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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 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 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.