Pricing Decisions
G Pricing decisions are the most important between the marketing
decisions.
u
It affects profit both directly and indirectly
Profit=Revenue -Total cost
Π = R-TC
Directly: Revenue = Unit price x Quantity sold
Indirectly:
But:
Total cost = Unit cost x Quantity sold
R=P x q
TC=c x q
Quantity is a function of price (the demand curve)
q=q(P)
G Ineffective pricing can prevent the marketing efforts from
financial success.
Planning for Effective Pricing
5 factors must be taken into account in pricing decisions:
1. The objectives of the organization
2. Consumers willingness to pay for the product
3. The costs of producing and marketing the product
4. Competition
5. Changes in 2,3, and 4 over time
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1
Monopoly Pricing for Profit Maximization in a
Static Environment
The situation:
4. & 5. - Not relevant
3. - Assume a fixed unit cost = c
1. - Profit maximization
2. - Consumers willingness to pay for the product
The usual way -- via the demand curve (number of
units that can be sold at various prices)
A. Homogenous market
B. Heterogeneous market
A Homogenous Market
Price, p
p(q)
p*
c=MC
3
2
5
.
1
12
5
.
0
34
0
5
0
q*
The firm s problem:
Demand, q
MR
Max Π = (p-c)q(p)
(
P
p* satisfies the FOC:
dΠ
Π /dp=0 (or Π (p)=0)
The optimizing price, p*: Marginal Revenue, MR=Marginal cost, MC
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2
Derivation of the Optimal Price
Π = (p-c)q(p)
(
dΠ
Π /dp = q+(p-c)dq/dp=0
or
p=c-q(dp/dq)
Price Elasticity
ε =-
∆q/q
=-
∆p/p
∆q
p
∆p
q
where:
ε
q
p
∆q
∆p
= elasticity of quantity demanded with respect to change in price,
=
=
=
=
quantity demanded before price change
old price
change in demand
change in price
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3
Optimal Price Analysis
p=c-q(dp/dq)
or
p=c
p
- dq/q = c+p/εε
dp/p
Willingness to pay
p* =
ε
ε− 1
c
Cost
Optimal Price Analysis - con t
Considering:
p=c+p/ε
We obtain:
p-c
=1 /ε
p
- if ε >1 (the demand rises or falls by more than price falls or rises in percentage terms)
then 1/ ε is small therefore p is close to the marginal cost
- if ε <1 (the demand rises or falls by less than price falls or rises in percentage terms)
then 1/ ε is large therefore p is large relative to the marginal cost
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4
Cost and Optimal Price
Total Cost = F + MC x Quantity
p* =
ε
ε− 1
ΜC
u
Therefore only MC is involved in the pricing decision
u
The fixed cost (F) is involved in the GO, NO-GO decision
Profit=Revenue-Total Cost (nonnegative)
Understanding
Price Discrimination
G If consumers are homogeneous, and only a single
price can be charged, then finding the best price
that maximizes the seller s profit it is the best the
firm can do.
G If consumers differ in their willingness to pay,
then the profit-maximizing firm can increase its
profits by charging a variety of prices, that is, by
price discriminating.
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5
Example
Suppose there are four equal-size segments of
customers in the market for a textbook, each
willing to pay a different price for it. Segment A is
willing to pay up to $40, segment B up to $30,
segment C up to $20, and segment D up to $10.
Assume that no customer will buy more than one
book and will buy only if his or her customer
surplus (that is, reservation price minus the price
asked) is nonnegative. Suppose the firm s variable
cost per book is $5, and there are no fixed costs.
The Best Single Price to Charge
No point in charging a price less than $10-everyone is
willing to pay at least $10, and there is no point in
charging a price in between the various reservation
prices.
N - is the number of
consumers in each
segment
Price ($)
Profits ($)
10
4N(10-5)=20N
20
3N(20-5)=45N
30
2N(30-5)=50N
40
N(40-5)=35N
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6
Charging a Variety of Prices
G Suppose that a monopolistic firm can charge four
different prices to the four segments.
G Firm s profits:
$N[(40-5)+(30-5)+(20-5)+(10-5)]=$80N.
This kind of price discrimination is known as
direct price discrimination
Single Price vs. Price Discrimination
Price
40
40
30
30
20
20
10
10
Optimal profit
under SINGLE
price
55
MC
11
22
33
44
Customer
Optimal profit under price discrimination
= (30-5)x2+10+(20-5)+(10-5)=80
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7
Market Served and Customer Surplus:
Single Price vs. Price Discrimination
customers
1& 2
0+10= 10
customers
1 , 2, 3& 4
0+0+0+0 =0
Under price discrimination:
❏ The firm extracts every customer s complete surplus.
❏ The firm serves every customer who is willing to pay at least as much as the firm s
cost (inclusion
inclusion).
Suppose the firm s variable cost per book is $15
Price
40
40
30
30
20
20
15
15
Optimal profit
under SINGLE
price
MC
10
10
11
22
33
44
Customer
❏ Customer 4 is excluded
excluded: The firm does not serve any customer
whose willingness-to-pay is less than the firm s costs.
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8
Features of Direct Price-Discrimination
1. The firm extracts every customer s complete surplus. (Extraction: No
money is left on the table. )
2. The firm serves every customer who is willing to pay at least as much as the
firm s cost (in the case $5: inclusion).
3. The firm does not serve any customer whose willingness-to-pay is less than
the firm s costs (exclusion: in the case $15).
Conclusion
Direct price discrimination, seems like an
excellent idea for firm, but implementing it
in practice involves several difficulties.
difficulties
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9
Difficulties Involved in Practicing Price
Discrimination
1
Identifying customers reservation prices is difficult.
2
Targeting a particular price to a particular segment is
difficult.
3
It is difficult to prevent arbitrage: consumers with low
reservation prices may buy up a lot of the product and
supply it to high-reservation-price consumers at a price
lower than their reservation price.
4 Charging different prices to different segments may be
illegal.
5
Customers may view price discrimination as unfair.
Despite the Difficulties DPD Does Exists
G Examples of direct price discriminations:
u
local telephone companies discriminate between residential
and business users in their prices
u
senior citizen and student discounts are forms of this type of
price discrimination.
In all these cases the points 1-5 (identification, targeting,
arbitrage prevention, legality requirements) are satisfied.
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10
Price Discrimination (Indirect)
Indirect Price Discrimination
To identity:
Their preferences
for some attributes
of the product
The reservation
prices of different
segments
The firm can tie its different prices to different levels of the
attributes and allow customers to freely choose the level of the
attribute they want to buy.
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11
Example of Indirect PD
Airline industry pricing: offer a variety of fares with various
restrictions (and some with no restrictions).
u
The higher fares are associated with no advance purchase
requirements, no cancellation penalties, and so on.
u
The lower fares have many of these restrictions.
The intention is to create a product line differentiated on the
restrictions attribute with different products to different
segments.
u
The business traveler finds the restrictions costly and
finds the higher unrestricted fares appealing.
u
The vacation traveler finds the lower fares appealing and
does not mind the restrictions.
Non-Linear Pricing or
Quantity Discounts
Purchase
Quantity
Reservation
Price
Two-part tariff
Block tariff
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12
Two-Part Tariff
G A fixed up-front payment F and then a per-unit charge p.
u
membership clubs
v membership fee and offer discounted merchandise
v video clubs (membership fee+per movie)
u
a durable good + supplies
v instant camera+ film
ò
fixed fee + per-unit charge of using the durable good
v razor + blades
v copying machines+copier paper
Two-Part Tariff (TPT) &
Linear Pricing (LP)
G A TPT is similar to a simple LP in that the marginal
price charged is constant in quantity.
G A TPT is a quantity discount scheme only because the
average price paid
(F/Q)+p
Q
G In a LP scheme both marginal and average prices are
constant for any quantity purchased.
G The presence of a fixed fee in a TPT allows the seller to
extract more consumer surplus than a simple LP
scheme.
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13
TPT Extracts Consumer Surplus
Price, p
Marginal revenue
A
Demand curve
E
p*
Marginal cost = C
F
B
Q*
p* = optimal LP
Demand, Q
Qc
(F*,p *)
(Fc,C)
Q* =Demand at p*
Fc =Area ABF=Fixed fee under optimal two-part tariff (unit price=C)
F* = Area Ap* E=Fixed fee under non-optimal two-part tariff (unit price=p* )
Optimal TPT: Two Segments
Price, p
QA
QB
A
R
S
p1
T
B
Marginal cost = C
O
qA
qB
Demand, Q
1. The seller offers the product only to segment B...
Fc =area ABO and has a profit equal to Π1= Fc .
2. The seller offers the product to segments A and B.
F1=area RST and will have a profit: Π2= 2F1 + (qA+qB)(p1-C),
where p1 maximizes Π2.
The optimal TPT is either (F1,p1) or (F c,C)
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14
Illustrative Example
Price, p
qA=5-p
qB=6-p
A
R
S
p1
T
B
Marginal cost = 1
O
qA
qB
Demand, Q
1. If the seller offers the product only to segment B...
Fc =area ABO=(6-1)(6-1)/2= 12.5 and has a profit equal to Π1= Fc = 12.5.
2. If the seller offers the product to segments A and B.
F1=area RST= (5-p1)(5-p1)/2 and will have a profit:
Π2= 2F1 + (qA+qB)(p1-C)= (5-p1)(5-p1)+(11-2p1)(p1-1),
where p1 maximizes Π2.
d Π2./dp1=0: p1=1.5, F1=6.125 Π2=16.25.
The optimal TPT is (F1,p1)= (6.125 , 1.5).
A Two-Part Tariff Can Also be Used to
Price Discriminate
G Through the fixed fee; it can be set so high that
some, but not all, consumers don t purchase the
product.
u
The consumers with demand curve A would not
purchase the product at all if the fixed fee is set equal to
the consumer surplus with demand curve B.
G By charging different average prices to different
customers.
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15
TPT to Price Discriminate
Price, p
QA
QB
A
R
S
p1
T
B
Marginal cost = C
O
qA
The optimal TPT is either
qB
(F1,p 1)
Demand, Q
or
(Fc,C);
F 1=Area
RST, Fc=Area ABO
1. If (F1 ,p 1) is the optimal TPT, then the price discrimination is trough average price.
Each customer pays a different average price:
F1/qA+p 1> F 1/qB+p1 .
2. If (Fc,C) is optimal then the price discrimination is trough the fixed fee since customer
A would not buy at a fixed fee which is greater than its surplus for this price.
Block Tariff
Are the most widely used form of quantity discount
It has at least two marginal prices; it may or may not have a
fixed fee
local telephone company tariffs typically have a fixed
subscription fee as well as several price breaks built
into the schedule
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16
Three-Block Tariff with no Fixed Fee
Total amount paid=p1Q 1+p 2(Q2-Q1)+p 3(Q 3-Q2)
(p1,Q1,p2,Q2-Q1,p3)
p3
Total
p2
Amount
Paid
p1
Q1
Q2
Q3 Quantity Purchased (Q)
Block Pricing Can Improve Two-Part Tariff
Price, p
QA
A
QB
R
S
p1
T
p2
B
Qa
F1=Area
RST,
Marginal cost = C
O
Fc =Area
Qb
Demand, Q
Qb
ABO
The optimal TPT is either (F1,p1) or (Fc, C). If (F1,p1) is the optimal TPT,
then the two-block scheme (p1,Qb,p2) with fixed-payment F1 yields even
greater profits.
profit by TPT = 2F1+(p1-C)(Qa+Qb)
profit by TB = 2F1+(p1-C)(Qa+Qb) + (p2 -C)(Qb -Qb)
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Optimal Block Pricing
Max Π = 2F1+(p1-C)(Qa+Qb ) + (p2-C)(Q b -Qb )
p1,p2
=(5-p1)2 + (p1 - 1)(11 - 2p1) + (p2- 1)(6- p2- 6+ p1)
Q a=5-p, Q b=6-p, C=1
2F1=(5-p1) 2
dΠ / dp1=0
p1*= 5/3=1.66
dΠ / dp2=0
p2*=4/3=1.33
Π∗∗=49/3=16.333>16.25
Other Forms of Price
Discrimination
G Price promotions (impose some inconvenience cost on the consumer)
u
Sales (limited-time reductions in price)
u
Coupons
u
Rebates
G Customer characteristics
u
Age
u
Income/education
u
Membership
G The distribution outlet
u
Specialty stores charge higher prices than supermarkets
G Brand differentiation
u
Selling generics at a lower (unbranded) price than their brand counterparts
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