1. -1- 5/5/2015 Math 267 Professor Luke Froeb Copyright 2002, Froeb Owen Graduate School of Management Vanderbilt University

2. -2- 5/5/2015 Pricing is an extent decision lPlProfit=Revenue-Cost lDlDefinition: Demand curves are functions that relate the price of a product to the quantity demanded by consumers. lDlDemand Curves help us make decisions to increase profits by modeling revenue »P»Particularly MR »S»Should I sell another unit?

3. -3- 5/5/2015 Aggregate Demand lAlAggregate Demand: each consumer wants one unit. lTlTo construct demand, sort by value. lDlDiscussion: Why do aggregate demand curves slope downward? »R»Role of heterogeneity? »H»How to estimate?

4. -4- 5/5/2015 Pricing Tradeoff lLlLower price  sell more, but earn less on each unit sold lHlHigher price  sell less, but earn more on each unit sold lTlTradeoff created by downward sloping demand

5. -5- 5/5/2015 Marginal Analysis lMlMarginal analysis finds the right solution to the pricing tradeoff. »A»Also requires less information. lDlDefinition: The marginal revenue (MR) is the change in total revenue with an extra unit. lPlProposition: If MR>0, then total revenue will increase if you sell one more unit. lPlProposition: If MR>MC, then total profits will increase if you sell one more unit. lPlProposition: Profits are max. when MR=MC

6. -6- 5/5/2015 Elasticity of Demand l Motivation: price elasticity is used to do marginal analysis. l Definition: price elas.=(%change in quantity demanded)  (%change in price) »If |e| is less than one, demand is said to be inelastic. »If |e| is greater than one, demand is said to be elastic. »If |e|=1, demand is said to be unitary elastic.

7. -7- 5/5/2015 Other Elasticities l Definition: income elasticity=(%change in quantity demanded)  (%change in income) »Inferior (neg.) vs. normal (pos). l Definition: cross-price elasticity of good one with respect to the price of good two = (%change in quantity of good one)  (%change in price of good two) »Substitute (pos.) vs. complement (neg.). l Definition: advertising elasticity=(%change in quantity)  (%change in advertising).

8. -8- 5/5/2015 Describing demand with price elasticity l First law of demand: e<0 (price goes up, quantity goes down). »Discussion: Do all demand curves slope downward? l Second law of demand: in the long run, |e| increases. »Discussion: Give an example of the second law of demand.

9. -9- 5/5/2015 Describing demand (cont.) l Third law of demand: as price increases, demand curves become more price elastic, |e| increases. »Discussion: Give an example of the third law of demand.

10. -10- 5/5/2015 Estimating Elasticities l Definition: Arc (price) elasticity=[(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)]. »Discussion: price changes from $10 to $8, quantity changes from 1 to 2. l Discussion: On a promotion week for Vlasic, the price of the Vlasic pickles drops by 25% and quantity increases by 300%.

11. -11- 5/5/2015 Estimating Elasticities (cont.) l 3-Liter Coke Promotion »Instituted to meet Wal-Mart Promotion

12. -12- 5/5/2015 Quick and Dirty Estimators l Linear Demand Curve Formula, e=p/(p max -p) l Discussion: How high would the price of the brand have to go before you would switch to another brand of running shoes? l Discussion: How high would the price of all running shoes have to go before you should switch to a different type of shoe?

13. -13- 5/5/2015 Market Share Formula l Proposition: The individual brand demand elasticity is approximately equal to the industry elasticity divided by the brand share. »Discussion: Suppose that the elasticity of demand for running shoes is –0.4 and the market share of a Saucony brand running shoe is 20%. What is the price elasticity of demand for Saucony running shoes? l Proposition: Demand for aggregate categories is less- elastic than demand for the individual brands in aggregate.

14. -14- 5/5/2015 Using Elasticities for Prediction l Discussion: The income elasticity of demand for WSJ is 0.50. Real income grew by 3.5% in the United States. »Estimate WSJ demand l Discussion: The 1998 real per-capita median income in Arizona income in Arizona is $30,863; and in Colorado, $40,706 »Estimate difference between per capita consumption in Colorado and in Arizona.

15. -15- 5/5/2015 Elasticity and Revenue l Approximate relationship »%  Rev.= %  P + %  Q »=%  P(1+ %  Q / %  P) »=%  P(1+ e) »=%  Price(1- |e|) l Discussion: In 1980, Marion Barry, mayor of the District of Columbia, raised the sales tax on gasoline sold in the District by 6%.

16. -16- 5/5/2015 Elasticity and MR l Proposition: MR=P(1-1/|e|) »If |e|>1, MR>0. »If |e|<1, MR<0. l Discussion: If demand for Nike sneakers is inelastic, should Nike raise or lower price? l Discussion: If demand for Nike sneakers is elastic, should Nike raise or lower price?

17. -17- 5/5/2015 Elasticity and Pricing l MR>MC is equivalent to »P(1-1/|e|)>MC »P>MC/(1-1/|e|) »(P-MC)/P>1/|e| l Discussion: elas= –2, p=$10 mc= $8, should you raise price? l Discussion: mark-up of 3-liter Coke is 2.7%. Should you raise price?

18. -18- 5/5/2015 Elasticity and pricing (cont.) l Discussion: Sales people MR>0. vs. marketing MR>MC. l Discussion: The Kentucky legislature allows only one race track to be open at a time.