1. Lecture 9 Elasticities Elasticities are measures of responsiveness Elasticities are measures of responsiveness –The response of one variable to changes in another –Can be positive or negative –If “close” to zero, relative unresponsive –If “far” from zero, relatively responsive Calculated as the ratio of two percentage changes: Calculated as the ratio of two percentage changes: E = (%∆Y)/(%∆X) E = (%∆Y)/(%∆X) –This is said to be “the elasticity of Y with respect to X”

2. Consider this hypothetical relationship The elasticity of grades The elasticity of grades with respect to with respect to time spent studying time spent studying –Likely positive –Ε = (%∆G)/(%∆S) > 0 –If E > 1, we say “elastic” (relatively responsive) –If E < 1, we say “inelastic” (relatively unresponsive) Grade Study Time/week 0

3. Another hypothetical example The elasticity of grades The elasticity of grades with respect to with respect to alcohol consumption alcohol consumption –Likely negative –E = (%∆G)/(%∆W) < 0 –If |E| >1, we say “elastic” (relatively responsive) –If |E| < 1, we say “inelastic” (relatively unresponsive) Real elasticity computation regarding alcohol: a 10% price increase leads to a 5.8% decline in traffic fatalities. Grades Alcohol Consumption/week 0

4. The (own) Price Elasticity of Demand Measures the responsiveness of quantity demanded to changes in the price of the good itself Measures the responsiveness of quantity demanded to changes in the price of the good itself –Defined thus: ε = [(%∆in quantity demanded)/(%∆ in price)] ε = [(%∆in quantity demanded)/(%∆ in price)] Or ε = [(%∆Qd)/(%∆P)] Or ε = [(%∆Qd)/(%∆P)] Note that ε must be negative (Law of Demand) Note that ε must be negative (Law of Demand) Sometimes convenient to refer to the absolute value |ε| so we can ignore the negative sign Sometimes convenient to refer to the absolute value |ε| so we can ignore the negative sign

5. Examples of demand elasticities Suppose a 10% rise in the price of a good causes a 20% reduction in the quantity demanded in a measured time period ε = -20%/+10% = -2 Suppose a 15% decline in the price of a good causes a 10% increase quantity demanded in a measured time period ε = +10%/-15% = -0.67

6. Categories of demand elasticities “Elastic” demand Elastic demand Elastic demand –|ε| > 1 –Qd relatively responsive to price –Price change leads to spending change in opposite direction –Thus, Higher price → lower spending Higher price → lower spending Lower price → higher spending Lower price → higher spending Price Q/time Demand

7. When is a good likely to have sensitive elasticity? If a product is not unique so it has many close substitutes and consumers know about the alternatives. When buyers’ expenditures are a large part of their income so they shop more carefully. The product is an input in production that is price sensitive, so the producer will keep close watch on input prices.

8. Demand elasticity... “Inelastic” demand Inelastic demand Inelastic demand –|ε| < 1 –Qd relatively unresponsive to price –Price change leads to spending change in same direction –Thus, Higher price → higher spending Higher price → higher spending Lower price → lower spending Lower price → lower spending Price Q/time Demand

9. When is elasticity likely to be less sensitive? When comparisons to substitutes is difficult. Door-to-door sales. Complex products that are hard to compare. When consumers pay only a fraction of the cost—when insurance covers most of the bill. When the cost of switching would be high— when the consumer has developed expertise in using a product. When a product is used with another product that the consumer is committed to—such as ink cartridges.

10. No close substitutes? In 2006 SCI, the largest player in the funeral business, with 14% of total industry revenue saw its average revenue per service (its product price) rise by 9%. In 2006 SCI, the largest player in the funeral business, with 14% of total industry revenue saw its average revenue per service (its product price) rise by 9%. At the same time, the number of funeral services performed fell by 5.8 percent. At the same time, the number of funeral services performed fell by 5.8 percent. The price elasticity of demand for its services is – (-5.8/9) = 0.64. Its price and quantity demanded suggest that its demand is inelastic—and we thus know from this calculation that its total revenue increased from these services increases.

11. Some uses of demand elasticities More Accurate Pricing More Accurate Pricing –Use of UPC bar codes to aid in pricing products (e.g., Wal-Mart and other retailers data) Trying to Maximize Profits Trying to Maximize Profits –A higher price is no guarantee of higher revenue (will study below) Plan ahead Plan ahead – If you think you know about future trends — plan more precisely (hotels and conventions)

12. Real World Elasticities (all negative numbers) Estimated Elasticity Product or Service Short Run Long Run Lamb2.65-- Bread0.15-- Coffee0.16-- Tires0.81.2 Auto Repairs1.42.4 Theatre & Opera0.20.3 Movies0.93.7 Foreign Travel by U.S. Residents0.11.8 Public Transportation0.61.2 Electricity0.11.8 Jewelry & Watches0.40.6 Alcohol and Tobacco0.30.9 Recreation1.13.5

13. Example The Macon Telegraph sponsored a road race for charity. Entry fee was $12 per runner. 1,600 runners participated. Fees were $19,200. To raise more money, fee raised to $20 the next year. Same weather. 900 runners participated. Fees $18,000. Price elasticity (arc) of demand? 1.12

14. Example ESPN football videogame: ESPN football videogame: 2003 price: $40 2003 price: $40 2004 price: $20 (50% decrease) 2004 price: $20 (50% decrease) 2003 Q d : 400,000 2003 Q d : 400,000 2004 Q d : 2.7 million (575% increase) 2004 Q d : 2.7 million (575% increase) E = 575%/50% = 11.5 E = 575%/50% = 11.5 Note: major competitor, Madden football, did not change price; its sales rose less than 10% from 2003 to 2004 Note: major competitor, Madden football, did not change price; its sales rose less than 10% from 2003 to 2004

15. Example Kelkoo.com, owned by Yahoo!, is 3 rd largest retail website in UK; 10 million users per month. Data for sales of PDAs in 100 days in 2003: 18 models sold by 19 retailers. If click on one model, may get prices offered by 12 retailers. Price elasticities of demand for various models offered by different retailers ranged from -1.75 to -14.7. Average was -4.6. Lowest price retailer saw demand rise 60.4%.

16. Cross-price elasticities Cross-price elasticity of demand Cross-price elasticity of demand –Measure of responsiveness of demand to changes in prices of substitutes and complements: (%∆ Dx) / (%∆ Py) (%∆ Dx) / (%∆ Py) –If positive, goods are substitutes, by definition –If negative, goods are complements, by definition

17. Estimates of Cross Elasticities These are estimates of cross elasticities of various goods (goods that are substitutes) in the U.S.: These are estimates of cross elasticities of various goods (goods that are substitutes) in the U.S.: Electricity and natural gas0.20 (weak substitutes) Beef and Pork0.20 Natural gas and fuel oil0.44 Margarine and butter0.81 (strong substitutes)

18. Income Elasticity Income elasticity of demand Income elasticity of demand –Measure of responsiveness of demand to changes in income: (%∆ Dx) / (%∆ l) (%∆ Dx) / (%∆ l) –If positive, good is normal, by definition (>1, superior) –If negative, good is inferior, by definition

19. Estimates of Income Elasticities Estimates of income elasticities from different studies in the U.S.: Estimates of income elasticities from different studies in the U.S.: Flour-0.36 (inferior good) Margarine-0.20 (inferior good) Milk and cream 0.07(little change) Beef 0.51 to 1.05 Apples 1.32 Dental Services 1.41(highly responsive to Restaurant meals 1.48 income increases) Personal air travel 1.8

20. Endless Elasticities Many measures of elasticity can be performed simultaneously. Many measures of elasticity can be performed simultaneously. The demand for cans of Coke varies across state. Even when price is the same, sales are higher in Southern states (Georgia has highest consumption) compared to Northern (ND lowest). The demand for cans of Coke varies across state. Even when price is the same, sales are higher in Southern states (Georgia has highest consumption) compared to Northern (ND lowest). What factors could you consider? What factors could you consider?

21. Elasticity A study of gasoline sales found that price elasticity for regular gasoline was -.6 and for premium gasoline was -.3. A study of gasoline sales found that price elasticity for regular gasoline was -.6 and for premium gasoline was -.3. What does that mean?