1. Slide 1 DEMAND ANALYSIS Overview of Chapter 3 Demand Relationships The Price Elasticity of Demand »Arc and point price elasticity »Elasticity and revenue relationships »Why some products are inelastic and others are elastic Income Elasticities Cross Elasticities of Demand Combined Effects of Elasticities ©2008 Thomson * South-Western

2. Slide 2 Health Care & Cigarettes Raising cigarette taxes reduces smoking »In Canada, over $4 for a pack of cigarettes reduced smoking 38% in a decade But cigarette taxes also helps fund health care initiatives »The issue then, should we find a tax rate that maximizes tax revenues? »Or a tax rate that reduces smoking?

3. Slide 3 Demand Analysis An important contributor to firm risk arises from sudden shifts in demand for the product or service. Demand analysis serves two managerial objectives: (1) it provides the insights necessary for effective management of demand, and (2) it aids in forecasting sales and revenues.

4. Slide 4 Downward Slope to the Demand Curve Economists presume consumers are maximizing their utility This is used to derive a demand curve from utility maximization Reasons that price and quantity are negatively related include: » income effect -- as the price of a good declines, the consumer can purchase more of all goods since his or her real income increased. So as the price falls, we typically buy more. » substitution effect -- as the price declines, the good becomes relatively cheaper. A rational consumer maximizes satisfaction by reorganizing consumption until the marginal utility in each good per dollar is equal. We buy more.

5. Slide 5 Foo d Entertainment Uo U1 a c demand b Indifference Curves to derive demand We can "derive" a demand curve graphically from maximization of utility subject to a budget constraint. Suppose the price of entertainment falls from line 1 to line 2 We tend to buy more from (i)the Income Effect and (ii)the Substitution Effect. From a to b, is the substitution effect. From b to c is the income effect. PEPE 1 2 Entertainment

6. Slide 6 The Price Elasticity of Demand Elasticity is measure of responsiveness or sensitivity Beware of using Slopes bushelshundred tons price per bu. Slopes change with a change in units of measure

7. Slide 7 Price Elasticity E D = % change in Q / % change in P Shortcut notation: E D = %  Q / %  P A percentage change from 100 to 150 is 50% A percentage change from 150 to 100 is -33% For arc price elasticities, we use the average as the base, as in 100 to 150 is +50/125 = 40%, and 150 to 100 is -40% Arc Price Elasticity -- averages over the two points D arc price elasticity E D =  Q/ [(Q 1 + Q 2 )/2]  P/ [(P 1 + P 2 )/2] Average price Average quantity

8. Slide 8 Arc Price Elasticity Example Q = 1000 when the price is $10 Q= 1200 when the price is reduced to $6 Find the arc price elasticity Solution: E D = %  Q/ %  P = +200/1100 - 4 / 8 or -.3636. The answer is a number. A 1% increase in price reduces quantity by.36 percent.

9. Slide 9 Point Price Elasticity Example Need a demand curve or demand function to find the price elasticity at a point. E D = %  Q/ %  P =(  Q/  P)(P/Q) If Q = 500 - 5P, find the point price elasticity at P = 30; P = 50; and P = 80 1.E D = (  Q/  P)(P/Q) = - 5(30/350) = -.43 2.E D = (  Q/  P)(P/Q) = - 5(50/250) = - 1.0 3.E D = (  Q/  P)(P/Q) = - 5(80/100) = - 4.0

10. Slide 10 Price Elasticity (both point price and arc elasticity ) If E D = -1, unit elastic If E D > -1, inelastic, e.g., - 0.43 If E D < -1, elastic, e.g., -4.0 price elastic region unit elastic inelastic region Straight line demand curve example quantity

11. Slide 11 Two Extreme Examples ( Figure 3.1) Perfectly Elastic | E D | = B and Perfectly Inelastic |E D | = 0 D D’ D D’

12. Slide 12 TR and Price Elasticities If you raise price, does TR rise? Suppose demand is elastic, and raise price. TR = PQ, so, %  TR = %  P+ %  Q If elastic, P, but Q a lot Hence TR FALLS !!! Suppose demand is inelastic, and we decide to raise price. What happens to TR and TC and profit?

13. Slide 13 Another Way to Remember Linear demand curve TR on other curve Look at arrows to see movement in TR A.Increasing price in the inelastic region raises revenue B.Increasing price in the elastic region lowers revenue Elastic Unit Elastic Inelastic TR QQQQ ( Figure 3.2) A B

14. Slide 14 MR and Elasticity Marginal revenue is  TR  Q To sell more, often price must decline, so MR is often less than the price.  MR = P ( 1 + 1/E D ) equation 3.7 on page 90 For a perfectly elastic demand, E D = - B. Hence, MR = P. If E D = -2, then MR =.5P, or is half of the price.

15. Slide 15 1979 Deregulation of Airfares Prices declined after deregulation And passengers increased Also total revenue increased What does this imply about the price elasticity of air travel ? »It must be that air travel was elastic, as a price decrease after deregulation led to greater total revenue for the airlines.

16. Slide 16 Determinants of the Price Elasticity The availability and the closeness of substitutes »more substitutes, more elastic The more durable is the product »Durable goods are more elastic than non-durables The percentage of the budget »larger proportion of the budget, more elastic The longer the time period permitted »more time, generally, more elastic »consider examples of business travel versus vacation travel for all three above.

17. Slide 17 Empirical Price Elasticities Table 3.5 Apparel (whole market) -1.1 Apparel (one firm) -4.1 Beer -.84 Wine -.55 Liquor -.50 Regular coffee -.16 Instant coffee -.36 Adult visits to dentist »men -.65 »Women -.78 Children visit to dentist -1.4 Furniture -3.04 Glassware & China -1.2 School lunches -.47 Flights to Europe -1.25 Shoes -.73 Soybean meal -1.65 Telephones -.10 Tires -.60 Tobacco -.46 Tomatoes -2.22 Wool -1.32

18. Slide 18 Free Trade and Price Elasticities NAFTA (North American Free Trade Agreement) and Europe having a common currency in the Euro are examples of greater freedom in trade What does that do to price elasticities? With more substitutes, we expect that products become More Elastic Consumers gain as firms are less able to raise their prices, but firm face stiffer competition

19. Slide 19 Income Elasticity E Y = %  Q/ %  Y = (  Q/  Y)( Y/Q) point income arc income elasticity: »suppose dollar quantity of food expenditures of families of $20,000 is $5,200; and food expenditures rises to $6,760 for families earning $30,000. »Find the income elasticity of food »%  Q/ %  Y = (1560/5980)(10,000/25,000) =.652 »With a 1% increase in income, food purchases rise.652% E Y =  Q/ [(Q 1 + Q 2 )/2] arc income  Y/ [(Y 1 + Y 2 )/2] elasticity

20. Slide 20 Income Elasticity Definitions If E Y >0, then it is a normal or income superior good »some goods are Luxuries: E Y > 1 with a high income elasticity »some goods are Necessities: E Y < 1 with a low income elasticity If E Y is negative, then it’s an inferior good Consider these examples: 1.Expenditures on new automobiles 2.Expenditures on new Chevrolets 3.Expenditures on 1996 Chevy Cavaliers with 150,000 miles Which of the above is likely to have the largest income elasticity? Which of the above might have a negative income elasticity?

21. Slide 21 Point Income Elasticity Problem Suppose the demand function is: Q = 10 - 2P + 3Y find the income and price elasticities at a price of P = 2, and income Y = 10 So: Q = 10 -2(2) + 3(10) = 36 E Y = (  Q/  Y)( Y/Q) = 3( 10/ 36) =.833 E D = (  Q/  P)(P/Q) = -2(2/ 36) = -.111 Characterize this demand curve, which means describe them using elasticity terms.

22. Slide 22 Cross Price Elasticities E X = %  Q A / %  P B = (  Q A /  P B )(P B /Q A ) Substitutes have positive cross price elasticities: Butter & Margarine Complements have negative cross price elasticities: DVD machines and the rental price of DVDs at Blockbuster When the cross price elasticity is zero or insignificant, the products are not related

23. Slide 23 PROBLEM: Find the point price elasticity, the point income elasticity, and the point cross-price elasticity at P=10, Y=20, and P s =9, if the demand function were estimated to be: Q D = 90 - 8·P + 2·Y + 2·P s Is the demand for this product elastic or inelastic? Is it a luxury or a necessity? Does this product have a close substitute or complement? Find the point elasticities of demand.

24. Slide 24 Answer First find the quantity at these prices and income: Q D = 90 - 8·P + 2·Y + 2·P s = 90 -8·10 + 2·20 + 2·9 =90 -80 +40 +18 = 68 E D = (  Q/  P)(P/Q) = (-8)(10/68)= -1.17 which is elastic E Y = (  Q/  Y)(Y/Q) = (2)(20/68) = +.59 which is a normal good, but a necessity E X = (  Q A /  P B )(P B /Q A ) = (2)(9/68) = +.26 which is a mild substitute

25. Slide 25 Combined Effect of Demand Elasticities Most managers find that prices and income change every year. The combined effect of several changes are additive. %  Q = E D (%  P) + E Y (%  Y) + E X (%  P R ) »where P is price, Y is income, and P R is the price of a related good. If you knew the price, income, and cross price elasticities, then you can forecast the percentage changes in quantity.

26. Slide 26 Example: Combined Effects of Elasticities Toro has a price elasticity of -2 for snow-throwers Toro snow throwers have an income elasticity of 1.5 The cross price elasticity with professional snow removal for residential properties is +.50 What will happen to the quantity sold if you raise price 3%, income rises 2%, and professional snow removal companies raises its price 1%? »%  Q = E P %  P +E Y %  Y + E X %  P x = -2 3% + 1.5 2% +.50 1% = -6% + 3% +.5% »%  Q = -2.5%. We expect sales to decline 2.5%. Q: Will Total Revenue for your product rise or fall? A: Total revenue will rise slightly (about +.5%), as the price rises 3% and the quantity of snow-throwers sold falls 2.5%.