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程序代写案例-EC620
时间：2021-11-16
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 1 of 39
Topic 1 : Monopoly and Price Discrimination
Lecture Topic Readings*
1 – Sept 13
Slides 2-7
Overview, Calculus tools,
Profit max., Welfare & Monopoly
2.1
2 – Sept 15
Slides 8-17
Group Pricing, Customization
Linear algebra tool
5.1 5.3,
6.2
3 – Sept 20
Slides 18-23
Versioning
Durable goods monopoly
6.1, 6.2, 2.2.2
4 – Sept 22
Slide 24-30
Two-part tariffs
Block Pricing
5.4
5 – Sept 27
Slide 31-35
Bundling and Mixed Bundling
Bundling and Entry deterrence
6.3
6 – Sept 29
Slide 36-39
Cost-based Rationale for Bundling
Complementary products
6.3
MyLS
* Readings refer to the textbook chapter sections
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 2 of 39
What is Industrial Organization?
• Impact of market structure on
➢ …market power, collusion and welfare
➢ …responsiveness of price to demand and cost
➢ …incentives to innovate
➢ …profitability of merger
• Determinants of market structure
➢ …costs and market size
➢ …innovation and advertising
➢ …entry deterrence and predation
• Profit and welfare consequences of business strategy
➢ …price discrimination and versioning
➢ …bundling, tie-ins, 2 part tariffs and block pricing
➢ …mergers, price fixing and vertical restraints
➢ …entry, entry deterrence and innovation
• Tools of industrial organization
➢ …calculus and unconstrained optimization
➢ …methods for solving linear models
➢ …welfare economics
➢ …game theory
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 3 of 39
Unconstrained optimization
• Maximize objective function f(x)
➢ FOC:
= ′() = 0 SOC:
2
< 0
• Maximize objective function f(x1, x2)
FOC.
= 0 i = 1,2, SOC. If =
2
SOC are
< 0 = 1,2 and 1122 − 1221 > 0
• Rules of calculus
f(x,y) = ax2 + bx +c + dxy→
= 2 + +
∫ +
0
= + 0.52
() = →
= = ()
() = →
= −1 =
()
(()())
= ()′() + ()′()
((())
=
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 4 of 39
Monopoly
(QD = (a – P)N, C = cq + d(½)q2 +F)
• Maximize (Q) = P(Q)Q – C(Q)
= ( −
) − −
2
2 −
➢ FOC:
= () + ′() − ′() = 0
= −
2
− ( + ) = 0
➢ SOC:
2
< 0 → −
2
− < 0 (satisfied if d > −
2
)
Figure 1: Profit Maximization
Figure 1
P
MC
MR
D
Q1 Q2 Q3 Q
TC
TR
P
MC
MR
TR
TC
Q1 Q2 Q3 Q
Solution. Use FOC to find Q. Sub Q into demand to get P.
=
( − )
2 +
, =
(1 + ) +
2 +
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 5 of 39
Pricing and Elasticity
= −
% ℎ
% ℎ
= −
∆ ⁄
∆ ⁄
= −
∆
∆
• Demand is more elastic if good…
➢ has close substitutes and search costs are low
➢ takes up large portion of the budget
• Marginal revenue (MR) = TR/Q consists of
➢ …price charged to new buyers minus revenue loss
from price cut to existing buyers
➢ …equals price if firm is a price taker ( =∝)
• Elasticity and MR. Since TR = R(Q) = P(Q)Q then
=
= () + ′() = () (1 −
1
)
• Elasticity and Pricing. MR = MC implies
=
1−
1
→
−
=
1
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 6 of 39
Welfare function if P = a – bQ
Method 1. Welfare = Total Benefit – Total costs
= ∫ ( − ) −
0
∑ ()
=1
= − 0.52 − ∑ ()
=1
Method 2. Welfare = Consumer surplus + profit
= − 0.52 − + ∑
=1
Substitute P = a – bQ
= 0.52 + ∑
=1
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 7 of 39
Method 3. Welfare = Total surplus minus Fixed Costs
Total surplus = Area between Demand and Marginal cost
Example : If () = + then
= ( − ) − 0.52 −
Figure 2 : Total Surplus
a
c
Q
D
MC = AVC = c
Total
Surplus
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 8 of 39
Efficiency and Deadweight Loss
• An allocation is efficient if it maximizes welfare which
implies that goods…
➢ …go to buyers with highest willingness to pay
➢ …are produced at the lowest cost
➢ …go to all buyers willing to pay MC (i.e. P = MC)
• Deadweight loss (DWL)…
➢ …measures the welfare loss due to P > MC
➢ …is illustrated as the triangle between the demand
and MC curves and the P = MC and P > MC outputs
(see Figure 3)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 9 of 39
Figure 3: Deadweight loss & welfare effects of entry
130
PM = 70
10
C
A
QM = 60 QE = 120
MC
D
B
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 10 of 39
Monopoly, welfare effects of entry and DWL
If MC = 10, P = 130 – Q and FC = F then π and W are
= (130 − ) − 10 − and = 0.52 +
Monopoly output. Set
= 0 to get
= 130 − 2 − 10 = 0 → Q = 60
Substitute Q = 60 into demand, profits and welfare to get
P = 70, = 3600 − , WM = 5400 – F
Conclusion. Profitable monopoly entry raises welfare
(i.e. F < 3600 implies F < 5400) because it increases
consumer surplus and has zero impact on existing firms.
Efficient output. Set P = MC = 10 (or set
= 0) to get
130 – Q = 10 →Q = 120
Substitute Q = 120 into demand, profits and welfare to get
P = 10, = −, WE = 7200 – F
Deadweight loss is thus equal to
WE – WM = (7200 – F) – (5400 – F) = 1800
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 11 of 39
Price discrimination is…
• …the practice of charging buyers different prices for
the same product for non-cost reasons
• …feasible if the seller can
➢ ...identify different buyers
➢ ...prevent re-sale between buyers because of…
▪ …transactions costs, nature of product, legal
restrictions (e.g. ROW import bans in Europe).
• …profitable because it allows firms to
➢ …eliminate some deadweight loss (Area C, Figure 3)
➢ …extract more consumer surplus (Area A, Figure 3)
• …legal in Canada provided
➢ …your intent is not predatory
• ...welfare enhancing if more markets are served
• ...welfare reducing if output is re-allocated
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 12 of 39
Group Pricing: Monopolist can price discriminate
[Pi = ai – 4Qi, MC = 8, a1 = 48, a2 = 32]
Use FOC in each market to find output.
FOC:
= +
−
= 0 = 1,2
= ai – 8Qi − 8 = 0
Qi = (ai – 8)/8
Q1 = 5, Q2 = 3
Check SOC
ii = − 8 < 0 i = 1,2, (satisfied)
1122 - 2112 = (-8)(-8) – (0)(0) ≥ 0 (satisfied)
Sub. Qi into demand functions to find prices
P1 = 28, P2 = 20
Profits are given by
π = (28 – 8)5 + (20 – 8)3 = 100 + 36 = 136 > 128
Find consumer surplus in both markets
CS = (½)(48 – 28)(5) + (½) (32 – 20)3 = 50 + 18 = 68
Welfare is given by
W = π + CS = 136 + 68 = 204 < 208
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 13 of 39
Monopolist cannot price discriminate
[Pi = ai – 4Qi, MC = 8, a1 = 48, a2 = 32]
Find market demand and then invert
Q = Q1 + Q2 = (1/4)(48 – P) + (1/4)(32 – P)
P = 40 – 2Q
Use FOC to find Q
FOC:
= +
−
= 0
40 – 4Q − 8 = 0 → Q = 8
SOC: QQ = -4 < 0 (satisfied)
Sub. Q into inverted market demand to find p
P = 40 – 2(8) → P = 24
Sub. p into individual demand to find qi
Qi = (1/4)(ai – P)→Q1 = 6, Q2 = 2
Find profits.
= (24 – 8)8 = 128 > 100 (Serve both markets)
Find consumer surplus in both markets
CSi = (1/2)(48 – 24)6 + (1/2)(32 – 24)2 = 72 + 8 = 80
Welfare is given by
W = + CS = 128 + 80 = 208 > 204
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 14 of 39
Figure 4 : Welfare Loss due to Price Discrimination
P = 24
D1
MC
5 6
Market 1
L
D2
MC
2 3
Market 2
G
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 15 of 39
Group Pricing and non-constant MC
Can price Discriminate.
First order conditions
+
−
= 0 = 1,2
Non-constant MC implies that FOC is a function of Q1
and Q2 and must be solved simultaneously via Cramer’s
Rule. The cross partial derivatives of the profit function
are not zero and this will affect SOC.
Cannot price discriminate
1. Serve both markets. Similar to the constant MC case.
If you get QLD < 0 then serve HD only.
2. Serve high demand only. Set output in LD market
equal to zero and then set MR = MC in HD market.
Note. Since MC is not constant then ‘serve HD only’
solution will not be the same as HD output under price
discrimination.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 16 of 39
Solving linear model using Cramer’s Rule
• Exogenous parameters: aij, ci,
• Endogenous variables : xi
Write system of equations as follows
a11x1 + a12x2 = c1
a21x1 + a22x2 = c2
Express the equations in matrix form
[
11 12
21 22
] [
1
2
] = [
1
2
]
Apply Cramer’s Rule to get solution for x1 and x2
1 =
|
1 12
2 22
|
|
11 12
21 22
|
=
122 − 212
1122 − 2112
2 =
|
11 1
21 2
|
|
11 12
21 22
|
=
112 − 211
1122 − 2112
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 17 of 39
Figure 5a :Price discrimination
Figure 5b: No Price discrimination
D
2
D
1
MR2
MR1 MR
2
1
1
2
QD
MC
D2
D1
D
1
MR
P
1
2
1
QN
MC
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 18 of 39
Price discrimination by location or customization
MCB = 4, MCM = 4 + t, PB = 36 – 4QB, PM = 36 – 4QM, FC = 0
Find MR in both markets
MRB = 36 – 8QB and MRM = 36 – 8QM
Set MR = MC in each market to solve for QU and QE
36 – 8QB = 4 → QB = 4
36 – 8QM = 4 + t →QM = (32 – t)/8
Substitute outputs into inverted demand to find prices
PB = 20 and PM = 20 + t/2
Since difference in prices t/2 are less than the difference in
customization/transportation cost t then the above (i)
represents price discrimination and (ii) eliminates
arbitrage.
Non-linear demand. If demand is not linear then price
differences can be greater, lower or equal to the
transportation/customization cost.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 19 of 39
Versioning/Product proliferation
• Versioning is
➢ …the practice of offering low and high quality
versions of the same product for different prices.
▪ e.g. flights, books
➢ …more profitable than selling a single version if
▪ …the variance in willingness to pay is low for low
quality and high for high quality.
➢ …is price discrimination if difference in prices do not
reflect differences cost of providing quality
• Damaged goods are a special case of versioning…
➢ …in which low quality goods cost more to produce
than high quality goods because of
➢ …the cost of disabling certain product features in the
low quality good
▪ …e.g. printers, software
• Product proliferation : Offerring many horizontally
differentiated products to deter entry.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 20 of 39
Versioning example : Software
N = number of experts, N = number of students
Buyers buy only 1 version
Version Student Expert Costs
Basic $50 $75 $10
Full $100 $400 $20
Single version
Basic Full
PB Profit PF Profit
50 (50 − 10)(N + N) 100 (100 − 20)(N + N)
75 (75 − 10)N 400 (400 − 20)N
Menu of versions
Seller offer : A menu of versions
Basic: pB = __________
Full: pF = _________
Buyer choice
Consumer surplus
Student Expert
Basic
Full
Choice
Profit: π = N(__________) + N(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 21 of 39
Versioning with endogenous quality
NL = number of LD, NH = number of HD, Buyers buy only 1 version
> , () > ()
Version Low Demand High Demand Unit Costs
Low quality c(sL)
High quality c(sH)
Single version
Price Profit
( − c(s))(NL + NH)
( − c(s))NH
Menu of versions
Seller offer : A menu of versions
Low quality: pL = ____________
High quality: pH = ____________
Buyer choice
Consumer surplus
Low Demand High Demand
LQ
HQ
Choice
Profit: π = NL(__________) + NH(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 22 of 39
Durable goods monopoly
• Coase conjecture: If buyers have similar valuations then
durability can ↓ market power and ↑Welfare because…
➢ …buyers who buy exit the market which
➢ …lowers demand and price over time
➢ …buyers thus choose to wait for low prices
➢ …and thus the seller lowers price in early periods
➢ …To avoid the Coase problem the seller can
▪ …lease rather than sell
• Case Study: Features of textbook market are...
➢ …textbooks are durable
➢ …used books compete with new books
➢ …new editions help to eliminate used books market
➢ …fewer books purchased if new edition is expected
➢ …publisher revenue is unaffected by # of editions
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 23 of 39
Durable goods examples
Assumptions: Zero cost, No discounting (R = 1), 2 buyers
Example 1 Valuations: $50 for Buyer 1, $30 for Buyer 2
Strategy
Period 1
profit
Period 2
profit
Total
profit
Consumer
surplus
Welfare
Sell to both buyers
in Period 1
2×2×30 - 120 1×2×
(50 – 30)
160
Sell to Buyer 1 in
Period 1 and to
Buyer 2 in Period 2
1×2×50 –
(50 – 30)
1×1×30 110
1×1×
(50 − 30)
130
Lease to both
buyers in both
periods
2×1×30 2×1×30 120 1×2×
(50 – 30)
160
Example 2 Valuations: $50 for Buyer 1, $20 for Buyer 2
Strategy
Period 1
profit
Period 2
profit
Total
profit
Consumer
surplus
Welfare
Sell to both buyers
in Period 1
2×2×20 - 80 1×2×
(50 − 20)
140
Sell to Buyer 1 in
Period 1 and to
Buyer 2 in Period 2
1×2×50 –
(50 – 20)
1×1×20 90
1×1×
(50 − 20)
120
Lease to Buyer 1 in
both periods
1×1×50 1×1×50 100 0 100
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 24 of 39
Two-part tariffs
• Two-part tariffs…
➢ …specify a fixed fee (F) & a user fee (P)
▪ e.g. utilities, memberships
➢ …can be achieved via tie-ins (Ch 6.3.2)
▪ e.g. video players/video games
➢ …let the seller capture (i) more buyer surplus & (ii)
the efficiency loss from setting P > MC.If buyers are
identical then the profit-maximizing strategy is to set
P = MC and F = CS.
• If buyers are not identical and price discrimination is
possible then Pi = MC and Fi = CSi
C
Q0 Q1
A
P0
P1
Demand
MC
B
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 25 of 39
Two buyer types and a Single two-part tariff
qL qH qH *
A
B
C
D
E
F
MC
HD LD
G
pL
Set p = MC, F = CSHD = ________
π = NLD(______________) + NHD(____________)
Set p = pL > MC, F = CSLD = ______________
π = NLD(______________) + NHD(____________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 26 of 39
Two buyer types and a Menu of two part tariffs
qL qH qH *
A
B
C
D
E
F
MC
HD LD
G
pL
pH
Seller offer : A menu of two-part tariffs given by
Contract L: pL > MC, FL = CSLD = ____________
Contract H: pH = MC, FH = FL + CSHD = ________
Buyer choice
Net consumer surplus
LD Buyer HD Buyer
Contract L
Contract H
Choice
Profit: π = NLD(__________) + NHD(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 27 of 39
Block Pricing Menu
qL
A
B
C
D
MC
HD
LD
G
F
E
qH *
Seller offer : Block pricing menu
Contract L: ≤ , pL = 0, FL = TBLD = __________
Contract H: ≤
∗ , pH = 0, FH = FL + TBHD = ____
Buyer choice
Net consumer surplus
LD Buyer HD Buyer
Contract L
Contract H
Choice
Profit: π = NLD(__________) + NHD(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 28 of 39
Buyer demand () = − → () =
−
1
Consumer surplus used for 2-part tariffs
Since () =
−
then from slide 6 we get
(()) = 0.5 (
1
) ()2
=
= (
1
()) (−) = −()
or Sub q(p) into CS(q(p)) to get () =
.5(−)2
Total Benefit used for Block pricing
Since () =
−
then from slide 6 we get
() = (
) − 0.5 (
1
) 2
=
−
1
= ()
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 29 of 39
Profit maximizing two part tariffs
Single 2 part tariff
= ( − )() + ( + )()
ℎ () = () + ()
() = (())
Set
= 0 then sub
,
,(), () to solve for p.
2 part tariff menu
= [][( − )() + ()]
+ [][()]
ℎ () = (())
() = () + ( = ) − (())
Set
= 0 then sub
,
,
, (), ()
to solve for pL.
Corner solution: If qLD ≤ 0 then serve HD only.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 30 of 39
Profit maximizing block pricing menu
= [() − ] + [() −
∗ ]
ℎ () = ()
() = () + ( =
∗ ) − ()
Set
= 0 then sub
,
to solve for qL.
Corner solution : If you get qL < 0 or
< 0 then firm
serves HD only.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 31 of 39
Bundling is…
• …selling related products as a package
➢ …e.g. cable TV, software, vacation travel, concert
series, automobile option packages
• …more profitable than selling goods individually
➢ …if the variation in the willingness to pay among
buyers is lower for the bundle than for the goods
individually (i.e. bundling ↑ elasticity).
▪ Bundling effects in Cable TV.
• ↑Elasticity (average (0.16), specialty (0.197),
general interest (0.10))
• ↑profits (4.7%), ↓consumer surplus (5%)
➢ … if the incumbent wants to deter entry
➢ …if there are economies of scope
• Mixed bundling is…
• …the practice of selling related products as a package
and individually
• …is more profitable than bundling if…
➢ …buyers who are willing to pay the highest price
for the bundle are not willing to pay the highest
price for the goods individually
➢ …or if the willingness to pay for a good in the
bundle does not exceed its marginal cost
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 32 of 39
Bundling and Mixed bundling example
N = Number of each type, MC = $2.50
Buyer A Buyer B Buyer C Buyer D
Good 1 $8 $5 $9 $1
Good 2 $4 $5 $1 $9
Bundle $12 $10 $10 $10
Mixed bundling
Seller offer : p1 = _____ p2 = _____ pB = ______
Buyer A Buyer B Buyer C Buyer D
Good 1 $8 − $5 − $9 − $1 −
Good 2 $4 − $5 − $1 − $9 −
Bundle $12 − $10 − $10 − $10 −
Choice
π = N(__ ) + N( __) + N(_ _) + N( __) = _____
5.00
2.50
10
N 4N
9
Good 1 Good 2 Bundle
9
5
N 2N 3N 4N
4 2.50
8
N 2N 3N 4N
5
PT = 9 T = (9−2.5)×N PS = 9 S = (9−2.5)×N PB = 12 = (12−5)×N
PT = 8 T = (8−2.5)×2N PS = 5 S = (5−2.5)×2N PB = 10 = (10−5)×4N
PT = 5 T = (5−2.5)×3N PS = 4 S = (4−2.5)×3N
Sell Individually : = 11N + 6.5N =17.5N Bundle: = 20N
12
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 33 of 39
Bundling and entry deterrence
10 buyers of each type (A,B),
MC = 0, Entrant Fixed Cost F = 60
Incumbent produces Good 1. Both firms produce good 2.
Buyer A Buyer B Buyer C
Good 1 $7 $1.50 $8
Good 2 $6 $6.50 $2.50
Bundle $13 $8 $10.50
a) No threat of entry (i.e. Monopoly)
P1 = 8 1 = 8×10 P2 = 6.50 2 = 6.50×10 Pb = 13 = 13×10
P1 = 7 1 = 7×20 P2 = 6 2 = 6×20 Pb = 10.50 = 10.5×20
P1 = 1.5 1 = 1.5×30 P2 = 2.50 2 = 2.5×30 Pb = 8 = 8×30
Sell individually
= 140 + 120 = 260 Bundle
= 240
Conclusion : Bundling is not profitable if there is no threat
of entry (240 < 260).
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 34 of 39
bi) Threat of entry, Sell separately
Buyer behaviour. Buy from entrant if entrant at least
matches incumbent’s price.
Entrant’s best response to incumbent’s good 2 price (p2i )
P2i = 6 P2i = 2
Q2e AC2e P2e Buyers P2e Buyers
10 6 − − − −
20 3 6 > 3 A,B − −
30 2 2.5 > 2 A,B,C 2 = 2 A,B,C
Incumbent choice. Incumbent sets P2i = 2 which induces
the entrant to make zero profits and therefore to stay out.
The incumbent’s profits are
= 7×20 + 2×30 = 200
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 35 of 39
bii) Threat of entry, Bundling
Buyer behaviour. Buy from entrant if entrant undercuts
the bundle price by at least the WTP for good 1.
Entrant’s best response to incumbent’s bundle price (pBi )
PBi = 8 PBi = 7.5
Q2e AC2e P2e Buyers P2e Buyers
10 6 8 − 1.5= 6.5 > 6 B 7.5 − 1.5= 6 = 6 B
20 3 8 – 7 = 1 < 3 B,A 7.5 – 7 = 0.5 < 3 B,A
30 2 8 – 8 = 0 < 2 B,A,C 7.5 – 8 = -0.5 B,A,C
Incumbent choice. Incumbent sets PB = 7.5 which induces
the entrant to make zero profits and therefore to stay out.
The incumbents profits are
= 7.5×30 = 225 > 200
Conclusion. Bundling is profitable if and only if there
is a threat of entry. (225 > 200, 240 < 260)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 36 of 39
Cost Based Reasons for Bundling
• Cost efficiency reason for bundling. Firms bundle to
achieve economies of scope.
Pain relief Decongestant Both
# Buyers 50 50 100
Fixed cost $300 $300 $300
MC $4 $4 $7
Separate
goods
$4 +
$300
150
= $6 $4 +
$300
150
= $6 $6 + $6 = $12
Bundling - - $7 +
$300
200
= $8.50
Mixed
Bundling
$4 +
$300
50
= $10 $4 +
$300
50
= $10 $7 +
$300
100
= $10
Bundling
and Good 1
$4 +
$300
50
= $10 - $7 +
$300
150
= $9
Bundling
and Good 2
- $4 +
$300
50
= $10 $7 +
$300
150
= $9
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 37 of 39
Bundling is an equilibrium
• Goods offered separately is not an equilibrium because a
firm will enter and offer a bundle at $10 < $12 and
attract the buyers who want both.
• Mixed bundling is not an equilibrium because a firm
could enter and offer the bundle at $8.50 < $10 and
attract all the buyers.
• Bundling and Good 1 or Good 2 is not an equilibrium
because no buyer would buy Good 1 or Good 2
separately ($10 > $9).
• Bundling is an equilibrium because any firm entering
separately could only attract 50 buyers and thus the
lowest price they could offer is $10 which is greater than
the bundle price of $8.50
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 38 of 39
Complementary products
• If complementary products are produced by different
monopolists then prices are too high as firms ignore the
external benefit of lowering price and boosting sales of
the complementary product.
• Solutions: Mergers, Competition.
Model
qO = qB = 12 – (pO + pB), MCO = MCB = 0
Firm O’s profits and profit maximizing price are
= (12 − − )
= 12 − 2
0
−
= 0
: = 6 − 0.5
If firm B is a monopolist then pB = 6 – 0.5pO and so
pO = pB = 4 which yields O = B = 16
If firm B is a competitive firm then pB = MC = 0 and
pO = 6 which yields O = 36, B = 0
If firm B merges with firm O and p = pO + pB then
= (12 − )
= 12 − 2 = 0 → = 6, = 36
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 39 of 39
Microsoft Case
• Operating System: Microsoft Windows
• Browser: Microsoft Explorer, Netscape Navigator
• Microsoft bundled Windows and Explorer
• Efficiency Motive. Bundling induced more competition
from Netscape which reduced prices and raised industry
profits (due to complementarity between Netscape
Navigator and Microsoft Windows).
• Monopolization Motive. Microsoft wanted to induce
Netscape to exit to prevent them from becoming an
alternate Operating System and weakening Microsoft’s
Network effect advantage.
• The popularity of Microsoft Windows created a
network effect as its large customer base created
demand for applications and the creation of Windows
based applications created a feedback effect which
made Windows even more popular.
• Verdict. Court ruled that Microsoft engaged in
monopolization (i.e. abused its market power)
• Remedy. Restrictions on Microsoft’s actions.
学霸联盟
EC620 Topic 1: Monopoly and Price Discrimination 1 of 39
Topic 1 : Monopoly and Price Discrimination
Lecture Topic Readings*
1 – Sept 13
Slides 2-7
Overview, Calculus tools,
Profit max., Welfare & Monopoly
2.1
2 – Sept 15
Slides 8-17
Group Pricing, Customization
Linear algebra tool
5.1 5.3,
6.2
3 – Sept 20
Slides 18-23
Versioning
Durable goods monopoly
6.1, 6.2, 2.2.2
4 – Sept 22
Slide 24-30
Two-part tariffs
Block Pricing
5.4
5 – Sept 27
Slide 31-35
Bundling and Mixed Bundling
Bundling and Entry deterrence
6.3
6 – Sept 29
Slide 36-39
Cost-based Rationale for Bundling
Complementary products
6.3
MyLS
* Readings refer to the textbook chapter sections
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 2 of 39
What is Industrial Organization?
• Impact of market structure on
➢ …market power, collusion and welfare
➢ …responsiveness of price to demand and cost
➢ …incentives to innovate
➢ …profitability of merger
• Determinants of market structure
➢ …costs and market size
➢ …innovation and advertising
➢ …entry deterrence and predation
• Profit and welfare consequences of business strategy
➢ …price discrimination and versioning
➢ …bundling, tie-ins, 2 part tariffs and block pricing
➢ …mergers, price fixing and vertical restraints
➢ …entry, entry deterrence and innovation
• Tools of industrial organization
➢ …calculus and unconstrained optimization
➢ …methods for solving linear models
➢ …welfare economics
➢ …game theory
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 3 of 39
Unconstrained optimization
• Maximize objective function f(x)
➢ FOC:
= ′() = 0 SOC:
2
< 0
• Maximize objective function f(x1, x2)
FOC.
= 0 i = 1,2, SOC. If =
2
SOC are
< 0 = 1,2 and 1122 − 1221 > 0
• Rules of calculus
f(x,y) = ax2 + bx +c + dxy→
= 2 + +
∫ +
0
= + 0.52
() = →
= = ()
() = →
= −1 =
()
(()())
= ()′() + ()′()
((())
=
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 4 of 39
Monopoly
(QD = (a – P)N, C = cq + d(½)q2 +F)
• Maximize (Q) = P(Q)Q – C(Q)
= ( −
) − −
2
2 −
➢ FOC:
= () + ′() − ′() = 0
= −
2
− ( + ) = 0
➢ SOC:
2
< 0 → −
2
− < 0 (satisfied if d > −
2
)
Figure 1: Profit Maximization
Figure 1
P
MC
MR
D
Q1 Q2 Q3 Q
TC
TR
P
MC
MR
TR
TC
Q1 Q2 Q3 Q
Solution. Use FOC to find Q. Sub Q into demand to get P.
=
( − )
2 +
, =
(1 + ) +
2 +
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 5 of 39
Pricing and Elasticity
= −
% ℎ
% ℎ
= −
∆ ⁄
∆ ⁄
= −
∆
∆
• Demand is more elastic if good…
➢ has close substitutes and search costs are low
➢ takes up large portion of the budget
• Marginal revenue (MR) = TR/Q consists of
➢ …price charged to new buyers minus revenue loss
from price cut to existing buyers
➢ …equals price if firm is a price taker ( =∝)
• Elasticity and MR. Since TR = R(Q) = P(Q)Q then
=
= () + ′() = () (1 −
1
)
• Elasticity and Pricing. MR = MC implies
=
1−
1
→
−
=
1
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 6 of 39
Welfare function if P = a – bQ
Method 1. Welfare = Total Benefit – Total costs
= ∫ ( − ) −
0
∑ ()
=1
= − 0.52 − ∑ ()
=1
Method 2. Welfare = Consumer surplus + profit
= − 0.52 − + ∑
=1
Substitute P = a – bQ
= 0.52 + ∑
=1
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 7 of 39
Method 3. Welfare = Total surplus minus Fixed Costs
Total surplus = Area between Demand and Marginal cost
Example : If () = + then
= ( − ) − 0.52 −
Figure 2 : Total Surplus
a
c
Q
D
MC = AVC = c
Total
Surplus
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 8 of 39
Efficiency and Deadweight Loss
• An allocation is efficient if it maximizes welfare which
implies that goods…
➢ …go to buyers with highest willingness to pay
➢ …are produced at the lowest cost
➢ …go to all buyers willing to pay MC (i.e. P = MC)
• Deadweight loss (DWL)…
➢ …measures the welfare loss due to P > MC
➢ …is illustrated as the triangle between the demand
and MC curves and the P = MC and P > MC outputs
(see Figure 3)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 9 of 39
Figure 3: Deadweight loss & welfare effects of entry
130
PM = 70
10
C
A
QM = 60 QE = 120
MC
D
B
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 10 of 39
Monopoly, welfare effects of entry and DWL
If MC = 10, P = 130 – Q and FC = F then π and W are
= (130 − ) − 10 − and = 0.52 +
Monopoly output. Set
= 0 to get
= 130 − 2 − 10 = 0 → Q = 60
Substitute Q = 60 into demand, profits and welfare to get
P = 70, = 3600 − , WM = 5400 – F
Conclusion. Profitable monopoly entry raises welfare
(i.e. F < 3600 implies F < 5400) because it increases
consumer surplus and has zero impact on existing firms.
Efficient output. Set P = MC = 10 (or set
= 0) to get
130 – Q = 10 →Q = 120
Substitute Q = 120 into demand, profits and welfare to get
P = 10, = −, WE = 7200 – F
Deadweight loss is thus equal to
WE – WM = (7200 – F) – (5400 – F) = 1800
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 11 of 39
Price discrimination is…
• …the practice of charging buyers different prices for
the same product for non-cost reasons
• …feasible if the seller can
➢ ...identify different buyers
➢ ...prevent re-sale between buyers because of…
▪ …transactions costs, nature of product, legal
restrictions (e.g. ROW import bans in Europe).
• …profitable because it allows firms to
➢ …eliminate some deadweight loss (Area C, Figure 3)
➢ …extract more consumer surplus (Area A, Figure 3)
• …legal in Canada provided
➢ …your intent is not predatory
• ...welfare enhancing if more markets are served
• ...welfare reducing if output is re-allocated
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 12 of 39
Group Pricing: Monopolist can price discriminate
[Pi = ai – 4Qi, MC = 8, a1 = 48, a2 = 32]
Use FOC in each market to find output.
FOC:
= +
−
= 0 = 1,2
= ai – 8Qi − 8 = 0
Qi = (ai – 8)/8
Q1 = 5, Q2 = 3
Check SOC
ii = − 8 < 0 i = 1,2, (satisfied)
1122 - 2112 = (-8)(-8) – (0)(0) ≥ 0 (satisfied)
Sub. Qi into demand functions to find prices
P1 = 28, P2 = 20
Profits are given by
π = (28 – 8)5 + (20 – 8)3 = 100 + 36 = 136 > 128
Find consumer surplus in both markets
CS = (½)(48 – 28)(5) + (½) (32 – 20)3 = 50 + 18 = 68
Welfare is given by
W = π + CS = 136 + 68 = 204 < 208
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 13 of 39
Monopolist cannot price discriminate
[Pi = ai – 4Qi, MC = 8, a1 = 48, a2 = 32]
Find market demand and then invert
Q = Q1 + Q2 = (1/4)(48 – P) + (1/4)(32 – P)
P = 40 – 2Q
Use FOC to find Q
FOC:
= +
−
= 0
40 – 4Q − 8 = 0 → Q = 8
SOC: QQ = -4 < 0 (satisfied)
Sub. Q into inverted market demand to find p
P = 40 – 2(8) → P = 24
Sub. p into individual demand to find qi
Qi = (1/4)(ai – P)→Q1 = 6, Q2 = 2
Find profits.
= (24 – 8)8 = 128 > 100 (Serve both markets)
Find consumer surplus in both markets
CSi = (1/2)(48 – 24)6 + (1/2)(32 – 24)2 = 72 + 8 = 80
Welfare is given by
W = + CS = 128 + 80 = 208 > 204
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 14 of 39
Figure 4 : Welfare Loss due to Price Discrimination
P = 24
D1
MC
5 6
Market 1
L
D2
MC
2 3
Market 2
G
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 15 of 39
Group Pricing and non-constant MC
Can price Discriminate.
First order conditions
+
−
= 0 = 1,2
Non-constant MC implies that FOC is a function of Q1
and Q2 and must be solved simultaneously via Cramer’s
Rule. The cross partial derivatives of the profit function
are not zero and this will affect SOC.
Cannot price discriminate
1. Serve both markets. Similar to the constant MC case.
If you get QLD < 0 then serve HD only.
2. Serve high demand only. Set output in LD market
equal to zero and then set MR = MC in HD market.
Note. Since MC is not constant then ‘serve HD only’
solution will not be the same as HD output under price
discrimination.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 16 of 39
Solving linear model using Cramer’s Rule
• Exogenous parameters: aij, ci,
• Endogenous variables : xi
Write system of equations as follows
a11x1 + a12x2 = c1
a21x1 + a22x2 = c2
Express the equations in matrix form
[
11 12
21 22
] [
1
2
] = [
1
2
]
Apply Cramer’s Rule to get solution for x1 and x2
1 =
|
1 12
2 22
|
|
11 12
21 22
|
=
122 − 212
1122 − 2112
2 =
|
11 1
21 2
|
|
11 12
21 22
|
=
112 − 211
1122 − 2112
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 17 of 39
Figure 5a :Price discrimination
Figure 5b: No Price discrimination
D
2
D
1
MR2
MR1 MR
2
1
1
2
QD
MC
D2
D1
D
1
MR
P
1
2
1
QN
MC
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 18 of 39
Price discrimination by location or customization
MCB = 4, MCM = 4 + t, PB = 36 – 4QB, PM = 36 – 4QM, FC = 0
Find MR in both markets
MRB = 36 – 8QB and MRM = 36 – 8QM
Set MR = MC in each market to solve for QU and QE
36 – 8QB = 4 → QB = 4
36 – 8QM = 4 + t →QM = (32 – t)/8
Substitute outputs into inverted demand to find prices
PB = 20 and PM = 20 + t/2
Since difference in prices t/2 are less than the difference in
customization/transportation cost t then the above (i)
represents price discrimination and (ii) eliminates
arbitrage.
Non-linear demand. If demand is not linear then price
differences can be greater, lower or equal to the
transportation/customization cost.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 19 of 39
Versioning/Product proliferation
• Versioning is
➢ …the practice of offering low and high quality
versions of the same product for different prices.
▪ e.g. flights, books
➢ …more profitable than selling a single version if
▪ …the variance in willingness to pay is low for low
quality and high for high quality.
➢ …is price discrimination if difference in prices do not
reflect differences cost of providing quality
• Damaged goods are a special case of versioning…
➢ …in which low quality goods cost more to produce
than high quality goods because of
➢ …the cost of disabling certain product features in the
low quality good
▪ …e.g. printers, software
• Product proliferation : Offerring many horizontally
differentiated products to deter entry.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 20 of 39
Versioning example : Software
N = number of experts, N = number of students
Buyers buy only 1 version
Version Student Expert Costs
Basic $50 $75 $10
Full $100 $400 $20
Single version
Basic Full
PB Profit PF Profit
50 (50 − 10)(N + N) 100 (100 − 20)(N + N)
75 (75 − 10)N 400 (400 − 20)N
Menu of versions
Seller offer : A menu of versions
Basic: pB = __________
Full: pF = _________
Buyer choice
Consumer surplus
Student Expert
Basic
Full
Choice
Profit: π = N(__________) + N(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 21 of 39
Versioning with endogenous quality
NL = number of LD, NH = number of HD, Buyers buy only 1 version
> , () > ()
Version Low Demand High Demand Unit Costs
Low quality c(sL)
High quality c(sH)
Single version
Price Profit
( − c(s))(NL + NH)
( − c(s))NH
Menu of versions
Seller offer : A menu of versions
Low quality: pL = ____________
High quality: pH = ____________
Buyer choice
Consumer surplus
Low Demand High Demand
LQ
HQ
Choice
Profit: π = NL(__________) + NH(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 22 of 39
Durable goods monopoly
• Coase conjecture: If buyers have similar valuations then
durability can ↓ market power and ↑Welfare because…
➢ …buyers who buy exit the market which
➢ …lowers demand and price over time
➢ …buyers thus choose to wait for low prices
➢ …and thus the seller lowers price in early periods
➢ …To avoid the Coase problem the seller can
▪ …lease rather than sell
• Case Study: Features of textbook market are...
➢ …textbooks are durable
➢ …used books compete with new books
➢ …new editions help to eliminate used books market
➢ …fewer books purchased if new edition is expected
➢ …publisher revenue is unaffected by # of editions
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 23 of 39
Durable goods examples
Assumptions: Zero cost, No discounting (R = 1), 2 buyers
Example 1 Valuations: $50 for Buyer 1, $30 for Buyer 2
Strategy
Period 1
profit
Period 2
profit
Total
profit
Consumer
surplus
Welfare
Sell to both buyers
in Period 1
2×2×30 - 120 1×2×
(50 – 30)
160
Sell to Buyer 1 in
Period 1 and to
Buyer 2 in Period 2
1×2×50 –
(50 – 30)
1×1×30 110
1×1×
(50 − 30)
130
Lease to both
buyers in both
periods
2×1×30 2×1×30 120 1×2×
(50 – 30)
160
Example 2 Valuations: $50 for Buyer 1, $20 for Buyer 2
Strategy
Period 1
profit
Period 2
profit
Total
profit
Consumer
surplus
Welfare
Sell to both buyers
in Period 1
2×2×20 - 80 1×2×
(50 − 20)
140
Sell to Buyer 1 in
Period 1 and to
Buyer 2 in Period 2
1×2×50 –
(50 – 20)
1×1×20 90
1×1×
(50 − 20)
120
Lease to Buyer 1 in
both periods
1×1×50 1×1×50 100 0 100
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 24 of 39
Two-part tariffs
• Two-part tariffs…
➢ …specify a fixed fee (F) & a user fee (P)
▪ e.g. utilities, memberships
➢ …can be achieved via tie-ins (Ch 6.3.2)
▪ e.g. video players/video games
➢ …let the seller capture (i) more buyer surplus & (ii)
the efficiency loss from setting P > MC.If buyers are
identical then the profit-maximizing strategy is to set
P = MC and F = CS.
• If buyers are not identical and price discrimination is
possible then Pi = MC and Fi = CSi
C
Q0 Q1
A
P0
P1
Demand
MC
B
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 25 of 39
Two buyer types and a Single two-part tariff
qL qH qH *
A
B
C
D
E
F
MC
HD LD
G
pL
Set p = MC, F = CSHD = ________
π = NLD(______________) + NHD(____________)
Set p = pL > MC, F = CSLD = ______________
π = NLD(______________) + NHD(____________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 26 of 39
Two buyer types and a Menu of two part tariffs
qL qH qH *
A
B
C
D
E
F
MC
HD LD
G
pL
pH
Seller offer : A menu of two-part tariffs given by
Contract L: pL > MC, FL = CSLD = ____________
Contract H: pH = MC, FH = FL + CSHD = ________
Buyer choice
Net consumer surplus
LD Buyer HD Buyer
Contract L
Contract H
Choice
Profit: π = NLD(__________) + NHD(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 27 of 39
Block Pricing Menu
qL
A
B
C
D
MC
HD
LD
G
F
E
qH *
Seller offer : Block pricing menu
Contract L: ≤ , pL = 0, FL = TBLD = __________
Contract H: ≤
∗ , pH = 0, FH = FL + TBHD = ____
Buyer choice
Net consumer surplus
LD Buyer HD Buyer
Contract L
Contract H
Choice
Profit: π = NLD(__________) + NHD(________)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 28 of 39
Buyer demand () = − → () =
−
1
Consumer surplus used for 2-part tariffs
Since () =
−
then from slide 6 we get
(()) = 0.5 (
1
) ()2
=
= (
1
()) (−) = −()
or Sub q(p) into CS(q(p)) to get () =
.5(−)2
Total Benefit used for Block pricing
Since () =
−
then from slide 6 we get
() = (
) − 0.5 (
1
) 2
=
−
1
= ()
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 29 of 39
Profit maximizing two part tariffs
Single 2 part tariff
= ( − )() + ( + )()
ℎ () = () + ()
() = (())
Set
= 0 then sub
,
,(), () to solve for p.
2 part tariff menu
= [][( − )() + ()]
+ [][()]
ℎ () = (())
() = () + ( = ) − (())
Set
= 0 then sub
,
,
, (), ()
to solve for pL.
Corner solution: If qLD ≤ 0 then serve HD only.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 30 of 39
Profit maximizing block pricing menu
= [() − ] + [() −
∗ ]
ℎ () = ()
() = () + ( =
∗ ) − ()
Set
= 0 then sub
,
to solve for qL.
Corner solution : If you get qL < 0 or
< 0 then firm
serves HD only.
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 31 of 39
Bundling is…
• …selling related products as a package
➢ …e.g. cable TV, software, vacation travel, concert
series, automobile option packages
• …more profitable than selling goods individually
➢ …if the variation in the willingness to pay among
buyers is lower for the bundle than for the goods
individually (i.e. bundling ↑ elasticity).
▪ Bundling effects in Cable TV.
• ↑Elasticity (average (0.16), specialty (0.197),
general interest (0.10))
• ↑profits (4.7%), ↓consumer surplus (5%)
➢ … if the incumbent wants to deter entry
➢ …if there are economies of scope
• Mixed bundling is…
• …the practice of selling related products as a package
and individually
• …is more profitable than bundling if…
➢ …buyers who are willing to pay the highest price
for the bundle are not willing to pay the highest
price for the goods individually
➢ …or if the willingness to pay for a good in the
bundle does not exceed its marginal cost
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 32 of 39
Bundling and Mixed bundling example
N = Number of each type, MC = $2.50
Buyer A Buyer B Buyer C Buyer D
Good 1 $8 $5 $9 $1
Good 2 $4 $5 $1 $9
Bundle $12 $10 $10 $10
Mixed bundling
Seller offer : p1 = _____ p2 = _____ pB = ______
Buyer A Buyer B Buyer C Buyer D
Good 1 $8 − $5 − $9 − $1 −
Good 2 $4 − $5 − $1 − $9 −
Bundle $12 − $10 − $10 − $10 −
Choice
π = N(__ ) + N( __) + N(_ _) + N( __) = _____
5.00
2.50
10
N 4N
9
Good 1 Good 2 Bundle
9
5
N 2N 3N 4N
4 2.50
8
N 2N 3N 4N
5
PT = 9 T = (9−2.5)×N PS = 9 S = (9−2.5)×N PB = 12 = (12−5)×N
PT = 8 T = (8−2.5)×2N PS = 5 S = (5−2.5)×2N PB = 10 = (10−5)×4N
PT = 5 T = (5−2.5)×3N PS = 4 S = (4−2.5)×3N
Sell Individually : = 11N + 6.5N =17.5N Bundle: = 20N
12
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 33 of 39
Bundling and entry deterrence
10 buyers of each type (A,B),
MC = 0, Entrant Fixed Cost F = 60
Incumbent produces Good 1. Both firms produce good 2.
Buyer A Buyer B Buyer C
Good 1 $7 $1.50 $8
Good 2 $6 $6.50 $2.50
Bundle $13 $8 $10.50
a) No threat of entry (i.e. Monopoly)
P1 = 8 1 = 8×10 P2 = 6.50 2 = 6.50×10 Pb = 13 = 13×10
P1 = 7 1 = 7×20 P2 = 6 2 = 6×20 Pb = 10.50 = 10.5×20
P1 = 1.5 1 = 1.5×30 P2 = 2.50 2 = 2.5×30 Pb = 8 = 8×30
Sell individually
= 140 + 120 = 260 Bundle
= 240
Conclusion : Bundling is not profitable if there is no threat
of entry (240 < 260).
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 34 of 39
bi) Threat of entry, Sell separately
Buyer behaviour. Buy from entrant if entrant at least
matches incumbent’s price.
Entrant’s best response to incumbent’s good 2 price (p2i )
P2i = 6 P2i = 2
Q2e AC2e P2e Buyers P2e Buyers
10 6 − − − −
20 3 6 > 3 A,B − −
30 2 2.5 > 2 A,B,C 2 = 2 A,B,C
Incumbent choice. Incumbent sets P2i = 2 which induces
the entrant to make zero profits and therefore to stay out.
The incumbent’s profits are
= 7×20 + 2×30 = 200
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 35 of 39
bii) Threat of entry, Bundling
Buyer behaviour. Buy from entrant if entrant undercuts
the bundle price by at least the WTP for good 1.
Entrant’s best response to incumbent’s bundle price (pBi )
PBi = 8 PBi = 7.5
Q2e AC2e P2e Buyers P2e Buyers
10 6 8 − 1.5= 6.5 > 6 B 7.5 − 1.5= 6 = 6 B
20 3 8 – 7 = 1 < 3 B,A 7.5 – 7 = 0.5 < 3 B,A
30 2 8 – 8 = 0 < 2 B,A,C 7.5 – 8 = -0.5 B,A,C
Incumbent choice. Incumbent sets PB = 7.5 which induces
the entrant to make zero profits and therefore to stay out.
The incumbents profits are
= 7.5×30 = 225 > 200
Conclusion. Bundling is profitable if and only if there
is a threat of entry. (225 > 200, 240 < 260)
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 36 of 39
Cost Based Reasons for Bundling
• Cost efficiency reason for bundling. Firms bundle to
achieve economies of scope.
Pain relief Decongestant Both
# Buyers 50 50 100
Fixed cost $300 $300 $300
MC $4 $4 $7
Separate
goods
$4 +
$300
150
= $6 $4 +
$300
150
= $6 $6 + $6 = $12
Bundling - - $7 +
$300
200
= $8.50
Mixed
Bundling
$4 +
$300
50
= $10 $4 +
$300
50
= $10 $7 +
$300
100
= $10
Bundling
and Good 1
$4 +
$300
50
= $10 - $7 +
$300
150
= $9
Bundling
and Good 2
- $4 +
$300
50
= $10 $7 +
$300
150
= $9
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 37 of 39
Bundling is an equilibrium
• Goods offered separately is not an equilibrium because a
firm will enter and offer a bundle at $10 < $12 and
attract the buyers who want both.
• Mixed bundling is not an equilibrium because a firm
could enter and offer the bundle at $8.50 < $10 and
attract all the buyers.
• Bundling and Good 1 or Good 2 is not an equilibrium
because no buyer would buy Good 1 or Good 2
separately ($10 > $9).
• Bundling is an equilibrium because any firm entering
separately could only attract 50 buyers and thus the
lowest price they could offer is $10 which is greater than
the bundle price of $8.50
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 38 of 39
Complementary products
• If complementary products are produced by different
monopolists then prices are too high as firms ignore the
external benefit of lowering price and boosting sales of
the complementary product.
• Solutions: Mergers, Competition.
Model
qO = qB = 12 – (pO + pB), MCO = MCB = 0
Firm O’s profits and profit maximizing price are
= (12 − − )
= 12 − 2
0
−
= 0
: = 6 − 0.5
If firm B is a monopolist then pB = 6 – 0.5pO and so
pO = pB = 4 which yields O = B = 16
If firm B is a competitive firm then pB = MC = 0 and
pO = 6 which yields O = 36, B = 0
If firm B merges with firm O and p = pO + pB then
= (12 − )
= 12 − 2 = 0 → = 6, = 36
Fall 2021
EC620 Topic 1: Monopoly and Price Discrimination 39 of 39
Microsoft Case
• Operating System: Microsoft Windows
• Browser: Microsoft Explorer, Netscape Navigator
• Microsoft bundled Windows and Explorer
• Efficiency Motive. Bundling induced more competition
from Netscape which reduced prices and raised industry
profits (due to complementarity between Netscape
Navigator and Microsoft Windows).
• Monopolization Motive. Microsoft wanted to induce
Netscape to exit to prevent them from becoming an
alternate Operating System and weakening Microsoft’s
Network effect advantage.
• The popularity of Microsoft Windows created a
network effect as its large customer base created
demand for applications and the creation of Windows
based applications created a feedback effect which
made Windows even more popular.
• Verdict. Court ruled that Microsoft engaged in
monopolization (i.e. abused its market power)
• Remedy. Restrictions on Microsoft’s actions.
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