elry, and works of art.

Income Inelastic Demand If the percentageincrease in the quantity demanded is less than thepercentage increase in income, the income elasticityof demand is positive and less than 1. In this case, thequantity demanded increases as income increases, butincome increases faster than the quantity demanded.The demand for the good is income inelastic. Goodsin this category include food, clothing, newspapers,and magazines.

Inferior Goods If when income increases the quan-tity demanded of a good decreases, the income elas-ticity of demand is negative. Goods in this categoryinclude small motorcycles, potatoes, and rice. Low-income consumers buy most of these goods.

20%5%

4.

Income elasticityof demand

Percentage changein quantity demanded

Percentage change in income.

90 CHAPTER 4 E L A S T I C I T Y

Youve now completed your study of the crosselasticity of demand and the income elasticity ofdemand. Lets look at the other side of a marketand examine the elasticity of supply.

M O R E E L A S T I C I T I E S O F D E M A N D 91

Real-World Income Elasticitiesof Demand

Table 4.2 shows estimates of some real-world incomeelasticities of demand. The demand for a necessitysuch as food or gasoline is income inelastic, while thedemand for a luxury such as transportation, whichincludes airline and foreign travel, is income elastic.

But what is a necessity and what is a luxurydepends on the level of income. For people with a lowincome, food and clothing can be luxuries. So the levelof income has a big effect on income elasticities ofdemand. Figure 4.8 shows this effect on the incomeelasticity of demand for food in 10 countries. In coun-tries with low incomes, such as Tanzania and India, theincome elasticity of demand for food is high. In coun-tries with high incomes, such as the United States, theincome elasticity of demand for food is low.

1 What does the cross elasticity of demand measure?2 What does the sign (positive versus negative) of

the cross elasticity of demand tell us about therelationship between two goods?

3 What does the income elasticity of demandmeasure?

4 What does the sign (positive versus negative) ofthe income elasticity of demand tell us about agood?

5 Why does the level of income influence themagnitude of the income elasticity of demand?

FIGURE 4.8 Income Elasticities in10 Countries

0 0.2 0.4 0.6 0.8 1.0

Tanzania

India

Korea

Brazil

Greece

Spain

Japan

France

Canada

United States

Income elasticity

Country

3.3

5.2

20.4

36.8

41.3

55.9

61.6

81.1

99.2

100

Income(percentage of U.S. income)

As income increases, the income elasticity of demand forfood decreases. For low-income consumers, a larger per-centage of any increase in income is spent on food than forhigh-income consumers.

Source: Henri Theil, Ching-Fan Chung, and James L. Seale, Jr., Advances inEconometrics, Supplement 1, 1989, International Evidence on ConsumptionPatterns (Greenwich, Conn.: JAI Press, Inc., 1989).

TABLE 4.2 Some Real-World IncomeElasticities of Demand

Elastic Demand

Airline travel 5.82

Movies 3.41

Foreign travel 3.08

Electricity 1.94

Restaurant meals 1.61

Local buses and trains 1.38

Haircuts 1.36

Automobiles 1.07

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: H.S. Houthakker and Lester D. Taylor, Consumer Demand in theUnited States (Cambridge, Mass.: Harvard University Press, 1970), and HenriTheil, Ching-Fan Chung, and James L. Seale, Jr., Advances in Econometrics,Supplement 1, 1989, International Evidence on Consumption Patterns (Green-wich, Conn.: JAI Press, Inc., 1989).

Elasticity of Supply

Y , price rises and the quantity increases. But does theprice rise by a large amount and the quantity increaseby a little? Or does the price barely rise and the quan-tity increase by a large amount?

The answer depends on the responsiveness of thequantity supplied to a change in price. You can seewhy by studying Fig. 4.9, which shows two possiblescenarios in a local pizza market. Figure 4.9(a) showsone scenario, and Fig. 4.9(b) shows the other.

In both cases, demand is initially D0. In part (a),the supply of pizza is shown by the supply curve SA.In part (b), the supply of pizza is shown by the sup-ply curve SB. Initially, in both cases, the price is $20 apizza and the quantity produced and consumed is 10pizzas an hour.

Now increases in income and population increasethe demand for pizza. The demand curve shifts right-ward to D1. In case (a), the price rises by $10 to $30a pizza, and the quantity increases by only 3 to 13 anhour. In contrast, in case (b), the price rises by only$1 to $21 a pizza, and the quantity increases by 10 to20 pizzas an hour.

The different outcomes arise from differingdegrees of responsiveness of the quantity supplied to achange in price. We measure the degree of responsive-ness by using the concept of the elasticity of supply.

Calculating the Elasticity of Supply

The elasticity of supply measures the responsivenessof the quantity supplied to a change in the price of agood when all other influences on selling plans remainthe same. It is calculated by using the formula:

We use the same method that you learned when youstudied the elasticity of demand. (Refer back to page83 to check this method.) Lets calculate the elasticityof supply for the supply curves in Fig. 4.9.

In Fig. 4.9(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, so the increase

Elasticityof supply

Percentage change inquantity supplied

Percentage change in price.

92 CHAPTER 4 E L A S T I C I T Y

FIGURE 4.9 How a Change in DemandChanges Price and Quantity

252015105

An increase in demand brings ...

... a largeprice rise ...

... and a smallquantity increase

13 2520151050

10.00

20.00

30.00

40.00

D1

SA

D0

(a) Large price change and small quantity changePr

ice

(dol

lars

per

piz

za)

Quantity (pizzas per hour)

An increasein demandbrings ...

... a smallprice rise ...

... and a largequantity increase

0

10.00

20.0021.00

30.00

40.00

D1

SB

D0

(b) Small price change and large quantity change

Pric

e (d

olla

rs p

er p

izza

)

Quantity (pizzas per hour)

Initially, the price is $20 a pizza, and the quantity sold is 10pizzas an hour. Then increases in incomes and populationincrease the demand for pizza. The demand curve shiftsrightward to D1. In part (a) the price rises by $10 to $30 apizza, and the quantity increases by only 3 to 13 pizzas anhour. In part (b), the price rises by only $1 to $21 a pizza,and the quantity increases by 10 to 20 pizzas an hour. Theprice change is smaller and the quantity change is larger incase (b) than in case (a). The quantity supplied is moreresponsive to price in case (b) than in case (a).

is 3, the average quantity is 11.5, and the quantityincreases by 26 percent. The elasticity of supply isequal to 26 percent divided by 40 percent, whichequals 0.65.

In Fig. 4.9(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 4.8 percent of the aver-age price. The quantity increases from 10 to 20, sothe increase is 10, the average quantity is 15, and thequantity increases by 67 percent. The elasticity ofsupply is equal to 67 percent divided by 4.8 percent,which equals 13.67.

Figure 4.10 shows the range of supply elasticities.If the quantity supplied is fixed regardless of theprice, the supply curve is vertical and the elasticity ofsupply is zero. Supply is perfectly inelastic. This caseis shown in Fig. 4.10(a). A special intermediate caseis when the percentage change in price equals thepercentage change in quantity. Supply is then unitelastic. This case is shown in Fig. 4.10(b). No matterhow steep the supply curve is, if it is linear and passesthrough the origin, supply is unit elastic. If there is aprice at which sellers are willing to offer any quantityfor sale, the supply curve is horizontal and the elastic-ity of supply is infinite. Supply is perfectly elastic.This case is shown in Fig. 4.10(c).

The Factors That Influence theElasticity of Supply

The magnitude of the elasticity of supply depends on

Resource substitution possibilities Time frame for the supply decision

Resource Substitution Possibilities Some goodsand services can be produced only by using unique orrare productive resources. These items have a low,even perhaps a zero, elasticity of supply. Other goodsand services can be produced by using commonlyavailable resources that could be allocated to a widevariety of alternative tasks. Such items have a highelasticity of supply.

A Van Gogh painting is an example of a goodwith a vertical supply curve and a zero elasticity ofsupply. At the other extreme, wheat can be grown onland that is almost equally good for growing corn.So it is just as easy to grow wheat as corn, and theopportunity cost of wheat in terms of forgone corn isalmost constant. As a result, the supply curve ofwheat is almost horizontal and its elasticity of supplyis very large. Similarly, when a good is produced inmany different countries (for example, sugar andbeef ), the supply of the good is highly elastic.

E L A S T I C I T Y O F S U P P LY 93

FIGURE 4.10 Inelastic and Elastic Supply

Pric

e

S 2

0 Quantity

(b) Unit elastic supply

Pric

e S1

0 Quantity

(a) Perfectly inelastic supply

Pric

e

S3

0 Quantity

(c) Perfectly elastic supply

Elasticity ofsupply = 0

Elasticity ofsupply = 1

Elasticity ofsupply =

Each supply illustrated here has a constant elasticity. Thesupply curve in part (a) illustrates the supply of a good thathas a zero elasticity of supply. The supply curve in part (b)illustrates the supply for a good with a unit elasticity of

supply. All linear supply curves that pass through the originillustrate supplies that are unit elastic. The supply curve inpart (c) illustrates the supply for a good with an infinite elas-ticity of supply.

The supply of most goods and services liesbetween the two extremes. The quantity producedcan be increased but only by incurring a higher cost.If a higher price is offered, the quantity suppliedincreases. Such goods and services have an elasticityof supply between zero and infinity.

Time Frame for Supply Decisions To study theinfluence of the length of time elapsed since a pricechange, we distinguish three time frames of supply:

1. Momentary supply2. Long-run supply3. Short-run supply

When the price of a good rises or falls, the momen-tary supply curve shows the response of the quantitysupplied immediately following a price change.

Some goods, such as fruits and vegetables, have aperfectly inelastic momentary supply a verticalsupply curve. The quantities supplied depend oncrop-planting decisions made earlier. In the case oforanges, for example, planting decisions have to bemade many years in advance of the crop being avail-able. The momentary supply curve is vertical because,on a given day, no matter what the price of oranges,producers cannot change their output. They havepicked, packed, and shipped their crop to market,and the quantity available for that day is fixed.

In contrast, some goods have a perfectly elasticmomentary supply. Long-distance phone calls are anexample. When many people simultaneously make acall, there is a big surge in the demand for telephonecables, computer switching, and satellite time, andthe quantity bought increases. But the price remainsconstant. Long-distance carriers monitor fluctuationsin demand and reroute calls to ensure that the quan-tity supplied equals the quantity demanded withoutchanging the price.

The long-run supply curve shows the response ofthe quantity supplied to a change in price after all thetechnologically possible ways of adjusting supplyhave been exploited. In the case of oranges, the longrun is the time it takes new plantings to grow to fullmaturity about 15 years. In some cases, the long-run adjustment occurs only after a completely newproduction plant has been built and workers havebeen trained to operate it typically a process thatmight take several years.

The short-run supply curve shows how the quan-tity supplied responds to a price change when only

some of the technologically possible adjustments toproduction have been made. The short-run responseto a price change is a sequence of adjustments. Thefirst adjustment that is usually made is in the amountof labor employed. To increase output in the shortrun, firms work their labor force overtime and per-haps hire additional workers. To decrease their outputin the short run, firms either lay off workers or reducetheir hours of work. With the passage of time, firmscan make additional adjustments, perhaps trainingadditional workers or buying additional tools andother equipment.

The short-run supply curve slopes upwardbecause producers can take actions quite quickly tochange the quantity supplied in response to a pricechange. For example, if the price of oranges falls,growers can stop picking and leave oranges to rot onthe trees. Or if the price rises, they can use more fer-tilizer and improved irrigation to increase the yieldsof their existing trees. In the long run, they can plantmore trees and increase the quantity supplied evenmore in response to a given price rise.

94 CHAPTER 4 E L A S T I C I T Y

You have now studied the theory of demand andsupply, and you have learned how to measure theelasticities of demand and supply. All the elasticitiesthat youve met in this chapter are summarized inTable 4.3. In the next chapter, we are going to studythe efficiency of competitive markets. But beforedoing that, take a look at Reading Between the Lineson pp. 9697 to see elasticity in action.

1 Why do we need to measure the responsivenessof the quantity supplied of a good or service toa change in its price?

2 Can you define and calculate the elasticity ofsupply?

3 What are the main influences on the elasticityof supply that make the supply of some goodselastic and the supply of other goods inelastic?

4 Can you provide examples of goods or serviceswhose elasticity of supply are (a) zero, (b) greaterthan zero but less than infinity, and (c), infinity?

5 How does the time frame over which a supplydecision is made influence the elasticity ofsupply?

E L A S T I C I T Y O F S U P P LY 95

TABLE 4.3 A Compact Glossary of Elasticities

Price Elasticities of Demand

A relationship is described as When its magnitude is Which means that

Perfectly elastic or Infinity The smallest possible increase in price causes an infinitelyinfinitely elastic large decrease in the quantity demanded*Elastic Less than infinity The percentage decrease in the quantity demanded

but greater than 1 exceeds the percentage increase in priceUnit elastic 1 The percentage decrease in the quantity demanded equals

the percentage increase in priceInelastic Greater than zero The percentage decrease in the quantity demanded is less

but less than 1 than the percentage increase in pricePerfectly inelastic Zero The quantity demanded is the same at all pricesor completely inelastic

Cross Elasticities of Demand

A relationship is described as When its value is Which means that

Perfect substitutes Infinity The smallest possible increase in the price of one good causes an infinitely large increase in the quantity demanded of the other good

Substitutes Positive, less If the price of one good increases, the quantity demandedthan infinity of the other good also increases

Independent Zero If the price of one good increases, the quantity demanded of the other good remains the same

Complements Less than zero If the price of one good increases, the quantity demanded of the other good decreases

Income Elasticities of Demand

A relationship is described as When its value is Which means that

Income elastic Greater than 1 The percentage increase in the quantity demanded is (normal good) greater than the percentage increase in incomeIncome inelastic Less than 1 but The percentage increase in the quantity demanded is (normal good) greater than zero less than the percentage increase in incomeNegative income elastic Less than zero When income increases, quantity demanded decreases(inferior good)

Elasticities of Supply

A relationship is described as When its magnitude is Which means that

Perfectly elastic Infinity The smallest possible increase in price causes an infinitely large increase in the quantity supplied

Elastic Less than infinity but The percentage increase in the quantity supplied greater than 1 exceeds the percentage increase in the price

Inelastic Greater than zero but The percentage increase in the quantity supplied is less less than 1 than the percentage increase in the price

Perfectly inelastic Zero The quantity supplied is the same at all prices

*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 thequantity demanded.

Essence of the Story

The Organization ofPetroleum ExportingCountries (OPEC) saidthat it would cut oil pro-duction by 1.5 millionbarrels a day, or 6 per-cent, if non-OPECmembers also made deepcuts to production.

On the same day, theprice of oil fell andOPEC ministers predict-ed a price of $10 a barrelif non-OPEC producersdidnt decrease output.

Analysts did not ex-pect other producers todecrease output.

Elasticities of Demand and Supply in the Global Oil Market

96

Please see page 96 of yourprinted textbook to

read this article.

97

Economic Analysis

OPEC predicted thatdemand would decreasein 2002 to D2002 so withno change in supply, theprice would fall to $10 abarrel and the quantitywould decrease to 71million barrels a day.

If OPEC cuts produc-tion by 1.5 million bar-rels a day, supply in 2002would decrease to S2002.

We can work out theeffect of OPEC's cut inproduction on price andquantity because we haveestimates of the priceelasticity of demand andthe elasticity of supply.

Figure 3 shows thatthe price would rise to$11.50 a barrel and thequantity would decreaseto 70.5 million barrels aday.

Because demand is in-elastic, a small quantitydecrease brings a largeprice rise.

But because the pricerises, non-OPEC pro-ducers increase produc-tion an increase in thequantity supplied.

The decrease in quan-tity of 0.5 million barrelsa day equals OPECs cutof 1.5 million barrels aday minus the 1 millionbarrels a day increase inproduction by the rest ofthe world.

D2001

D2002

0 71 807565

Pric

e (d

olla

rs p

e ba

rrel

)

Quantity (millions of barrels per day)

18.00

30.00

10.00Price in 2002with no cut inproduction

S2001

Figure 2 The oil market with no production cuts

Pri

ce (

dolla

rs p

er b

arr

el)

Year/quarter

20

25

30

10

15

1987:2 1999:4 2001:2 2002:4

Price rise asdemandincreased

Price fall asdemanddecreased

Forecastsmade in 2001

72

D2002

0 7170.5 7573 7469

Pric

e (d

olla

rs p

e ba

rrel

)

Quantity (millions of barrels per day)

10.00

15.00

11.50

Decreasein OPECproduction

S2002 S2001

Figure 3 OPEC production cut

Price in 2002with OPECproduction cut

Increasein non-OPECquantitysupplied

Decreasein demand

Figure 1 The price of crude oil

20.00

Demand and supplyin a global market deter-mine the price of crude oil.

OPEC is the largestsupplier of oil (with a 36percent market share), andit tries to limit productionto raise the price.

But the actions of in-dividual OPEC membersand of non-OPEC pro-ducers make it impossi-ble for OPEC to controlthe price of crude oil.

Figure 1 shows thatthe price of crude oilfluctuates (an example ofa price roller coaster).

During 2001, theprice fell below $20 abarrel and OPEC wor-ried that without adecrease in supply, theprice might fall to $10a barrel.

Figure 2 shows de-mand and supply in themarket for crude oil.

The elasticity of de-mand is 0.05, and theelasticity of supply is 0.1.These elasticity values aresuggested by GeoffreyHeal of Columbia Uni-versity, a leading naturalresource economist.

In 2001, the supplycurve was S2001 and thedemand curve was D2001.The quantity was 75 mil-lion barrels a day, and theprice was $18 a barrel.

98 CHAPTER 4 E L A S T I C I T Y

Elasticity of Supply (pp. 9294)

Elasticity of supply measures the responsiveness ofthe quantity supplied of a good to a change in itsprice.

The elasticity of supply is usually positive andranges between zero (vertical supply curve) andinfinity (horizontal supply curve).

Supply decisions have three time frames: momen-tary, long run, and short run.

Momentary supply refers to the response of sellersto a price change at the instant that the pricechanges.

Long-run supply refers to the response of sellers toa price change when all the technologically feasibleadjustments in production have been made.

Short-run supply refers to the response of sellers toa price change after some of the technologicallyfeasible adjustments in production have been made.

K E Y F I G U R E S A N D T A B L E

Figure 4.2 Calculating the Elasticity ofDemand, 83

Figure 4.3 Inelastic and Elastic Demand, 84Figure 4.4 Elasticity Along a Straight-Line

Demand Curve, 85Figure 4.5 Elasticity and Total Revenue, 86Figure 4.7 Cross Elasticity of Demand, 89Table 4.3 A Compact Glossary of

Elasticities, 95

K E Y T E R M S

Cross elasticity of demand, 89Elastic demand, 85Elasticity of supply, 92Income elasticity of demand, 90Inelastic demand, 85Perfectly elastic demand, 85Perfectly inelastic demand, 84Price elasticity of demand, 82Total revenue, 86Total revenue test, 86Unit elastic demand, 84

K E Y P O I N T S

Elasticity of Demand (pp. 8288)

Elasticity is a measure of the responsiveness of thequantity demanded of a good to a change in itsprice.

Price elasticity of demand equals the percentagechange in the quantity demanded divided by thepercentage change in price.

The larger the magnitude of the elasticity ofdemand, the greater is the responsiveness of thequantity demanded to a given change in price.

Price elasticity of demand depends on how easilyone good serves as a substitute for another, theproportion of income spent on the good, and thelength of time elapsed since the price change.

If demand is elastic, a decrease in price leads to anincrease in total revenue. If demand is unit elastic,a decrease in price leaves total revenue unchanged.And if demand is inelastic, a decrease in price leadsto a decrease in total revenue.

More Elasticities of Demand (pp. 8991)

Cross elasticity of demand measures the respon-siveness of demand for one good to a change inthe price of a substitute or a complement.

The cross elasticity of demand with respect to theprice of a substitute is positive. The cross elasticityof demand with respect to the price of a comple-ment is negative.

Income elasticity of demand measures the respon-siveness of demand to a change in income. For anormal good, the income elasticity of demand ispositive. For an inferior good, the income elastic-ity of demand is negative.

When the income elasticity is greater than 1, asincome increases, the percentage of income spenton the good increases.

When the income elasticity is less than 1 butgreater than zero, as income increases, the percent-age of income spent on the good decreases.

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

*5. If the quantity of dental services demandedincreases by 10 percent when the price of dentalservices falls by 10 percent, is the demand fordental service inelastic, elastic, or unit elastic?

6. If the quantity of haircuts demanded decreasesby 10 percent when the price of a haircut risesby 5 percent, is the demand for haircuts elastic,inelastic, or unit elastic?

*7. The demand schedule for computer chips is

Price Quantity demanded(dollars per chip) (millions of chips per year)

200 50250 45300 40350 35400 30

a. What happens to total revenue if the priceof a chip falls from $400 to $350?

b. What happens to total revenue if the priceof a chip falls from $350 to $300?

c. At what price is total revenue at a maximum?Use the total revenue test to answer thisquestion.

d. At an average price of $350, is the demandfor chips elastic or inelastic? Use the totalrevenue test to answer this question.

8. The demand schedule for sugar is

Price Quantity demanded(dollars per pound) (millions of pounds per year)

5 2510 2015 1520 1025 5

a. What happens to total revenue if the priceof sugar rises from $5 to $15 per pound?

b. What happens to total revenue if the pricerises from $15 to $25 per pound?

c. At what price is total revenue at a maxi-mum? Use the total revenue test to answerthis question.

d. At an average price of $20 a pound, is thedemand for sugar elastic or inelastic? Use thetotal revenue test to answer this question.

*9. In problem 7, at $250 a chip, is the demand forchips elastic or inelastic? Use the total revenuetest to answer this question.

P R O B L E M S 99

*1. Rain spoils the strawberry crop. As a result, theprice rises from $4 to $6 a box and the quanti-ty demanded decreases from 1,000 to 600boxes a week. Over this price range,a. What is the price elasticity of demand?b. Describe the demand for strawberries.

2. Good weather brings a bumper tomato crop.The price falls from $7 to $5 a basket, and thequantity demanded increases from 300 to 500baskets a day. Over this price range,a. What is the price elasticity of demand?b. Describe the demand for tomatoes.

*3. The figure shows the demand for videotaperentals.

a. Calculate the elasticity of demand for a risein rental price from $3 to $5.

b. At what price is the elasticity of demandequal to 1?

4. The figure shows the demand for pens.

a. Calculate the elasticity of demand for a risein price from $6 to $10.

10

4

6

8

200 40 60 80

Pric

e (d

olla

rs p

er p

en)

Pens per day

2

100 120

12

D

5

2

3

4

250 50 75 100

Pric

e (d

olla

rs p

er v

ideo

tape

)

Videotapes per day

1

125 150

6

D

10. In problem 8, at $10 a pound, is the demandfor sugar elastic or inelastic? Use the total rev-enue test to answer this question.

*11. If a 12 percent rise in the price of orange juicedecreases the quantity of orange juice demandedby 22 percent and increases the quantity ofapple juice demanded by 14 percent, calculatethe cross elasticity of demand between orangejuice and apple juice.

12. If a 5 percent fall in the price of chickendecreases the quantity of beef demanded by 20percent and increases the quantity of chickendemanded by 15 percent, calculate the crosselasticity of demand between chicken and beef.

*13. Alexs income has increased from $3,000 to$5,000. Alex increased his consumption ofbagels from 4 to 8 a month and decreased hisconsumption of doughnuts from 12 to 6 amonth. Calculate Alexs income elasticity ofdemand for (a) bagels and (b) doughnuts.

14. Judys income has increased from $13,000 to$17,000. Judy increased her demand for con-cert tickets by 15 percent and decreased herdemand for bus rides by 10 percent. CalculateJudys income elasticity of demand for (a) con-cert tickets and (b) bus rides.

*15. The table gives the supply schedule for long-distance phone calls.

Price Quantity supplied(cents per minute) (millions of minutes per day)

10 20020 40030 60040 800

Calculate the elasticity of supply whena. The price falls from 40 cents to 30 cents a

minute.b. The price is 20 cents a minute.

16. The table gives the supply schedule for jeans.

Price Quantity supplied(dollars per pair) (millions of pairs per year)

120 2,400125 2,800130 3,200135 3,600

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

100 CHAPTER 4 E L A S T I C I T Y

1. Study Reading Between the Lines (pp. 9697) onthe market for crude oil and then answer thefollowing questions:a. Why did the price of oil fall during 2001?b. What is the elasticity that tells us the effect

of a change in supply on the price and quan-tity of crude oil?

c. What is the elasticity that tells us the effectof a change in demand on the price andquantity of crude oil?

d. Why did OPEC want to cut productionduring 2002?

e. Calculate the elasticity of supply in Figure 2on page 97 when demand decreases and con-firm that it is (approximately) 0.1.

f. Calculate the elasticity of demand in Figure3 on page 97 when supply decreases andconfirm that it is (approximately) 0.05.

g. By how much would OPEC have needed tocut production to raise the price to $15 abarrel (assuming demand D2002)?

1. Use the link on the Parkin Web site anda. Find the price of gasoline in the summer of

2002.b. Use the concepts of demand, supply, and

elasticity to explain recent changes in theprice of gasoline.

c. Find the price of crude oil.d. Use the concepts of demand, supply, and

elasticity to explain recent changes in theprice of crude oil.

2. Use the link of the Parkin Web site and:a. Find the number of gallons in a barrel and

the cost of crude oil in a gallon of gasoline.b. What are the other costs that make up the

total cost of a gallon of gasoline?c. If the price of crude oil falls by 10 percent,

by what percentage would you expect theprice of gasoline to change, other thingsremaining the same?

d. Which demand do you think is more elastic:that for crude oil or gasoline? Why?

3. Use the link of the Parkin Web site to reviewand write a brief report on Geoffrey Heals lec-ture on the market for oil during the 1990s.

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eia99: html:

eia100: html: