Chapter 6Simple Pricing

Managerial Economics: A Problem Solving Approach (2nd Edition)Luke M. Froeb, luke.froeb@owen.vanderbilt.edu

Brian T. McCann, brian.mccann@owen.vanderbilt.edu

Website, managerialecon.com

COPYRIGHT © 2008Thomson South-Western, a part of The Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license.

Chapter 6 – Summary of main points• 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 – Summary (cont.)• MR > MC implies that (P - MC)/P > 1/|e|; in words, if the

actual markup is bigger than the desired markup, reduce price• Equivalently, sell more

• 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.

Introductory anecdote: Gas prices

• US: From early 2007 to mid 2008 gas prices rose in the US.• Gas prices caused people to find alternate methods of work and

travel to avoid using gas. • Some farms began using mules instead of tractors

• India: In Rajasthan, the rising gas prices caused many farmers to switch from tractors to camels on farms.• As oil prices rose, demand for camels increased.• Prices for camels tripled over a two-year period.

• A US company, NNS, that produces potash fertilizer experienced an increase in input costs due to their use of petrochemicals.• NNS doubled the price of the generic fertilizer, and priced it’s

branded fertilizer at a 35% premium above the generic price. • Costs increased rapidly over the first two quarters combined

with NNS’s policy of quarterly price revision led to stockouts and a price that ended up being 25% below the generic – NNS could have earned $13 million but failed to maintain their premium

Background: consumer surplus and demand curves• First Law of Demand - consumers demand (purchase)

more as price falls, assuming other factors are held constant.

• Consumers make consumption decisions using marginal analysis, consume more if marginal value > price

• But, the marginal value of consuming each subsequent unit diminishes the more you consume.

• Consumer surplus = value to consumer - 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 price is $3, consumer will purchase 3 hot dogs

Background: aggregate demand• Aggregate Demand: the buying behavior of a group of

consumers; a total of all the individual demand curves.

• To construct demand, sort by value.

• Discussion: Why do aggregate demand curves slope downward?

• Role of heterogeneity?

• How to estimate?

Price Quantity RevenueMarginal Revenue

$7.00 1 $7.00 $7.00$6.00 2 $12.00 $5.00$5.00 3 $15.00 $3.00$4.00 4 $16.00 $1.00$3.00 5 $15.00 -$1.00$2.00 6 $12.00 -$3.00$1.00 7 $7.00 -$5.00

$0.00

$2.00

$4.00

$6.00

$8.00

$0.00 $2.00 $4.00 $6.00 $8.00

Pricing trade-off• Pricing is an extent decision

• Profit= Revenue - Cost

• Demand curves turn pricing decisions into quantity decisions: “what price should I charge?” is equivalent to “how much should I sell?”

• Fundamental tradeoff:

• Lower price sell more, but earn less on each unit sold

• Higher price sell less, but earn more on each unit sold

• Tradeoff created by downward sloping demand

Marginal analysis of pricing• Marginal analysis finds the profit increasing solution

to the pricing tradeoff.

• It tells you only whether to raise or lower price, not .

• 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: finding the optimal price

• Start from the top

• If MR > MC, reduce price (sell one more unit)

• Continue until the next price cut (additional sale) until MR<MC

How do we estimate MR?

• Price elasticity is a factor in calculating MR.

• Definition: price elasticity of demand (e)

• (%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=

[(q1-q2)/(q1+q2)] [(p1-p2)/(p1+p2)].

• Discussion: Why, when price changes from $10 to $8, does quantity changes from 1 to 2?

• Example: On a promotion week for Vlasic, the price of Vlasic pickles dropped by 25% and quantity increased by 300%.

• Is the price elasticity of demand -12?

• HINT: could something other than price be changing?

Estimating elasticities (cont.)• 3-Liter Coke Promotion (Instituted to meet Wal-

Mart promotion)• Compute price elasticity of 3 liter coke; cross price

elasticity of 2 liter coke with respect to 3 liter price;

Initial Final % Change Elasticity3 Liter Q 3-liter 210 420 66.67% -3.78

P of 3-liter $1.79 $1.50 -17.63%

2 Liter Q 2-liter 120 48 -85.71% 4.86P of 3-liter $1.79 $1.50 -17.63%

Total Liters Q liters 870 1356 43.67% -2.69P liters $0.60 $0.51 -16.23%

Product

Intuition: MR and price elasticity

• Revenue and price elasticity are related. • %Rev ≈ %P + %Q

• Elasticity tells you the size of |%P| relative to |%Q|

• If demand is elastic • If P↑ then Rev↓• If P↓ then Rev↑

• 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%. What happened to gas sales and availability of gas? Why?

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 prices?

• Discussion: mark-up of 3-liter Coke is 2.7%. Should you raise the 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 ( as 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.

Sugar Price

HFCS Quantity

HFCS Price

HFCS Demand

Other elasticities• Definition: income elasticity measures the change in

demand arising from a change in income

• (%change in quantity demanded) (%change in income)

• Inferior (neg.) vs. normal (pos).

• 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.).

• Definition: advertising elasticity; a change in demand arising form a change in advertising

• (%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 the same profit level

• Q1 = Q0*(P0-VC0)/(P1-VC0)

• When combined with information about the elasticity of demand, the analysis gives a quick answer to the question of whether or not 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

$16

$18

$20

$22

$24

$26

$28

$30

300 400 500 600 700 800 900 1000

Elastic Demand (e = -4.0)

Inelastic Demand (e = -0.5)

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.

Alternate introductory anecdote

• In 1994, the peso devalued by 40% in Mexico• Interest rates and unemployment shot up• Overall economy slowed dramatically and consumer

income fell

• Concurrently, 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 than a luxury item.

• Surveys revealed the decline was mostly confined to premium hot dogs

• And, consumers were using creative substitutes• Lower priced brands did take off but were priced too low.

• Failure to understand demand and to price accordingly was costly

261. Introduction: What this book is about2. The one lesson of business3. Benefits, costs and decisions4. Extent (how much) decisions5. Investment decisions: Look ahead and reason back6. Simple pricing7. Economies of scale and scope8. Understanding markets and industry changes9. Relationships between industries: The forces moving us towards long-run equilibrium10. Strategy, the quest to slow profit erosion11. Using supply and demand: Trade, bubbles, market making 12. More realistic and complex pricing13. Direct price discrimination14. Indirect price discrimination15. Strategic games16. Bargaining 17. Making decisions with uncertainty 18. Auctions19. The problem of adverse selection20. The problem of moral hazard21. Getting employees to work in the best interests of the firm22. Getting divisions to work in the best interests of the firm23. Managing vertical relationships24. You be the consultantEPILOG: Can those who teach, do?

Managerial Economics - Table of contents