1. Slide 1  2005 South-Western Publishing DEMAND ANALYSIS Overview of Chapter 3 Demand Relationships Demand Elasticities Income Elasticities Cross Elasticities of Demand Combined Effects of Elasticities

2. Slide 2 Health Care & Cigarettes Raising cigarette taxes reduces smoking »In Canada, $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 Demand Curves Individual Demand Curve the greatest quantity of a good demanded at each price the consumers are willing to buy, holding other influences constant $/Q Q /time unit $5 20

5. Slide 5 The Market Demand Curve is the horizontal sum of the individual demand curves. The Demand Function includes all variables that influence the quantity demanded 4 3 7 Sam +Diane = Market Q = f( P, P s, P c, Y, N W, P E ) - + - ? + ? + P is price of the good P S is the price of substitute goods P C is the price of complementary goods Y is income, N is population, W is wealth, and P E is the expected future price

6. Slide 6 Downward Slope to the Demand Curve 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. » 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:

7. Slide 7 Elasticity as Sensitivity 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

8. Slide 8 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 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

9. Slide 9 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.

10. Slide 10 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

11. Slide 11 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

12. Slide 12 Two Extreme Examples ( Figure 3.3) Perfectly Elastic | E D | = B and Perfectly Inelastic |E D | = 0 D D’ D D’

13. Slide 13 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?

14. Slide 14 Another Way to Remember Linear demand curve TR on other curve Look at arrows to see movement in TR Elastic Unit Elastic Inelastic TR QQQQ ( Figure 3.4 )

15. Slide 15 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.

16. Slide 16 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.

17. Slide 17 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.

18. Slide 18 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

19. Slide 19 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?

20. Slide 20 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.

21. Slide 21 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

22. Slide 22 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.

23. Slide 23 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

24. Slide 24 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.

25. Slide 25 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. Q: Will Total Revenue for your product rise or fall? A: Total revenue will rise slightly (about +.5%), as the price went up 3% and the quantity of snow-throwers sold will fall 2.5%.