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Chapter 14: Advanced Pricing
Techniques
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Advanced Pricing Techniques
• Price discrimination
• Multiple products
• Cost-plus pricing
14-2
Capturing Consumer Surplus
• Uniform pricing
• Charging the same price for every unit of the
product
• Price discrimination
• More profitable alternative to uniform pricing
• Market conditions must allow this practice to
be profitably executed
• Technique of charging different prices for the
same product
• Used to capture consumer surplus (turning
consumer surplus into profit)
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The Trouble with Uniform Pricing
(Figure 14.1)
14-4
Price Discrimination
• Exists when the price-to-marginal cost
ratio differs between two markets
PA
PB

MC A MCB
14-5
Price Discrimination
Three conditions necessary to practice
price discrimination profitably:
1) Firm must possess some degree of market
power
2) A cost-effective means of preventing resale
between lower- and higher-price buyers
(consumer arbitrage) must be implemented
3) Price elasticities must differ between
individual buyers or groups of buyers
14-6
First-Degree (Perfect)
Price Discrimination
• Every unit is sold for the maximum price
each consumer is willing to pay
• Allows the firm to capture entire consumer
surplus
• Difficulties
• Requires precise knowledge about every
buyer’s demand for the good
• Seller must negotiate a different price for every
unit sold to every buyer
14-7
First-Degree (Perfect) Price
Discrimination (Figure 14.2)
14-8
Second-Degree Price Discrimination
• Lower prices are offered for larger
quantities and buyers can self-select the
price by choosing how much to buy
• When the same consumer buys more
than one unit of a good or service at a
time, the marginal value placed on
additional units declines as more units
are consumed
14-9
Examples of Second Degree Price
Discrimination
• Two-part pricing
• Block pricing
14-10
14-10
Second-Degree Price Discrimination
• Two-part pricing
• Charges buyers a fixed access charge (A) to
purchase as many units as they wish for a constant
fee (f) per unit
• Total expenditure (TE) for q units is: TE  A  fq
TE A  fq
Average price (p) is: p 

q
q
Average price declines
as more is purchased
A
 f
q
14-11
Second-Degree Price Discrimination
• When consumers have identical
demands, entire consumer surplus can
be captured by:
• Setting f *= MC
• Setting A* = consumer surplus (CS)
• Optimal usage fee when two groups of
buyers have identical demands is the
level for which MRf = MCf
14-12
Inverse Demand Curve for Each of 100
Identical Senior Golfers (Figure 14.3)
14-13
Summary of Two Part Pricing
• Consumers will purchase product until marginal
benefit = unit price
• Unit price will at least cover marginal cost
• With consumers with different preferences unit price
will be above marginal cost
• Consumers will choose to purchase as long as
consumer surplus given unit price is greater than
lump-sum fee (right to purchase)
• With identical preferences monopolist will capture the
entire consumer surplus
• With different preferences some consumers will retain
part of their consumer surplus
14-14
14-14
Second-Degree Price Discrimination
• Declining block pricing
• Offers quantity discounts over successive
discrete blocks of quantities purchased
14-16
Block Pricing with Five Blocks
(Figure 14.5)
Compare unit price of an additional block to MC
14-17
Third-Degree Price Discrimination
• If a firm sells in two markets, 1 & 2
• Allocate output (sales) so MR1 = MR2
• Optimal total output is that for which
MRT = MC
• For profit-maximization, allocate sales of
total output so that
MRT = MC = MR1 = MR2
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Third-Degree Price Discrimination
• Equal-marginal-revenue principle
• Allocating output (sales) so MR1 = MR2
which will maximize total revenue for the
firm (TR1 + TR2)
• More elastic market gets lower price
• Less elastic market gets higher price
• IF MR1 ≠ MR2 then shifting a unit of sales
from the lower marginal revenue market to
the higher marginal revenue market will
increase revenue and leave total cost
unchanged.
14-19
Allocating Sales Between Markets
(Figure 14.6)
14-20
Constructing the Marginal Revenue
Curve (Figure 14.7)
Horizontally sum MR curves
14-21
Profit-Maximization Under Third-Degree
Price Discrimination (Figure 14.8)
14-22
Third degree price discrimination
MR A  MRB
1
1
PA (1 
)  PB (1 
)
EA
EB
if
E A  Eb
then PA  PB
14-23
Example of third degree price
discrimination
• Bigsoft sells software to students and
commercial users
• It prices the software at $100 for commercial
users and $50 to students.
• Commercial users have a price elasticity of
demand of -1.5 and students have a price
elasticity of demand of -4 at the current
prices.
• Is the firm practicing optimal third degree
price discrimination?
14-24
Bigsoft example
• MR = P(1+1/E)
• Commercial users
• MR= $100(1-1/1.5) =$100 (1-.67)= $33
• Student users
• MR = $50 (1-1/4) = $37.5
• How much can Bigsoft increase revenues by
shifting one sale?
• $37.5-33 = 4.5
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Bigsoft example
• Suppose we have constant price
elasticities of demand and constant
marginal cost
• Ec = -1.5
• Es = -4
• MC = $40
• What are optimal prices?
14-26
Bigsoft example
• MRc = MRs = MC
• MRc = $40, MRs = $40
• Given that MR = P(1+1/E) then
P = MR/(1+1/E)
• Pc = $120 and Ps = $53.33
14-27
Multiple Products
• Related in consumption
• For two products, X & Y, produce & sell
levels of output for which
MRX = MCX and MRY = MCY
• MRX is a function not only of QX but also
of QY (as is MRY) – conditions must be
satisfied simultaneously
• Example: Disney sells DVD and
complementary toys
14-28
Disney studios
• Disney is considering lowering the price of its
latest DVD from $20 to $15. This will increase
unit sales but lower profits from the sale of
the DVD’s by $10 million.
• Increased sales of the DVDs will produce
more sales of action figures. If the profit
margin on an action figure is $5, how many
more action figures must Disney sell to offset
the decline in profits on the DVDs?
• Answer ($10 million/$5) = 2 million
14-29
14-29
Multiple Products
• Related in production as substitutes
• For two products, X & Y, allocate
production facility so that
MRPX = MRPY
• Optimal level of facility usage in the long
run is where MRPT = MC
• For profit-maximization:
MRPT = MC = MRPX = MRPY
14-30
JBL Plastics
• JBL has a vacuum press that can produce plastic
cars or tanks.
• The marginal cost of producing two cars or one tank
is $5.
• The marginal revenue from the sale of a toy car is $3
and the price is $6.
• The marginal revenue from the sale of a toy tank is $7
and the price is $14.
• MRPc from toy cars is $3x2= $6
• MRPt from toy tanks is $7x1=$7
• Should JBL readjust the ratio of cars to tanks it is
producing so that
MRPt= MRPc= MC
14-31
14-31
Profit-Maximizing Allocation of
Production Facilities (Figure 14.9)
Horizontally sum MRP curves
14-32
14-32
Multiple Products
• Related in production as complements
• To maximize profit, set joint marginal revenue
equal to marginal cost:
MRJ = MC
• If profit-maximizing level of joint production
exceeds output where MRJ kinks, units
beyond zero MR are disposed of rather than
sold
• Profit-maximizing prices are found using
demand functions for the two goods
14-33
14-33
Profit-Maximization with Joint
Products (Figure 14.11)
Vertically sum MR curves
14-34
14-34
Farmer Jones
• The marginal revenue from another cow
brought to market includes marginal
revenue of $300 from the sale of beef at a
price of $500 and a price of $50 and
marginal revenue $25 from the sale of the
hide.
• If the marginal cost of bringing another
cow to market is $350, should he
slaughter another cow?
14-35
14-35
Farmer Jones
Product
Marginal Revenue
Beef
$300
Hide
25
Total MR
$325
Marginal Cost
$350
14-36
Bundling Multiple Products
• When price discrimination is not possible,
bundling multiple goods and charging a
single price can be more profitable than
charging individual prices for multiple
goods
• Two conditions for profitable bundling
• Consumers must have different demand
prices for each good in the bundle
• Demand prices must be negatively correlated
across consumer types
14-37
Bundling of Tickets to Football Game
(a) Max TR =$3,300 = 2 x $1,400 + $500
(b) Max TR = $4,000 = 2 x $2,000
14-38
Cost-Plus Pricing
• Common technique for pricing when firms
do not wish to estimate demand & cost
conditions to apply the MR = MC rule for
profit-maximization
• Price charged represents a markup
(margin) over average cost:
P = (1 + m) ATC
Where m is the markup on unit cost
14-39
Cost-Plus Pricing
• Does not generally produce profitmaximizing price
• Fails to incorporate information on demand
& marginal revenue
• Uses average, not marginal, cost
14-40
Practical Problems with
Cost-Plus Pricing (Figure 14.13)
Manager assumes the firm can produce 5,000
units and sell at a 50 percent mark-up
14-41
Consider Optimal Markup Over MC
Relative to Price
P  MC
Lerner index 
P
MR  MC
1
P(1  )  MC
E
P  MC
1

P
E
14-42