Managerial economics 3rd by froeb ch06

11

Chapter 6
Simple Pricing
1

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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.
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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,
which is how businesses use marginal analysis.

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Introductory anecdote: Hot
Wheels
• Mattel: introduced Hot Wheels in 1968, kept price
below $1.00 for 40 years, even as production costs
rose
• Finally tested a price increase, experienced profits
increase of 20%

• Why? Profit=(P-C)xQ
• Businesses tend to focus on C and Q, neglect P

• In many instances, companies can make money by
simply raising prices

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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
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Background: consumer surplus
and demand curves (cont.)
• Pizza consumer

• Values first slice at $5, next at $4 . . . fifth at $1

• Note that if pizza slice price is $3, consumer will
purchase 3 slices

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•

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

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
$8.00

•

$6.00
Discussion: Why do aggregate
demand curves slope downward?

P r ic e

• Role of heterogeneity?
$4.00
• How to estimate?
$2.00

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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
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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
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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
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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.

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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?

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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;

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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?

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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?

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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.

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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.

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•

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.

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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

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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
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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.

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Stay-even curve example
• Note that if
demand is elastic,
price cuts
increase revenue
• When demand is
inelastic, price
increases will
increase revenue

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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?

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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.

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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

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