Chapter 6
Simple 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 © 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 – 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.
Price
$7.00
$6.00
$5.00
$4.00
$3.00
$2.00
$1.00
Quantity
1
2
3
4
5
6
7
Revenue
$7.00
$12.00
$15.00
$16.00
$15.00
$12.00
$7.00
Marginal
Revenue
$7.00
$5.00
$3.00
$1.00
-$1.00
-$3.00
-$5.00
$8.00
• Discussion: Why do aggregate demand curves slope downward?
$6.00
• How to estimate?
Price
• Role of heterogeneity?
$4.00
$2.00
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;
3 Liter
2 Liter
Product
Q 3-liter
P of 3-liter
Initial
210
$1.79
Final
420
$1.50
% Change
66.67%
-17.63%
Elasticity
-3.78
Q 2-liter
P of 3-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
Total Liters Q liters
P liters
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.
HFCS
Price
Sugar Price
HFCS Demand
HFCS Quantity
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
$30
$28
Inelastic Demand (e = -0.5)
• When demand is
inelastic, price
increases will increase
revenue
$26
$24
$22
$20
Elastic Demand (e = -4.0)
$18
$16
300
400
500
600
700
800
900
1000
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
26
1. Introduction: What this book is about
Managerial Economics 2. The one lesson of business
3. Benefits, costs and decisions
Table of contents
4. Extent (how much) decisions
5. Investment decisions: Look ahead and reason back
6. Simple pricing
7. Economies of scale and scope
8. Understanding markets and industry changes
9. Relationships between industries: The forces moving us towards long-run equilibrium
10. Strategy, the quest to slow profit erosion
11. Using supply and demand: Trade, bubbles, market making
12. More realistic and complex pricing
13. Direct price discrimination
14. Indirect price discrimination
15. Strategic games
16. Bargaining
17. Making decisions with uncertainty
18. Auctions
19. The problem of adverse selection
20. The problem of moral hazard
21. Getting employees to work in the best interests of the firm
22. Getting divisions to work in the best interests of the firm
23. Managing vertical relationships
24. You be the consultant
EPILOG: Can those who teach, do?