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

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-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?

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-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?

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-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

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-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

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-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.

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-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).

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-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.

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-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.

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-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%.

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

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-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?

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-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.

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-14- 5/5/2015 Using Elasticities for Prediction l Discussion: The income elasticity of demand for WSJ is 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.

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-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%.

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-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?

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-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?

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-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.

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