economics of the firm strategic pricing techniques
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Market Structures
Recall that there is an entire spectrum of market structures
Perfect CompetitionMany firms, each with zero market shareP = MCProfits = 0 (Firm’s earn a reasonable rate of return on invested capital)NO STRATEGIC INTERACTION!
MonopolyOne firm, with 100% market shareP > MCProfits > 0 (Firm’s earn excessive rates of return on invested capital)NO STRATEGIC INTERACTION!
Most industries, however, don’t fit the assumptions of either perfect competition or monopoly. We call these industries oligopolies
OligopolyRelatively few firms, each with significant market shareSTRATEGIES MATTER!!!
Wireless (2002)Verizon: 30% Cingular: 22% AT&T: 20% Sprint PCS: 14% Nextel: 10% Voicestream: 6%
US Beer (2001)Anheuser-Busch: 49% Miller: 20% Coors: 11% Pabst: 4% Heineken: 3%
Music Recording (2001)Universal/Polygram: 23% Sony: 15% EMI: 13% Warner: 12% BMG: 8%
Market shares are not constant over time in these industries!
9
11
14
15
20
21
Airlines (1992) Airlines (2002)
American
Northwest
Delta
United
Continental
US Air 7
9
11
15
17
19American
United
Delta
Northwest
Continental
SWest
While the absolute ordering didn’t change, all the airlines lost market share to Southwest.
Another trend is consolidation
44
55
677
888
9
Retail Gasoline (1992) Retail Gasoline (2001)
Shell
ExxonTexaco
Chevron
Amoco
Mobil
7
10
16
18
20
24Exxon/Mobil
Shell
BP/Amoco/Arco
Chev/Texaco
Conoco/PhillipsCitgoBP
Marathon
SunPhillips
Total/Fina/Elf
The key difference in oligopoly markets is that price/sales decisions can’t be made independently of your competitor’s decisions
Monopoly
PQQ Oligopoly
NPPPQQ ,..., 1
Your Price (-)
Your N Competitors Prices (+)
Oligopoly markets rely crucially on the interactions between firms which is why we need game theory to analyze them!
Strategy Matters!!!!!
Prisoner’s Dilemma…A Classic!
Jake
Two prisoners (Jake & Clyde) have been arrested. The DA has enough evidence to convict them both for 1 year, but would like to convict them of a more serious crime.
Clyde
The DA puts Jake & Clyde in separate rooms and makes each the following offer:
Keep your mouth shut and you both get one year in jail
If you rat on your partner, you get off free while your partner does 8 years
If you both rat, you each get 4 years.
Jake
Clyde
Confess Don’t Confess
Confess -4 -4 0 -8
Don’t Confess
-8 0 -1 -1
Jake is choosing rows Clyde is choosing columns
Jake
Clyde
Confess Don’t Confess
Confess -4 -4 0 -8
Don’t Confess
-8 0 -1 -1
Suppose that Jake believes that Clyde will confess. What is Jake’s best response?
If Clyde confesses, then Jake’s best strategy is also to confess
Jake
Clyde
Confess Don’t Confess
Confess -4 -4 0 -8
Don’t Confess
-8 0 -1 -1
Suppose that Jake believes that Clyde will not confess. What is Jake’s best response?
If Clyde doesn’t confesses, then Jake’s best strategy is still to confess
Jake
Clyde
Confess Don’t Confess
Confess -4 -4 0 -8
Don’t Confess
-8 0 -1 -1
Dominant Strategies
Jake’s optimal strategy REGARDLESS OF CLYDE’S DECISION is to confess. Therefore, confess is a dominant strategy for Jake
Note that Clyde’s dominant strategy is also to confess
Nash Equilibrium
Jake
Clyde
Confess Don’t Confess
Confess -4 -4 0 -8
Don’t Confess
-8 0 -1 -1
The Nash equilibrium is the outcome (or set of outcomes) where each player is following his/her best response to their opponent’s moves
Here, the Nash equilibrium is both Jake and Clyde confessing
“Winston tastes good like a cigarette should!”
“Us Tareyton smokers would rather fight than switch!”
Advertise Don’t Advertise
Advertise 10 10 30 5
Don’t Advertise
5 30 20 20
How about this game?
$.95 $1.30 $1.95
$1.00 3 6 7 3 10 4
$1.35 5 1 8 2 14 7
$1.65 6 0 6 2 8 5
Alli
ed
Acme
Acme and Allied are introducing a new product to the market and need to set a price. Below are the payoffs for each price combination.
What is the Nash Equilibrium?
Iterative Dominance
$.95 $1.30 $1.95
$1.00 3 6 7 3 10 4
$1.35 5 1 8 2 14 7
$1.65 6 0 6 2 8 5
Alli
ed
Acme
Note that Allied would never charge $1 regardless of what Acme charges ($1 is a dominated strategy). Therefore, we can eliminate it from consideration.
With the $1 Allied Strategy eliminated, Acme’s strategies of both $.95 and $1.30 become dominated.
With Acme’s strategies reduced to $1.95, Allied will respond with $1.35
Repeated GamesJake Clyde
The previous example was a “one shot” game. Would it matter if the game were played over and over?
Suppose that Jake and Clyde were habitual (and very lousy) thieves. After their stay in prison, they immediately commit the same crime and get arrested. Is it possible for them to learn to cooperate?
Time0 1 2 3 4 5
Play PD Game
Play PD Game
Play PD Game
Play PD Game
Play PD Game
Play PD Game
Repeated GamesJake Clyde
Time0 1 2 3 4 5
Play PD Game
Play PD Game
Play PD Game
Play PD Game
Play PD Game
Play PD Game
We can use backward induction to solve this.
At time 5 (the last period), this is a one shot game (there is no future). Therefore, we know the equilibrium is for both to confess.
Confess Confess
However, once the equilibrium for period 5 is known, there is no advantage to cooperating in period 4
Confess Confess
Confess Confess
Confess Confess
Confess Confess
Confess Confess
Similar arguments take us back to period 0
Infinitely Repeated Games Jake Clyde
0 1 2
Play PD Game
Play PD Game
Play PD Game ……………
Suppose that Jake knows Clyde is planning on NOT CONFESSING at time 0.
Option #1: Don’t confess, get 1 year in jail (rather than 0 if he confesses), but establish trust for the next time
Option #2: Confess, get 0 years in jail (rather than 1 if he doesn’t confess), but ruins trust for the next time
You need to value the future for this option to be viable
Suppose that McDonald’s is currently the only restaurant in town, but Burger King is considering opening a location. Should McDonald's fight for it’s territory?
IN
Out
Fight
Cooperate
0
2
1
5
0
2
Now, suppose that this game is played repeatedly. That is, suppose that McDonald's faces possible entry by burger King is 20 different locations. Can entry deterrence be a credible strategy?
Enter Enter EnterDon’t Fight
Don’t Fight
Don’t Fight
2
Enter Don’t Enter
Don’t Enter
Fight Don’t Enter
Don’t Enter
0
OR
2 2
5 5 5 5
Total =2*20 = 40
Total =19*5 = 95
Enter
Don’t Enter
Enter
Don’t Enter
Enter
Don’t Enter
Fight
Don’t Fight
Fight
Don’t Fight
Fight
Don’t Fight
End of Time
Does McDonald’s have an incentive to fight here?
What will Burger King do here?
If there is an “end date” then McDonald's threat loses its credibility!!
Now, suppose that this game is played repeatedly. That is, suppose that McDonald's faces possible entry by burger King is 20 different locations. Can entry deterrence be a credible strategy?
Don’t Audit
Audit
Cheat 5 -5 -25 5
Don’t Cheat
0 0 -1 -1
What is the equilibrium to this game?
Ever Cheat on your taxes?
In this game you get to decide whether or not to cheat on your taxes while the IRS decides whether or not to audit you
If the IRS never audited, your best strategy is to cheat (this would only make sense for the IRS if you never cheated)
The Equilibrium for this game will involve mixed strategies!
Don’t Audit
Audit
Cheat 5 -5 -25 5
Don’t Cheat
0 0 -1 -1
If the IRS always audited, your best strategy is to never cheat (this would only make sense for the IRS if you always cheated)
A quick detour: Expected Value
Suppose that I offer you a lottery ticket: This ticket has a 2/3 chance of winning $100 and a 1/3 chance of losing $100. How much is this ticket worth to you?
Suppose you played this ticket 6 times:
Attempt Outcome
1 $100
2 $100
3 -$100
4 $100
5 -$100
6 $100
Total Winnings: $200Attempts: 6Average Winnings: $200/6 = $33.33
A quick detour: Expected Value
Given a set of probabilities, Expected Value measures the average outcome
Expected Value = A weighted average of the possible outcomes where the weights are the probabilities assigned to each outcome
Suppose that I offer you a lottery ticket: This ticket has a 2/3 chance of winning $100 and a 1/3 chance of losing $100. How much is this ticket worth to you?
33.33$100$3
1100$
3
2
EV
Cheating on your taxes!
Don’t Audit
Audit
Cheat 5 -5 -25 5
Don’t Cheat
0 0 -1 -1
Suppose that the IRS Audits 25% of all returns. What should you do?
Cheat: 5.22525.575. EV
Don’t Cheat: 25.125.075. EV
If the IRS audits 25% of all returns, you are better off not cheating. But if you never cheat, they will never audit, …
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
The only way this game can work is for you to cheat sometime, but not all the time. That can only happen if you are indifferent between the two!
Cheat: 255 ADA ppEV
Don’t Cheat: 10 ADA PpEV
Suppose the government audits with probability Ap
Doesn’t audit with probability DAp
If you are indifferent…
DAA
ADA
AADA
pp
pp
ppp
24
5
245
255
1 DAA pp
29
24
124
29
124
5
DA
DA
DADA
p
p
pp
(83%)29
5Ap (17%)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
We also need for the government to audit sometime, but not all the time. For this to be the case, they have to be indifferent!
Audit: 51 CDC ppEV
Don’t Audit: 50 CDC PpEV
Suppose you cheat with probability Cp
Don’t cheat with probability DCp
If they are indifferent…
DCC
DCC
CDCC
pp
pp
ppp
10
1
10
55
1 DCC pp
11
10
110
11
110
1
DC
DC
DCDC
p
p
pp
(91%)11
1Ap (9%)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
Now we have an equilibrium for this game that is sustainable!
The government audits with probability %17ApDoesn’t audit with probability %83DAp
Suppose you cheat with probability %9Cp
Don’t cheat with probability %91DCp
We can find the odds of any particular event happening….
You Cheat and get audited: 0153.17.09. AC pp (1.5%)
(1.5%)(7.5%)
(15%)(75%)
The Airline Price Wars
p
Q
$500
$220
60 180
Suppose that American and Delta face the given demand for flights to NYC and that the unit cost for the trip is $200. If they charge the same fare, they split the market
P = $500 P = $220
P = $500 $9,000
$9,000
$3,600
$0
P = $220 $0
$3,600
$1,800
$1,800
American
Del
taWhat will the equilibrium be?
The Airline Price Wars
P = $500 P = $220
P = $500 $9,000
$9,000
$3,600
$0
P = $220 $0
$3,600
$1,800
$1,800
American
Del
ta
If American follows a strategy of charging $500 all the time, Delta’s best response is to also charge $500 all the time
If American follows a strategy of charging $220 all the time, Delta’s best response is to also charge $220 all the time
This game has multiple equilibria and the result depends critically on each company’s beliefs about the other company’s strategy
The Airline Price Wars: Mixed Strategy Equilibria
P = $500 P = $220
P = $500 $9,000
$9,000
$3,600
$0
P = $220 $0
$3,600
$1,800
$1,800
American
Del
ta
Charge $500: 09000 LH ppEV
Charge $220: 18003600 LH PpEV
Suppose American charges $500 with probability Hp
Charges $220 with probability Lp
LHH ppp 180036009000
HL pp 3
4
3Lp
4
1Hp(75%) (25%)
(56%)(19%)
(19%)(6%)
Suppose that we make the game sequential. That is, one side makes its decision (and that decision is public) before the other
Che
at
Aud
it
Aud
it
Don’t
Cheat
Don’t
Audit
Don’t
Audit
(-25, 5) (5, -5)(-1, -1) (0, 0)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
Your reward is on the left
If the IRS observes you cheating, their best choice is to Audit
Che
at
Aud
it
Aud
it
Don’t
Cheat
Don’t
Audit
Don’t
Audit
(-25, 5) (5, -5)(-1, -1) (0, 0)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
Your reward is on the leftvs
If the IRS observes you not cheating, their best choice is to not audit
Che
at
Aud
it
Aud
it
Don’t
Cheat
Don’t
Audit
Don’t
Audit
(-25, 5) (5, -5)(-1, -1) (0, 0)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
Your reward is on the leftvs
Knowing how the IRS will respond, you never cheat and they never audit!!
Che
at
Aud
it
Aud
it
Don’t
Cheat
Don’t
Audit
Don’t
Audit
(-25, 5) (5, -5)(-1, -1) (0, 0)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
Your reward is on the leftvs
(0%)(0%)
(0%)(100%)
Now, lets switch positions…suppose the IRS chooses first
Aud
it
Che
at
Che
at
Don’t
Audit
Don’t
Cheat
Don’t
Cheat
(-25, 5) (-1, -1)(5, -5) (0, 0)
Don’t Audit Audit
Cheat 5 -5 -25 5
Don’t Cheat 0 0 -1 -1
Your reward is on the left
(0%)(0%)
(100%)(0%)
Again, we could play this game sequentially
$500
$500
$500
$220
$220
$220
(9,000, 9,000) (3,600, 0) (0, 3,600) (1,800, 1,800)
Delta’s reward is on the left
P = $500 P = $220
P = $500 $9,000
$9,000
$3,600
$0
P = $220 $0
$3,600
$1,800
$1,800
(0%)(100%)
(0%)(0%)
Note: Even if the moves are made sequentially, if one party is not aware of the other’s move, we are back to the simultaneous move game
Che
at
Aud
it
Aud
it
Don’t
Cheat
Don’t
Audit
Don’t
Audit
(-25, 5) (5, -5)(-1, -1) (0, 0)
i.e., Al Capone might have cheated all the time, but if the IRS is unaware, they might not audit all the time!
Terrorists
Terrorists
President
Take
H
osta
ges
Neg
otia
te
Kill
Don’t Take
Hostages
Don’t K
ill
Don’t
Negotiate
(1, -.5)
(-.5, -1) (-1, 1)
(0, 1)
In the Movie Air Force One, Terrorists hijack Air Force One and take the president hostage. Can we write this as a game? (Terrorists payouts on left)
In the third stage, the best response is to kill the hostages
Given the terrorist response, it is optimal for the president to negotiate in stage 2
Given Stage two, it is optimal for the terrorists to take hostages
Terrorists
Terrorists
President
Take
H
osta
ges
Neg
otia
te
Kill
Don’t Take
Hostages
Don’t K
ill
Don’t
Negotiate
(1, -.5)
(-.5, -1) (-1, 1)
(0, 1)
The equilibrium is always (Take Hostages/Negotiate). How could we change this outcome?
Suppose that a constitutional amendment is passed ruling out hostage negotiation (a commitment device)
Without the possibility of negotiation, the new equilibrium becomes (No Hostages)
A bargaining example…How do you divide $20?
Two players have $20 to divide up between them. On day one, Player A makes an offer, on day two player B makes a counteroffer, and on day three player A gets to make a final offer. If no agreement has been made after three days, both players get $0.
Player A
Player B
Offer
Accept Reject
Player B
Offer
Player A
Accept Reject
Player A
Offer
Player B
Accept Reject
(0,0)
Day 1
Day 2
Day 3
Player A
Player B
Offer
Accept Reject
Player B
Offer
Player A
Accept Reject
Player A
Offer
Player B
Accept Reject
(0,0)
Day 1
Day 2
Day 3
If day 3 arrives, player B should accept any offer – a rejection pays out $0!
Player A: $19.99Player B: $.01
Player B knows what happens in day 3 and wants to avoid that!
Player A: $19.99Player B: $.01
Player A knows what happens in day 2 and wants to avoid that!
Player A: $19.99Player B: $.01
Player A
Player B
Offer
Accept Reject
Player B
Offer
Player A
Accept Reject
Player A
Offer
Player B
Accept Reject
(0,0)
Day 1
Day 2
Day 3
Lets consider a couple variations…
Variation #1: Negotiations take a lot of time and each player has an opportunity cost of waiting:
•Player A has an investment opportunity that pays 20% per year.•Player B has an investment strategy that pays 10% per year
Player A
Player B
Offer
Accept Reject
Player B
Offer
Player A
Accept Reject
Player A
Offer
Player B
Accept Reject
(0,0)
Year 1
Year 2
Year 3
If year 3 arrives, player B should accept any offer – a rejection pays out $0!
Player A: $19.99Player B: $.01
If player A rejects, she gets $19.99 in one year. That’s worth $19.99/1.20 today
Player A: $16.65Player B: $3.35
If player B rejects, she gets $3.35 in one year. That’s worth $3.35/1.10 today
Player A: $16.95Player B: $3.05
Continuous Choice Games
Consider the following example. We have two competing firms in the marketplace.
These two firms are selling identical products. Each firm has constant marginal costs of production.
What are these firms using as their strategic choice variable? Price or quantity?
Are these firms making their decisions simultaneously or is there a sequence to the decisions?
Cournot Competition: Quantity is the strategic choice variable
p
QD
There are two firms in an industry – both facing an aggregate (inverse) demand curve given by
Total Industry Production
Both firms have constant marginal costs equal to $20
21 qqQ
QP 20120
From firm one’s perspective, the demand curve is given by
1221 202012020120 qqqqP
Treated as a constant by Firm One
Solving Firm One’s Profit Maximization…
204020120 12 qqMR
40
20100 21
In Game Theory Lingo, this is Firm One’s Best Response Function To Firm 2
1q
2q
40
20100 21
05.2
0
1
2
q
q
If firm 2 drops out, firm one is a monopolist!
5.2
2040120
20120
1
1
1
q
qMR
qP
1q
2q
40
20100 21
What could firm 2 do to make firm 1 drop out?
5.2
0
1
2
q
q
0
5
1
2
q
q
MCP 20520120
1q
2q 40
20100 21
5.2
0
1
2
q
q
0
5
1
2
q
q
3
1
Firm 2 chooses a production target of 3
Firm 1 responds with a production target of 1
QP 20120
40420120 P
60320340
20120140
2
1
The game is symmetric with respect to Firm two…
1q
2q40
20100 12
5.2
0
2
1
q
q
0
5
2
1
q
q
Firm 1 chooses a production target of 1
Firm 2 responds with a production target of 2
QP 20120
60320120 P
160220260
40120160
2
1
1q
2q
Firm 1
Firm 2
67.1*
1q
67.1*2 q
Eventually, these two firms converge on production levels such that neither firm has an incentive to change
40
20100 12
40
20100 21
40
67.12010067.1
We would call this the Nash equilibrium for this model
Recall we started with the demand curve and marginal costs
20
20120
MC
QP
Mqq 67.1*2
*1
33.53$)33.3(20120 P
66.55$67.12067.133.53
66.55$67.12067.133.53
2
1
The markup formula works for each firm
33.53$)67.1(206.86
67.1*
P
MQ
1
1
MCp
6.167.1
33.53
20
1
iQ
P
P
Q
6.11
1
20$33.53$
20$
206.862020120 112
MC
qqqP
Had this market been serviced instead by a monopoly,
70$)5.2(20120
5.2*
P
MQ
20$
20120
MC
QP
1
1
MCp
4.15.2
70
20
1
Q
P
P
Q
4.11
1
20$70$
Had this market been instead perfectly competitive,
20$)5.2(20120
5*
P
MQ
20$
20120
MC
QP
1
1
MCp
1
1
20$20$
20$
20120
MC
QP
Monopoly
000,10
5.2
70$
5.2*
HHI
LI
P
MQ
Perfect Competition
0
0
20$
5*
HHI
LI
P
MQ
2 Firms
000,5
65.1
53$
67.1
33.3
HHI
LI
P
q
MQ
One more point…
125$5.2)20$70($
70$
5.2*
P
MQ
55$67.1)2053($
33.53$
67.1*
P
MQ
Monopoly Duopoly
If both firms agreed to produce 1.25M chips (half the monopoly output), they could split the monopoly profits ($62.5 apiece). Why don’t these firms collude?
Suppose we increase the number of firms…say, to 3
QP 20120
Demand facing firm 1 is given by (MC = 20)
32120120 qqqP
132 202020120 qqqP
20402020120 132 qqqMR
40
2020100 321
qqq
The strategies look very similar!
Expanding the number of firms in an oligopoly – Cournot Competition
BN
cAqi )1(
BN
cANQ
)1(
cN
N
N
AP
11
Note that as the number of firms increases:Output approaches the perfectly competitive level of production Price approaches marginal cost.
Lets go back to the previous example…
cMC
BQAP
20$
20120
MC
QP
p
QD
$70
2.5
CS = (.5)(120 – 70)(2.5) = $62.5
$62.5
What would it be worth to consumers to add another firm to the industry?
Recall, we had an aggregate demand and a constant marginal cost of production.
Monopoly$120
000,10
5.2
70$
5.2*
HHI
LI
P
MQ
20$
20120
MC
QP
p
QD
$53
3.33
CS = (.5)(120 – 53)(3.33) = $112
$112
Recall, we had an aggregate demand for computer chips and a constant marginal cost of production.
000,5
65.1
53$
67.1
33.3
HHI
LI
P
q
MQ
Two Firms
20$
20120
MC
QP
p
QD
$45
3.75
CS = (.5)(120 – 45)(3.75) = $140
$140
267,3
25.1
45$
75.33
25.1
HHI
LI
P
Mqi
With three firms in the market…
Three Firms
0
10
20
30
40
50
60
70
80
0
1
2
3
4
5
6
Number of Firms
Firm Sales Industry Sales Price
Increasing Competition
Increasing Competition
0
50
100
150
200
250
300
Number of Firms
Consumer Surplus Firm Profit Industry Profit
20$
20120
MC
QP
Now, suppose that there were annual fixed costs equal to $10
How many firms can this industry support?
BN
cAqi )1(
c
N
N
N
AP
11
010$)20$( ii qP Solve for N
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
With a fixed cost of $10, this industry can support 7 Firms
1q
2q
Firm 1
Firm 2
The previous analysis was with identical firms.
67.1*2 q
67.1*1 q
Suppose Firm 2’s marginal costs increase to $30
20$
20120
MC
QP40
20100 12
40
20100 21
50%
50%
1q
2q
Firm 2
67.1*2 q
67.1*1 q
30$
20120
MC
QP
304020120
2020120
21
21
qqMR
qqP
Suppose Firm 2’s marginal costs increase to $30
40
2090 12
If Firm one’s production is unchanged
41.1
40
67.120902
q
41.1
1q
2q
Firm 1
Firm 233.12 q
83.1*1 q
Firm 2’s market share drops
42%
58%
40
2090 12
40
20100 21
64.3533.13033.18.56
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8.56$16.320120
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1q
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Firm 1
Firm 233.12 q
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Firm 2’s market share drops
42%
58%
The Process…
With a rise in marginal costs, Firm 2’s profit margins shrink
To bring profit margins back up, Firm 2 lowers production levels which lowers industry output and raises the price
A higher price raises Firm 1’s profit margins. This causes them to expand production
The previous analysis (Cournot Competition) considered quantity as the strategic variable. Bertrand competition uses price as the strategic variable.
p
QD
Q*
P*
Should it matter?
QP 20120 Just as before, we have an industry demand curve and two competing duopolies – both with marginal cost equal to $20.Industry Output
1qD
12 2020120 qqP PQ 05.6 Quantity Strategy
1p
1qD
Bertrand Case
220120 q
p
2p
Firm level demand curves look very different when we change strategic variables
If you are underpriced, you lose the whole market
If you are the low price you capture the whole market
At equal prices, you split the market
Price competition creates a discontinuity in each firm’s demand curve – this, in turn creates a discontinuity in profits
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As in the cournot case, we need to find firm one’s best response (i.e. profit maximizing response) to every possible price set by firm 2.
Firm One’s Best Response Function
mpp 2
Case #1: Firm 2 sets a price above the pure monopoly price:
220 pCase #3: Firm 2 sets a price below marginal cost
202 ppm
Case #2: Firm 2 sets a price between the monopoly price and marginal cost
mpp 1
21 pp
21 pp
2pc Case #4: Firm 2 sets a price equal to marginal cost
cpp 21
What’s the Nash equilibrium of this game?
However, the Bertrand equilibrium makes some very restricting assumptions…
Firms are producing identical products (i.e. perfect substitutes)Firms are not capacity constrained
Monopoly
000,10
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70$
5.2*
HHI
LI
P
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Perfect Competition
0
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20$
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2 Firms
000,5
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An example…capacity constraints
Consider two theatres located side by side. Each theatre’s marginal cost is constant at $10. Both face an aggregate demand for movies equal to
PQ 60000,6 Each theatre has the capacity to handle 2,000 customers per day.
What will the equilibrium be in this case?
PQ 60000,6 If both firms set a price equal to $10 (Marginal cost), then market demand is 5,400 (well above total capacity = 2,000)
Note: The Bertrand Equilibrium (P = MC) relies on each firm having the ability to make a credible threat:
“If you set a price above marginal cost, I will undercut you and steal all your customers!”
33.33$
60000,6000,4
P
P
At a price of $33, market demand is 4,000 and both firms operate at capacity
With competition in price, the key is to create product variety somehow! Suppose that we have two firms. Again, marginal costs are $20. The two firms produce imperfect substitutes.
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Product Differentiation
Recall Firm 1 has a marginal cost of $20
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Each firm needs to choose price to maximize profits conditional on the other firm’s choice of price.
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Firm 1 profit maximizes by choice of price
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Firm 1’s strategy
$30
Firm 2 sets a price of $50
Firm 1 responds with $55
1p
2p
Firm 1
Firm 2
30$
30$
60$
60$
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With equal costs, both firms set the same price and split the market evenly
Monopoly
000,10
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Perfect Competition
0
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2 Firms
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Firm 2
Suppose that Firm two‘s costs increase. What happens in each case?
Bertrand
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With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price
1p
2pFirm 1
Firm 2
Suppose that Firm two‘s costs increase. What happens in each case?
With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price
A higher price from firm two sends customers to firm 1. This allows firm 1 to raise price as well and maintain market share!
Cournot (Quantity Competition): Competition is for market shareFirm One responds to firm B’s cost increases by expanding production and increasing market shareBest response strategies are strategic substitutes
Bertrand (Price Competition): Competition is for profit marginFirm One responds to firm B’s cost increases by increasing price and maintaining market shareBest response strategies are strategic complements
1p
2pFirm 1
Firm 2
1q
2q
Firm 1
Firm 2
Bertrand Cournot
Stackelberg leadership
In the previous example, firms made price/quantity decisions simultaneously. Suppose we relax that and allow one firm to choose first.
20
20120
MC
QP
Both firms have a marginal cost equal to $20
Firm A chooses its output first
Firm B chooses its output second
Market Price is determined
Firm B has observed Firm A’s output decision and faces the residual demand curve:
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1q
5.2
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1
2
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Knowing Firm B’s response, Firm A can now maximize its profits:
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1
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qPFirm 1 produces the monopoly output!
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Monopoly
000,10
5.2
70$
5.2*
HHI
LI
P
MQ
Perfect Competition
0
0
20$
5*
HHI
LI
P
MQ
2 Firms
587,5
25.1
45$
25.1
5.2
75.3
2
1
HHI
LI
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q
q
MQ(67%)
(33%)
Sequential Bertrand Competition
We could also sequence events using price competition.
80
40121
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Product Differentiation
Both firms have a marginal cost equal to $20
Firm 2 chooses its price first
Firm 2 chooses its price second
Market sales are determined
38.1 qSequential Bertrand Competition
80$1 p
70$2 p 62.2 q
Monopoly
000,10
5.2
70$
5.2*
HHI
LI
P
MQ
Perfect Competition
0
0
20$
5*
HHI
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P
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2 Firms
288,5
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2
1
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Cournot vs. Bertrand: Stackelberg Games
Cournot (Quantity Competition): Firm One has a first mover advantage – it gains market share
and earns higher profits. Firm B loses market share and earns lower profits
Total industry output increases (price decreases)
Bertrand (Price Competition):Firm Two has a second mover advantage – it charges a lower price (relative to firm one), gains market share and increases profits.Overall, production drops, prices rise, and both firms increase profits.
Campbell’s Soup has accounted for 60% of the canned soup market for over 50 years
Market Dominance
Sotheby’s and Christie’s have controlled 90% of the auction market for two decades (each holds 50% of its own domestic market)
Intel has held 90% of the computer chip market for 10 years.
Microsoft has held 90% of the operating system market over the last 10 years
On average, the number one firm in an industry retains that rank for 17 – 28 years!
Entry/Exit and Profitability
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Its normally assumed that as demand patterns shift, resources are moved across sectors – as the price of bananas rises relative to apples, there is exit in the apple industry and entry in the banana industry (bananas are more profitable)
Bananas Apples
THIS IS INCONSISTANT WITH THE FACTS!!
Evolving Market Structures….Some Facts
Entry is common: Entry rates for industries in the US between 1963 – 1982 averaged 8-10% per year.
Entry occurs on a small scale: Entrants for industries in the US between 1963 – 1982 averaged 14% of the industry.
Survival Rates are Low: 61% of entrants will exit within 5 years. 79.6% exit within 10 years.
Entry is highly correlated with exit across industries: Industries with high entry rates also have high exit rates
Entry/Exit Rates vary considerably across industries: Clothing and Furniture have high entry/exit, chemical and petroleum have low entry/exit.
EntrantsMarket Dominated by Incumbents
Exits
The data suggests that most industries are like revolving doors – there is always a steady supply of new entrants trying to survive.
The key source of variation across industries is the rate of entry (which controls the rate of exit)
Is this a result of predatory practices by the incumbents?
Predatory Pricing vs. Profit Maximizing
Predatory pricing describes actions that are optimal only if they drive out rivals or discourage potential rivals!
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Recall the previous example…each firm has a marginal cost of $20
11070 qP With limit pricing, firm 1 chooses a production level to drive price down to marginal cost
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5
2
1
q
q
1q
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Firm 2Firm 1’s “entry deterring” output
Profit maximizing output
Entry deterrence generally involves overproducing today to drive your opponent out of business!
Firm 1
Overproduction by firm 1.
There have been numerous cases involving predatory pricing throughout history.
There are two good reasons why we would most likely not see predatory pricing in practice
1. It is difficult to make a credible threat (Remember the Chain Store Paradox)!
2. A merger is generally a dominant strategy!!
Standard Oil
American Sugar Refining Company
Mogul Steamship Company
Wall Mart
AT&T
Toyota
American Airlines
Capacity as a Commitment Device in Predatory Pricing
In 1945, the US Court of Appeals ruled that Alcoa was guilty of anti-competitive behavior. The case was predicated on the view that Alcoa had expanded capacity solely to keep out competition – Alcoa had expanded capacity eightfold from 1912 – 1934!!
In the 1970’s Safeway increased the number of stores in the Edmonton area from 25 to 34 in an effort to drive out new chains entering the area (It did work…the competition fell from 21 stores to 10)
In the 1970’s, there were 7 major firms in the titanium dioxide market (A whitener used in paint and plastics). Dupont held 34% of the market but had a proprietary production technique that generated less pollution. When stricter pollution controls were imposed, Dupont increased its market share to 60% while the rest of the industry stagnated.
The Bottom Line…
There have been numerous cases over the years alleging predatory pricing. However, from a practical standpoint we need to ask three questions:
1. Can predatory pricing be a rational strategy?
2. Can we distinguish predatory pricing from competitive pricing?
3. If we find evidence for predatory pricing, what do we do about it?
Price Fixing and Collusion
Prior to 1993, the record fine in the United States for price fixing was $2M. Recently, that record has been shattered!
Defendant Product Year Fine
F. Hoffman-Laroche Vitamins 1999 $500M
BASF Vitamins 1999 $225M
SGL Carbon Graphite Electrodes 1999 $135M
UCAR International Graphite Electrodes 1998 $110M
Archer Daniels Midland Lysine & Citric Acid 1997 $100M
Haarman & Reimer Citric Acid 1997 $50M
HeereMac Marine Construction 1998 $49M
In other words…Cartels happen!
01002003004005006007008009001000
1993 1994 1995 1996 1997 1998 1999
Antitrust Criminal Division Fines ($ Millions)
Cartel Formation
In a previous example, we had three firms, each with a marginal cost of $20 facing a market demand equal to
32120120 qqqP If we assume that these firms engage in Cournot competition, then we can calculate price, quantities, and profits
31$
45$
75.33
25.1
i
i
i
P
Mq
Firm Output
Industry Output
Market Price
Firm Profits
Total industry profit is $93
Cartel Formation
In a previous example, we had three firms, each with a marginal cost of $20 facing a market demand equal to
QP 20120 If these three firms can coordinate their actions, they could collectively act as a monopolist
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70$
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5.2
m
i
m
P
MQq
MQ
Splitting the profits equally gives each firm profits of $41.67!!
Cartel Formation
While it is clearly in each firm’s best interest to join the cartel, there are a couple problems:
With the high monopoly markup, each firm has the incentive to cheat and overproduce. If every firm cheats, the price falls and the cartel breaks down
Cartels are generally illegal which makes enforcement difficult!
Note that as the number of cartel members increases the benefits increase, but more members makes enforcement even more difficult!
Cartels - The Prisoner’s Dilemma
Jake
Clyde
Cooperate Cheat
Cooperate $20 $20 $10 $40
Cheat $40 $10 $15 $15
The problem facing the cartel members is a perfect example of the prisoner’s dilemma !
But we know that cartels do happen!!
Time0 1 2 3 4 5
Play Cournot Game
We can assume that cartel members are interacting repeatedly over time
Play Cournot Game
Play Cournot Game
Play Cournot Game
Play Cournot Game
Play Cournot Game
Cartel agreement made at time zero.
However, we’ve already shown that if there is a well defined endpoint in which the game ends, then the collusive strategy breaks down (threats are not credible)
Cartel members might cooperate now to avoid being punished later
Cooperation also occurs with an infinite horizon (i.e. the game never ends!!)
Time0 1 2 3 4 5
Play Cournot Game
Play Cournot Game
Play Cournot Game
Play Cournot Game
Play Cournot Game
Play Cournot Game
Cartel agreement made at time zero.
)()( CheatingPDVnCooperatioPDV
Firms will cooperate when its in their best interest to do so!
Cartels are easier to maintain when there are higher annual profits and interest rates are low!
Where is collusion most likely to occur?
High profit potential
The more profitable a cartel is, the more likely it is to be maintained
Inelastic Demand (Few close substitutes, Necessities)
Cartel members control most of the market
Entry Restrictions (Natural or Artificial)
Its common to see trade associations form as a way of keeping out competition (Florida Oranges, Got Milk!, etc)
April 15,1996 (“Grape Nut Monday”): Post Cereal, the third largest ready-to-eat cereal manufacturer announced a 20% cut in its cereal prices
Kellogg’s eventually cut their prices as well (after their market share fell from 35% to 32%)
The breakfast cereal industry had been a stable oligopoly for years….what happened?
Supermarket generic cereals created a more competitive pricing atmosphere
Changing consumer breakfast habits (bagels, muffins, etc)
Where is collusion most likely to occur?
Low cooperation costs
If it is relatively easy for member firms to coordinate their actions, the more likely it is to be maintained
Small Number of Firms with a high degree of market concentration
Similar production costs
Little product differentiation
Some cartels might require explicit side payments among member firms. This is difficult to do when cartels are illegal!
Detecting Collusion
In general, it is difficult to distinguish cartel behavior from regular competitive behavior (remember, the government does not know each firm’s costs, the nature of demand, etc)
Signs of Potential Collusion
Little relationship between price and costs
Little relationship between price and information sets
Excess Capacity (as a means of retaliation)