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Any Questions from Last Class? Chapter 6 Simple Pricing COPYRIGHT © 2008 Thomson South-Western, a part of The Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Chapter 6 – Take Aways Aggregate demand or market demand is the total number of units that will be purchased by a group of consumers at a given price. Pricing is an extent decision. Reduce price (increase quantity) if MR > MC. Increase price (reduce quantity) if MR < MC. The optimal price is where MR = MC. Price elasticity of demand, e = (% change in quantity demanded) ÷ (% change in price) Estimated price elasticity = [(Q1 - Q2)/(Q1 + Q2)] ÷ [(P1 - P2)/(P1 + P2)] is used to estimate demand from a price and quantity change. If |e| > 1, demand is elastic; if |e| < 1, demand is inelastic. %ΔRevenue ≈ %ΔPrice + %ΔQuantity Elastic Demand (|e| > 1): Quantity changes more than price. Inelastic Demand (|e| < 1): Quantity changes less than price. Chapter 6 – Take Aways MR > MC implies that (P - MC)/P > 1/|e|; that is, the more elastic demand is, the lower the price. Four factors make demand more elastic: Products with close substitutes (or distant complements) have more elastic demand. Demand for brands is more elastic than industry demand. In the long run, demand becomes more elastic. As price increases, demand becomes more elastic. Income elasticity, cross-price elasticity, and advertising elasticity are measures of how changes in these other factors affect demand. It is possible to use elasticity to forecast changes in demand: %ΔQuantity ≈ (factor elasticity)(%ΔFactor). Stay-even analysis can be used to determine the volume required to offset a change in costs or prices. Review of Chapter 5 Break-even quantity and entry decision Break-even price and shut-down decision Q=F/(P-MC) Profit=Q(P-AC) Sunk costs are vulnerable to postinvestment hold-up Discount rates indicate willingness to trade future for current dollars Introductory Anecdote In 1994, peso devalued by 40% in Mexico Interest rates and unemployment shot up Overall economy slowed dramatically and consumer income fell Demand for Sara Lee hot dogs declined This surprised managers because they thought demand would hold steady, or even increase, since hot dogs were more of a consumer staple Surveys revealed decline mostly confined to premium hot dogs And, consumers using creative substitutes Lower priced brands took off but were priced too low Failure to understand demand and to price accordingly was costly Background: Consumer Surplus and Demand Curves First Law of Demand - consumers demand (purchase) more as price falls, assuming other factors are held constant But, the marginal value of consuming each subsequent unit diminishes the more you consume Consumers attempt to maximize their surplus by using marginal analysis Consumer surplus = value to consumer less price paid Definition: Demand curves are functions that relate the price of a product to the quantity demanded by consumers Background: Consumer Surplus and Demand Curves (cont.) Hot dog consumer Values first dog at $5, next at $4 . . . fifth at $1 Note that if hot dogs priced at $3, consumer will purchase 3 hot dogs, not 5 Background: Aggregate Demand Aggregate Demand: each consumer wants one unit; arrange them by what they are willing to pay. To construct demand, sort by value. Price $7.00 $6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $8.00 Discussion: Why do aggregate demand curves slope downward? Role of heterogeneity? How to estimate? $6.00 Price Quantity 1 2 3 4 5 6 7 Marginal Revenue Revenue $7.00 $7.00 $12.00 $5.00 $15.00 $3.00 $16.00 $1.00 $15.00 -$1.00 $12.00 -$3.00 $7.00 -$5.00 $4.00 $2.00 Marginal Analysis of Pricing Pricing is an Extent Decision Profit=Revenue-Cost Lower prices mean higher sales Demand curves help us make decisions to increase profits by modeling revenue Particularly marginal revenue Should I sell another unit? Pricing Tradeoff Lower pricesell more, but earn less on each unit sold Higher pricesell less, but earn more on each unit sold Tradeoff created by downward sloping demand Marginal Analysis of Pricing Marginal analysis finds the right solution to the pricing tradeoff. But only direction, not magnitude. Definition: marginal revenue (MR) is change in total revenue from selling extra unit. If MR>0, then total revenue will increase if you sell one more. If MR>MC, then total profits will increase if you sell one more. Proposition: Profits are maximized when MR=MC Example Start from the top If MR>MC for next step, reduce price Continue until the next price cut would result in MR<MC Price Quantity Revenue $7.00 1 $7.00 $6.00 2 $12.00 $5.00 3 $15.00 $4.00 4 $16.00 $3.00 5 $15.00 $2.00 6 $12.00 $1.00 7 $7.00 MR $7.00 $5.00 $3.00 $1.00 –$1.00 –$3.00 –$5.00 MC $1.50 $1.50 $1.50 $1.50 $1.50 $1.50 $1.50 Profit $5.50 $9.00 $10.50 $10.00 $7.50 $3.00 –$3.50 How do We Estimate MR? Price elasticity is related to MR. Definition: price elasticity= (%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. Estimating Elasticities Definition: Arc (price) elasticity=[(q1q2)/(q1+q2)] [(p1-p2)/(p1+p2)]. Discussion: price changes from $10 to $8; quantity changes from 1 to 2. Example: On a promotion week for Vlasic, the price of Vlasic pickles drops by 25% and quantity increases by 300%. Estimating Elasticities (cont.) 3-Liter Coke Promotion Instituted to meet Wal-Mart promotion Product 3 Liter Q 3-liter P of 3-liter Initial 210 $1.79 Final 420 $1.50 % Change 66.67% -17.63% Elasticity -3.78 2 Liter 120 $1.79 48 $1.50 -85.71% -17.63% 4.86 870 $0.60 1356 $0.51 43.67% -16.23% -2.69 Q 2-liter P of 3-liter Total Liters Q liters P liters Intuition: MR and Price Elasticity %Rev ≈ %P + %Q Elasticity tells you the size of |%P| relative to |%Q| If demand is elastic If demand is inelastic If P↑ then Rev↑ If P↓ then Rev↓ Discussion: In 1980, Marion Barry, mayor of the District of Columbia, raised the sales tax on gasoline sold in the District by 6%. If P↑ then Rev↓ If P↓ then Rev↑ Formula: Elasticity and MR Proposition: MR=P(1-1/|e|) If |e|>1, MR>0. If |e|<1, MR<0. Discussion: If demand for Nike sneakers is inelastic, should Nike raise or lower price? Discussion: If demand for Nike sneakers is elastic, should Nike raise or lower price? Elasticity and Pricing MR>MC is equivalent to P(1-1/|e|)>MC P>MC/(1-1/|e|) (P-MC)/P>1/|e| Discussion: e= –2, p=$10, mc= $8, should you raise price? Discussion: mark-up of 3-liter Coke is 2.7%. Should you raise price? Discussion: Sales people MR>0 vs. marketing MR>MC. What Makes Demand More Elastic? Products with close substitutes have elastic demand. Demand for an individual brand is more elastic than industry aggregate demand. Products with many complements have less elastic demand. Describing Demand with Price Elasticity First law of demand: e<0 (price goes up, quantity goes down). Discussion: Do all demand curves slope downward? Second law of demand: in the long run, |e| increases. Discussion: Give an example of the second law of demand. Describing Demand (cont.) 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. HFCS Price Sugar Price HFCS Demand HFCS Quantity Other Elasticities Definition: income elasticity=(%change in quantity demanded) (%change in income) 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) Inferior (neg.) vs. normal (pos). Substitute (pos.) vs. complement (neg.). Definition: advertising elasticity=(%change in quantity) (%change in advertising) . Discussion: The income elasticity of demand for WSJ is 0.50. Real income grew by 3.5% in the United States. Estimate WSJ demand Stay-Even Analysis Stay-even analysis tells you how many sales you need when changing price to maintain same profit level Q1 = Q0*(P0-VC0)/(P1-VC0) When combined with information about elasticity of demand, the analysis gives a quick answer to the question of whether changing price makes sense To see the effect of a variety of potential price changes, we can draw a stay-even curve that shows the required quantities at a variety of price levels Stay-Even Curve Example Note that if demand is elastic, price cuts increase revenue When demand is inelastic, price increases will increase revenue $30 $28 Inelastic Demand (e = -0.5) $26 $24 $22 $20 Elastic Demand (e = -4.0) $18 $16 300 400 500 600 700 800 900 1000 Alternate Intro Anecdote 1993 Snickers was first Western-style candy bar in Russia Priced the same as in Great Britain Distributor marked up 600% and pocketed the difference Mars did not appreciate how novel their product was and how much customers would be willing to pay; the distributor, however, did understand. By the time Mars figured understood this, competitors had entered and the novelty had decreased dramatically The purpose of this chapter is to teach you how to price products and to avoid mistakes like this. Extra: Quick and Dirty Estimators Linear Demand Curve Formula, e=p/(pmax-p) Discussion: How high would the price of the brand have to go before you would switch to another brand of running shoes? Discussion: How high would the price of all running shoes have to go before you should switch to a different type of shoe? Extra: Market Share Formula 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? Proposition: Demand for aggregate categories is less-elastic than demand for the individual brands in aggregate.