# Chapter 6. Elasticity

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1 Chapter 6 Elasticity Both the elasticity coefficient and the total revenue test for measuring price elasticity of demand are presented in this chapter. The text discusses the major determinants of price elasticity. The chapter reviews a number of applications and presents empirical estimates for a variety of products. Cross and income elasticities of demand and price elasticity of supply are also examined. The Last Word is about how firms and colleges use price elasticities to set their price. 1

2 Key Terms price elasticity of demand midpoint formula elastic demand inelastic demand unit elasticity perfectly inelastic demand perfectly elastic demand total revenue (TR) total-revenue test price elasticity of supply market period short run long run cross elasticity of demand income elasticity of demand consumer surplus producer surplus efficiency losses (deadweight losses) 6-2 2

3 Price Elasticity of Demand Measures buyers responsiveness to price changes Elastic demand Sensitive to price changes Large change in quantity demanded Inelastic demand Insensitive to price changes Small change in quantity demanded LO1 The law of demand tells us that consumers will respond to a price decrease by buying more of a product (other things remaining constant), but it does not tell us how much more. The degree of responsiveness or sensitivity of consumers to a change in price is measured by the concept of price elasticity of demand. If demand is elastic, there is a large change in quantity demanded even when price changes by a small amount. When demand is inelastic, there is a very small change in quantity demanded even when there is a large change in price. 3

4 Price Elasticity of Demand Formula Formula for price elasticity of demand E d = percentage change in quantity demanded of product X percentage change in price of product X LO1 Quantitative measure of elasticity, E d = percentage change in quantity/percentage change in price. 4

5 Price Elasticity of Demand Formula Continued Use the midpoint formula Ensures consistent results Change in quantity E d = Sum of quantities/2 Change in price Sum of prices/2 LO1 Using traditional calculations, the measured elasticity over a given range of prices is sensitive to whether one starts at the higher price and goes down, or the lower price and goes up. The midpoint formula calculates the average elasticity over a range of prices to avoid that problem. 5

6 Price Elasticity of Demand Formula Concluded Use percentages Unit free measure Compare elasticities across products Eliminate the minus sign Easier to compare elasticities LO1 Absolute changes depend on the choice of units. For example, a change in the price of a \$10,000 car by \$1 is very different than a change in the price a of \$1 can of beer by \$1. The auto s price is rising by a fraction of a percent while the beer s price is rising 100 percent. Percentages also make it possible to compare elasticity of demand for different products. Because of the inverse relationship between price and quantity demanded, the actual elasticity of demand will be a negative number. However, we ignore the minus sign and use absolute value. This makes it less confusing to interpret the elasticity coefficient. 6

7 Interpretation of Elasticity of Demand E d > 1 demand is elastic E d = 1 demand is unit elastic E d < 1 demand is inelastic Extreme cases E d = 0 demand is perfectly inelastic E d = demand is perfectly elastic LO1 When the elasticity coefficient is greater than 1, it means that the percentage change in quantity demanded is greater than the percentage change in price (based on the formula), indicating that consumers are sensitive to the change in price, so demand is elastic. When the elasticity coefficient is less than 1, the percentage change in quantity demanded is less than the percentage change in price (based on the formula), indicating that consumers are not very sensitive to price changes. When the elasticity coefficient equals 1, this is a special case called unit elasticity. This means that the percentage change in price and the percentage change in quantity are exactly equal. Perfectly inelastic demand means that consumers will buy exactly the same amount no matter how high or low the price. Perfectly elastic demand means that nothing will be purchased if there is any deviation from the current price. 7

8 Extreme Cases P D 1 Perfectly inelastic demand (Ed = 0) 0 Perfectly inelastic demand LO1 This extreme situation is called perfectly inelastic demand and it is very rare. The demand curve would be vertical and graphs as a line parallel to the vertical axis. The elasticity coefficient is 0. An example of a perfectly inelastic demand might be a diabetic s demand for insulin. 8

9 Extreme Cases Continued P Perfectly elastic demand (Ed = ) D 2 0 Perfectly elastic demand LO1 This extreme situation, in which a small price reduction would cause buyers to increase their purchases from zero to all that is possible to obtain, is perfectly elastic demand, and the demand curve would be horizontal. The elasticity coefficient is infinite. An example of a perfectly elastic demand is a firm s demand curve in a purely competitive industry, such as the mining industry, that is unable to change the price. 9

10 Total Revenue Test Total Revenue = Price Quantity Total Revenue Test Inelastic demand P and TR move in the same direction Elastic demand P and TR move in opposite directions LO2 The total-revenue test is the easiest way to judge whether demand is elastic or inelastic. This test can be used in place of the elasticity formula, unless there is a need to determine the elasticity coefficient. The total revenue test is important to understand the relationship between price elasticity and total revenue. Demand is inelastic if a decrease in price results in a decrease in total revenue, or an increase in price results in a rise in total revenue. Demand is elastic if a decrease in price results in a rise in total revenue, or if an increase in price results in a decline in total revenue. Demand is unit elastic if total revenue does not change when the price changes. 10

11 Total Revenue Test with Elastic Demand Lower price and elastic demand Blue gain exceeds yellow loss P \$3 2 a 1 b D Q LO2 A lower price and elastic demand means that total revenue will rise. Blue gain (extra total revenue from extra sales) exceeds yellow loss (the loss in total revenue from the higher price). 11

12 Total Revenue Test with Inelastic Demand Lower price and inelastic demand Yellow loss exceeds blue gain P \$4 c d LO2 D Q A lower price and inelastic demand means that total revenue will fall. Blue gain (extra total revenue from extra sales) is less than the yellow loss (the loss in total revenue from the higher price). 12

13 Total Revenue Test with Unit-Elastic Demand Lower price and unit elastic demand Blue gain equals yellow loss P \$3 e 2 1 f D Q LO2 A lower price and unit-elastic demand means that total revenue is unchanged. Blue gain (extra total revenue from extra sales) is exactly equal to the yellow loss (the loss in total revenue from the higher price). 13

14 Total Revenue Test Continued Price Elasticity of Demand for Movie Tickets as Measured by the Elasticity Coefficient and the Total Revenue Test (1) Total Quantity of Tickets Demanded per Week, Thousands (2) Price per Ticket \$ ] ] ] ] ] ] ] (3) Elasticity Coefficient (E d ) (4) Total Revenue (1) X (2) \$ 8,000 14,000 18,000 20,000 20,000 18,000 14,000 8,000 ] ] ] ] ] ] ] (5) Total-Revenue Test Elastic Elastic Elastic Unit-elastic Inelastic Inelastic Inelastic LO2 Notice that in the high price region, demand for movie tickets is elastic and revenues increase as price falls. Midway demand for movie tickets is unit elastic and revenues stay the same as price falls. In the low price region, elasticities of demand are inelastic and revenues fall as the price falls. 14

15 Total Revenue Test Concluded Price \$8 7 a 6 b 5 c 4 d 3 e 2 f 1 g h D Quantity demanded Elastic E d > 1 Unit elastic E d = 1 Inelastic E d < 1 LO2 Total revenue (Thousands of dollars) \$ Quantity demanded TR This graph shows the relationship between price elasticity of demand for movie tickets and total revenue. Demand curve D in the top graph is based on Table 6.1 and is marked to show that the hypothetical weekly demand for movie tickets is elastic at higher price ranges and inelastic at lower price ranges. The total-revenue curve, TR, in the lower graph is derived from demand curve D. When price falls and TR increases, demand is elastic; when price falls and TR is unchanged, demand is unit elastic; and when price falls and TR declines, demand is inelastic. You can see from the graph that elasticity changes along a demand curve. Demand tends to be more elastic in the upper-left portion of demand and more inelastic in the lower-right portion of demand. 15

16 Summary of Price Elasticity of Demand Price Elasticity of Demand: A Summary Absolute Value of Elasticity Coefficient Demand Is: Description Greater than 1 (E d > 1) Elastic or relatively elastic Q d changes by a larger percentage than does price Impact on Total Revenue of a: Price Increase Total Revenue decreases Price Decrease Total Revenue increases Equal to 1 (E d = 1) Unit or unitary elastic Q d changes by the same percentage as does price Total revenue is unchanged Total revenue is unchanged Less than 1 (E d < 1) LO2 Inelastic or relatively inelastic Q d changes by a smaller percentage than does price Total revenue increases Total revenue decreases This is a summary of the rules and concepts related to the elasticity of demand. 16

17 Determinants of Price Elasticity of Demand Substitutability More substitutes, demand is more elastic Proportion of income Higher proportion of income, demand is more elastic LO3 With more substitutes available, consumers have more alternative options, so when there is a change in price, there is a greater percentage change in quantity demanded, making the demand more elastic. The broader the definition of the market, the more elastic the demand. With a more narrow definition of the market, demand is more inelastic. The greater the proportion of income needed to buy the good the more elastic the demand. Consumers will be more sensitive to changes in prices because the price change can result in thousands of dollars difference. 17

18 Determinants of Price Elasticity of Demand Continued Luxuries versus necessities Luxury goods, demand is more elastic Time More time available, demand is more elastic LO3 Since luxuries are goods that consumers can go without, they will change the amount they purchase by a greater amount even if the price changes by a small amount. It takes time to alter the amount being purchased, so the more time available, the more elastic the demand. A person doing his/her Christmas shopping on Christmas Eve has a very inelastic demand because he/she doesn t have the time to look around for alternative purchases. 18

19 Selected Price Elasticities of Demand Selected Price Elasticities of Demand Product or Service Price Elasticity of Demand (E d ) Product or Service Price Elasticity of Demand (E d ) Newspapers.10 Milk.63 Electricity (household).13 Household appliances.63 Bread.15 Liquor.70 MLB Tickets.23 Movies.87 Cigarettes.25 Beer.90 Telephone service.26 Shoes.91 Sugar.30 Motor vehicles 1.14 Medical Care.31 Beef 1.27 Eggs.32 China, glassware, tableware 1.54 Legal Services.37 Residential land 1.60 Automobile repair.40 Restaurant meals 2.27 Clothing.49 Lamb and mutton 2.65 Gasoline.60 Fresh peas 2.83 LO3 Some of the elasticities of the goods in this table are surprising. Use the determinants of demand to discuss why major league baseball tickets are not only inelastic, but they are more inelastic than gasoline. What makes newspapers, movies, and beer inelastic? 19

20 Applications of Price Elasticity of Demand Large crop yields Inelastic demand, lower total revenue Excise taxes Inelastic demand, more total revenue Decriminalization of illegal drugs Inelastic demand, more total revenue LO3 Large crop yields mean that the supply of crops increases and shifts to the right. When this occurs the equilibrium price falls. Since demand is inelastic, the lower price actually leads to lower revenue for farmers. Farmers are worse off when there is a large crop yield. When government wants to impose taxes on goods, it is important for them to understand the elasticity of demand for the good. If they place a tax on a good with an inelastic demand, the higher price won t decrease the quantity purchased by much, thereby increasing the amount of tax revenue that government collects. If heroin and cocaine were legalized, their prices would decline according to proponents of legalization. Demand for illegal drugs like this are inelastic for a drug addict so if the price dropped, the amount consumed at that lower price wouldn t change by much. Crime would subsequently decline since the addicts wouldn t need to steal as much to support their habit. Opponents of legalization say that lower prices for these drugs would simply increase the quantity demanded for them and not benefit society at all. 20

21 Price Elasticity of Supply Measures sellers responsiveness to price changes Elastic supply, producers are responsive to price changes Inelastic supply, producers are not as responsive to price changes LO4 At higher prices firms are willing and able to produce more, whereas at lower prices, firms are willing and able to produce less. Price elasticity of supply measures how sensitive firms are to price changes. If supply is elastic, small changes in price will result in firms greatly altering the quantity being produced. On the other hand, when supply is inelastic, the firm is unresponsive to price changes and therefore will not change the amount being produced by much, even when the change in price is large. 21

22 Price Elasticity of Supply Formula Formula for price elasticity of supply E s = percentage change in quantity supplied of product X percentage change in price of product X LO4 Quantitative measure of elasticity, E s = percentage change in quantity/ percentage change in price. The concept of price elasticity also applies to supply. We use percentages so it doesn t matter which unit of measure we are using. The elasticity formula is the same as that for demand, but we substitute the word supplied for the word demanded everywhere in the formula. Just like with price elasticity of demand, we will compute the price elasticity of supply using the midpoint formula. Elasticity of supply will always be positive since price and quantity supplied move in the same direction. 22

23 Price Elasticity of Supply Continued E s > 1 supply is elastic E s = 1 supply is unit elastic E s < 1 supply is inelastic Additionally, E s = 0 supply is perfectly inelastic LO4 Elasticity of supply depends on how easily producers can shift resources between alternative uses. 23

24 Price Elasticity of Supply and Time Time is primary determinant of elasticity of supply Time periods considered Immediate market period Short run Long run LO4 The ease of shifting resources between alternative uses is very important in price elasticity of supply because it will determine how much flexibility a producer has to adjust his/her output to a change in the price. The degree of flexibility, and therefore the time period, will be different in different industries. The immediate market period means that there is no time to adjust output in response to a price change. Some industries may not have an immediate market period if they are able to store their product. The short run means that there is enough time to adjust output by increasing or decreasing the variable inputs but not the fixed inputs. The long run means that there is enough time to adjust output by increasing or decreasing all inputs. 24

25 The Immediate Market Period Perfectly inelastic supply P S m P m P 0 Q 0 D 1 D 2 Q LO4 There is no time for sellers to adjust to a price change, making supply perfectly inelastic. With a perfectly inelastic supply, the increase in demand does not change the quantity demanded at all. 25

26 The Short Run Short run supply is more elastic than in the immediate market period P S s P s P 0 LO4 Q 0 Q s D 1 D 2 Q In the short run there is enough time to adjust output by increasing or decreasing the variable inputs but not the fixed inputs. Therefore, supply is more elastic in the short run than in the immediate market period, thereby resulting in a somewhat greater increase in quantity. 26

27 The Long Run Long run supply is even more elastic than in the short run P S L P l P 0 LO4 Q 0 Q l D 1 D 2 Q In the long run there is enough time to adjust output by increasing or decreasing all inputs since all inputs are variable by this time. This means that supply will be even more elastic and with the same increase in demand, there is an even greater increase in the quantity than in the short run. In the long run all inputs are variable, even the size of the firm; the firm can expand (reduce) the size of the firm in regard to long run price increases (decreases). 27

28 Applications of Elasticity of Supply Antiques Inelastic supply Reproductions More elastic supply Volatile gold prices Inelastic supply LO4 Antiques and other non-reproducible commodities have an inelastic supply, for one-of-akind antiques, the supply is perfectly inelastic. This makes their prices highly susceptible to fluctuations in demand. The more inelastic the supply, the greater the change in price when demand changes. Reproductions, on the other hand, have a much more elastic supply so the prices tend to remain lower even when there is an increase in demand. Gold prices are volatile because the supply of gold is highly inelastic, and unstable demand from speculation causes prices to fluctuate significantly. 28

29 Cross Elasticity of Demand Formula for cross elasticity of demand E xy = percentage change in quantity demanded of product X percentage change in price of product Y LO5 Consumption of a good can also be affected by a change in the price of a related good. Cross elasticity of demand will provide a way to quantify the degree of the change in consumption. 29

30 Cross Elasticity of Demand Continued Measures responsiveness of purchases of one good to change in the price of another good Substitute goods if elasticity is positive Complement goods if elasticity is negative Independent goods if elasticity is 0 LO5 Cross elasticity of demand refers to the effect of a change in a product s price on the quantity demanded for another product. If the goods are substitutes, they will have a positive cross elasticity of demand since the change in the price of one good and the change in the demand for its substitute move in the same direction. If the goods are complements, they will have a negative cross elasticity of demand since the change in the price of one good and the demand for its complement move in opposite directions. If the goods are unrelated they will show a cross elasticity of zero. 30

31 Cross Elasticity of Demand Concluded Applications of cross elasticity of demand Should a company change a price? Should the government allow a merger? LO5 Companies can use cross-price elasticity to determine whether raising the price of one of their products will affect sales of another of their products. Government can use it to determine whether to allow a proposed merger of two companies or not. If there is a high cross-price elasticity between the two companies products the government will likely not allow the merger. 31

32 Income Elasticity of Demand Formula for income elasticity of demand E i = percentage change in quantity demanded percentage change in income LO5 Consumption of a good can also be affected by a change in income. Income elasticity of demand is a measurement that reflects the percentage change in quantity demanded due to some percentage change in consumer income. 32

33 Income Elasticity of Demand Continued Measures responsiveness of buyers to changes in their income Normal goods if elasticity is positive Inferior goods if elasticity is negative LO5 Most goods are normal goods that have a positive income elasticity but the value of elasticity of income can vary widely among these goods. Consumers decrease their purchases of inferior goods when their income rises. Those industries with products that are income elastic will expand at a higher rate as the economy grows. 33

34 Income Elasticity Insights High income elasticities Most affected by a recession Low or negative income elasticity Not affected that much by a recession LO5 Income elasticity helps us understand which products and industries will be most affected when household incomes fall during economic downturns. 34

35 Cross and Income Elasticities Cross and Income Elasticities of Demand Value of Coefficient Description Type of Good(s) Cross elasticity: Positive (E wz > 0) Quantity demanded of W changes in same direction as change in price of Z Substitutes Negative (E xy < 0) Income elasticity: Positive (E i >0) Negative (E i <0) Quantity demanded of X changes in opposite direction from change in price of Y Quantity demanded of the product changes in same direction as change in income Quantity demanded of the product changes in opposite direction from change in income Complements Normal or superior Inferior LO5 This table summarizes many of the characteristics of cross-price elasticity and income elasticity. 35

36 Elasticity and Pricing Power Charge different prices to different buyers based on price elasticities Business air travelers Children discounts College tuition Some firms have market power or pricing power that allows them to set their product at prices that are in their best interests. For some goods and services, firms may find it advantageous to determine differences in price elasticity of demand and then charge different prices to different buyers. Business air travelers have a more inelastic demand for air travel, so they are charged higher prices since they will pay it. Families are sensitive to prices, so firms will charge lower prices for children as a result of the more elastic demand. Students from low income households are offered assistance with paying for college since they have a higher price elasticity of demand; students from higher income households will pay full price for their education unless they receive some type of merit based scholarship. 36

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