Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Oligopoly
E. Glen Weyl
University of Chicago
Clase 8
Teoría Avanzada de Precios y Estructuras de Mercado
Escuela de Verano 2012
Departamento de Economía
Universidad de los Andes
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Introduction
So far firms either price-takers or monopoly
Today imperfect competition or oligopoly
1
2
Static oligopoly solution concepts
Stigler’s theory of collusive oligopoly
Incentives for collusion
Factors facilitating and hampering collusion
3
Conjectural variations as a summary of collusion
The consistent conjectures solution concept
4
5
6
7
8
Incidence in oligopoly: symmetric v. asymmetric
Selection and cream-skimming distortions
Cournot’s Theorem in theory and practice
Competition policy: institutions and policies
Merger analysis: the first-order approach
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Cournot and oligopoly solutions
Most basic oligopoly model is that of Cournot
Demand P(Q); individual firm costs Ci (qi ); MCi ≡ Ci0
Each firm takes others’ q’s as given; P − MCi = qi P 0
Mark-up over cost because of infra-marginal quantity
But natural reaction: why take others’ quantity as given?
Let to long, complicated debate on solution concepts
We’ll start by giving a flavor of what this was like:
Price competition, differentiated products, collusion, etc.
Can get very confusing and Byzantine
In the end, though, details not so important
What really matters is overall competitiveness
How far off from monopoly do firms behave?
This can often be measured, reasoned about more directly
=⇒ Everything else just input to basic summary statistics
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
The Bertrand-Edgeworth paradox
To give flavor of debate, though, let’s go through bit of history
Bertrand and Edgeworth: firms take others’ price given
=⇒ Profits discontinuous! If I charge a bit below, get everyone
Suppose all have same, known cost?
=⇒ Positive mark-up cannot be equilibrium; undercut
Bertrand and Edgeworth’s Paradox
With N > 1, only equilibrium is P = c!
Called Bertrand-Edgeworth paradox or critique
Two firms enough for competition? Many think absurd
Unlikely sales change discontinuous; possible resolutions?
1
2
3
Firms differ in their costs, costs may not be known
Firms’ products are not the same (inherent or search)
Firms collude or don’t take others prices as given
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Cost heterogeneity and the Bertrand paradox
Simplest response is that firms differ in costs
This case like first-price auction
Each firm tries to just beat next firm
=⇒ P 6= min{ci }; rather P = E [c2 ], cost of 2nd lowest
Clearly not quite the average cost, but a lot less sensitive
As we get more firms, second lowest closer to first (?)
=⇒ Predictions more similar to Cournot than simple Bertrand
=⇒ Major virtue of Cournot greater robustness (and simplicity)
Broader: absurd conclusions indicate model problem
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Differentiated products: the most popular solution
Another, more popular, response is product differentiation
If one firm increases price, demand only falls continuously
1
Consumers view products as differentiated
2
Identical, but consumers have to search
Non-price characteristics as last week
Prices are not transparent, costly to go to store
=⇒ Once in store, monopolist competing against cost of 2nd visit
Either way we can write for firm i, Q i (p1 , . . . , pi , . . . , pN )
So long as nice, smooth, no Bertrand-style discontinuities
Each monopolist on own product, but others substitute
∂Q i
∂pj
> 0 for i 6= j
Very broad model, could quantities as strategies
However “Nash-in-prices” or “Bertrand” has become central
Called “Differentiated Products Nash-in-Prices” or (DPNiP)
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Pricing with differentiated products
Same basic principles hold for pricing in this case
We can define residual demand elasticity:
Elasticity of demand holding fixed other prices?
i
pi
ri = ∂Q
∂pi Q i
Then just follow Lerner rule:
pi −MCi
pi
=
1
ri
Nothing special about prices as strategies
1
Just as easily defines firm’s optimal quantity
2
Could also do à la Cournot/Nash-in-quantities
Key is holding fixed other firms’ prices
Then residual elasticity is holding fixed other quantities
Less common so we won’t get into math, but very similar
=⇒ No reason differentiated products needs price strategies
This is used extremely broadly in industrial economics
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
How oligopolists benefit from a cartel
Oligopolists create (pecuniary) externalities on one another?
1
Purely pecuniary under Cournot; why?
Believe all other firms’ quantities are given
2
Purely real under DPNiP; why?
Believe other firms’ prices are fixed, quantities change
=⇒ Quantities always too high under Cournot but...?
May be too high under DPNiP if other mark-ups larger
Regardless of social benefits or costs, firms benefit by avoiding
Because substitutes, q ↓ /p ↑ always benefits competitor
In fact, let’s define two firms competing by being substitutes
If they act to internalize this (pecuniary) externality we say?
They are “colluding” or “forming a cartel” or my favorite:
“Combination in the restraint of trade”
Denounced since Adam Smith, illegal under Sherman Act
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
A cartoon that help catalyze the antitrust act
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Legal restrictions on cartel formation
Once upon a time, cartel agreements were legally enforceable
1
In the US prior to the Sherman Act
2
In Continental Europe prior to the EU reforms
3
Hardly illegal in many developing countries (like Perú)
4
Britain all the way back to 18th century made illegal
Luckily the United States now leads the world on enforcement
1
Explicit agreement about prices/service illegal
Only competitors; complements are different as we’ll see
2
Even without communication (“tacit”) can be prosecuted
3
Criminal (jail time) and civil penalties
In practice much less because hard to prove
Usually “treble damages”: probability of detection ≈
=⇒ Many practical challenges in running a cartel today
=⇒ Collusion difficult, only possible in limited settings
Weyl Summer Course
Oligopoly
1
3
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Incentives to defect from a cartel
The basic problem is that cartel benefits all but...
Each firm has incentive to betray; why?
This is what it means to be an (pecuniary) externality
By reducing price/increasing quantity each benefits
Can steal business, from others, benefit from higher prices
=⇒ The more ambitious cartel is, the less stable?
Higher is the price, more incentive to steal the sales
Near competitive level, little or no incentive to cheat
=⇒ Extent of collusion is ability to deter cheating
Every cartel needs to create expectations of punishment
=⇒ Policy related to cartels all about this interplay
1
2
Goal of cartel is to ensure credible punishment of cheaters
Goal of agency, customers is to catch and prevent
Stigler bases oligopoly theory on this back-and-forth
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Detection, punishment and cartel enforcement
In order for the cartel to deter cheating it must?
1
Be able to determine what the optimal agreement is
Diffuse information, as in other externality problems
Hindered further here by government breathing down neck
2
Have clear what does and does not constitute cheating
Firms should be given some flexibility (private information)
But if too much flexibility then cartel does not function
3
Be able to detect cheating, distinguish from background
Many things might look like cheating but be innocent
4
Have cost-effective means of punishment
If you could tax and redistribute ideal
Shifting market share across firms works well
Price wars harm everyone so less effective
5
Be able to do this quickly (patience and frequency)
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Stigler’s factors facilitating/deterring collusion
Stigler’s theory is based on these necessities; factors?
He emphasizes factors facilitating/hindering these
1
Large, heterogeneous buyers hurt, small homo help
Hard to track, easy to extract undermining concession
2
Heterogeneity of product/firms hurts
Harder to define optimum, more incentive for one defect
3
Price transparency helps track defections
Ability to offer secret price cuts key
Case against collecting industry, offering info to consumers
4
5
6
7
Industry concentration helps reduce tracking, temptation
Variability of demand hurts monitoring
Frequency of interaction helps detect soon
Growing demand helps, declining hurts
If declining, grab what you can while you can
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Summarizing collusion through conjectures
All of these determine the extent of deterrence
Most deterrence happens through price cuts/wars
So simple way to summarize is firms’ conjectures
If I lower price, how much will rival lower (or raise?) hers?
Also works with quantity...how do they respond?
This varies depending on Stigler’s factors
=⇒ Models incorporating called Conjectural Variations (CV)
Usually capture by “parameter” of conjectured adjustment
Note this idea is useful to change price v. quantity models
Cournot is price model with conjectured “accommodation”
Price is quantity with conjectured “aggression”
=⇒ Thus CV is broad framework incorporating all theories
Good because it can be used to talk about all them
But to be useful requires more structure
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Cournot pricing with conjectural variations
Let’s consider simplest Cournot model
Again profits [P (Q−i + qi ) − c] qi
But now extra term, as other quantities not fixed:
Optimal pricing given by?
dQ
P + P 0 qi 1 + dq−ii = c
If
dQ−i
dqi
dQ−i
dqi
> 0 then MR further below P
Therefore called a “conjectured accommodating reaction”
If you are nice and reduce quantity, others follow you
This is how collusion is facilitated
On the other hand, if aggressive,
dQ−i
dqi
< 0, lower prices
This case was on your exam; if
dQ−i
dqi
= −1 then Bertrand
Also starting from Bertrand, DPNiP
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Estimating conjectures
Natural question is how much Stigler’s factors impact
Factors are all qualitative; CV parameter quantitative
Natural question is how much these change
Determines impact on amount of collusion
Natural approach: regress CV parameter on factors
Astonishingly, I don’t think anyone has ever done this!
To do this, though, we need to measure the CV parameter
This is difficult, but two approaches have been taken
1
Measure c, P 0 and solve for CV parameter
Works pretty well, but sometimes cost data difficult
“New empirical IO” (NEIO) tries to avoid using cost data...
2
Measure by comparing different types of demand shifts
If demand curve rotates, affects price ∝ market power
Thus size of impact measures CV parameter
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
T F. Bresnahan
/ The oligopoly
solution
Twisters v. shifters
(Bresnahan
1981)
concept is identified
P
MRl
Q
Fig. 2.
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
A hypothesis for measuring conjectures
This suggests another natural way to measure conjectures
Presumably, firm forms conjectures based on experience
In past, when c ↑ =⇒ p ↑, what happened?
Did my rival’s price rise or fall? By how much?
This seems a reasonable way to determine conjecture
This is called consistent conjecture hypothesis
Due to work by Bresnahan (1981) and others
If you think about it, other models a bit strange
In Cournot, if I change quantity, so does rival...
But I don’t take this into account!?
Also very convenient from empirical perspective
=⇒ If we observe shocks, we can measure conjecture
Similar: shock to firm cost shows relevant demand
For positive purposes, shocks to firm don’t move demand
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Static solution concepts
Stigler’s theory of collusion
Conjectural variations
Consistent conjectures: estimating residual demand
This lets us isolate the part of the market we want to consider
1
Residual demand facing a single firm
Measured by Baker and Bresnahan (1988)
Use firm-specific cost shocks (changes in factor prices)
Apply to brewing industry; breweries in different locations
Changes in transport costs, simple, easy methodology
2
Merger between two rival firms
Next class we’ll talk more about mergers
But key here is the effect of two firms merging
Useful to separate from rest of the industry...
Under consistent conjectures, you can do exactly this!
3
Could be applied more broadly (quality, antitrust)
This approach, for historical reasons, largely go lost
Great opportunity for a senior thesis!
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Conduct and incidence in symmetric oligopoly
Simple way to summarize total industry conduct:
All have price P(Q), each qi =
Q
n;
cost C(Q) = nc
Q
n
P
MC = C 0 (Q) = c 0 ; = QP
0
P−MC
·
=
θ;
summarizes
competitiveness
D
P
θ = 0 in perfect competition; θ = 1 under monopoly
Model nests/simplifies wide range of settings
Suppose that θ constant in tax, price
Same analysis as in monopoly shows ρ =
1
1+ D +θMS
S
In between monopoly and competition, indexed by θ
If θ ↑ (↓) with tax or price, ↑ (↓) pass-through
Incidence mix as well?
1
2
ρ
dPS
dCS
dt = −(1 − θρ)Q, dt = −ρQ, I = 1−θρ ; w constant MC:
θρ
dDWL
dPS
d q̃ = −θρM, d q̃ = − [1 + (1 − θ) ρ] M, Ĩ = 1+(1−θ)ρ
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Graph of general oligopoly pricing
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Application to specific models
Model a bit abstract; let’s note how others fit in
1
Cournot?
0
P − MC = −P 0 q = − PnQ so θ = n1 ; constant
2
Differentiated Bertrand?
P−MC
P
∂Q
∂P
i
n ∂qi
∂p
=
=
1
r
∂q i
∂pi
=−
q
+(n−1)
∂q i
∂pi
= − P Q∂Q
∂P
"
i
P ∂qi
∂p
∂q i
∂pj
∂Q
∂P
=⇒ θ =
#
i
i
n ∂qi
∂p
∂Q
∂P
i
n ∂qi
∂p
∂q
j
∂p
= 1 + (n − 1) ∂q
i
≡1−D
∂pi
∂q i
j
∂q j
i
∂pi
∂pi
∂p
∂p
D ≡ −(n − 1) ∂q
i = −(n − 1) ∂q i aggregate diversion ratio
Fraction of sales lost to me that go to one of my rivals
Measure of real externalities per sale, so makes sense
Not constant; usually falls with price so ρ bit overstated
As prices higher, diversion to rivals products less attractive
Everything earlier about incidence again applies here!
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Asymmetric oligopoly and misallocation
Why less DWL in oligopoly (θMdq) than monopoly (Mdq)?
Mdq = consumers substituting to perfectly competitive
good
=⇒ No real externalities from sales
But if consumers instead substitute to good with mark-up
=⇒ Subtract off real externality: M − M dq
M is average mark-up of substituted-to good
Directly (Bertrand) or indirectly (strategic under Cournot)
Symmetric oligopoly: just reduces DWL proportionally
Captured by θ
But more interesting when not symmetric
Then some firms may have higher mark-ups than others?
1
2
3
Differences in cost structure
Differences in conduct, sophistication, conjectural
parameters
Weyl Summer
Course
Oligopoly
Differentiated
product
quality
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Misallocation in standard models
1
Cournot
Each firm sets M = P 0 q so M ∝ q
=⇒ Beneficial to reallocate to largest firms
=⇒ Merger of big and small firm not always bad
2
Differentiated Bertrand
Firm mark-up inversely proportional to own-elasticity
Suppose one firm inelastic to outside good, other elastic
=⇒ If close substitutes, may be good to merge, shut-down elastic
Favoritism towards high mark-up firms
3
Monopolistic competition (Dixit-Stiglitz 1977)
Constant elasticity, all firms same elasticity
=⇒ Same (relative) mark-ups for all firms
If perfectly competitive numeraire, too little production, entry
But if whole economy, no distortion, first-best!
=⇒ Harm of overall market power is retreat to autarky
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Beneficial market power
Changes perspective on market power especially:
Heterogeneity of market power, not level, key problem
This leads to very different perspective on many issues
1
Strategy, collusion and conjectures in oligopoly
Very harmful if one firm acts more competitively than others
Persistent traitor to cartel arrangement can be bad!
2
Strategic behavior in mechanisms
Many mechanisms (e.g. Budish): strategy like market power
Lack of sophistication =⇒ inefficiency not just inequity
Unsophisticated do worse, but harm sophisticated more!
Who is the “bad guy” here?
3
Entry into industry with market power
Trade-off of infra-marginal surplus and business stealing
Keep out firms that are just copying, bring in really new
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Selection distortions in oligopoly
So market power not all bad: real externalities
Another case of real externalities is selection
Before we studied free entry/average cost pricing
Now let’s put into oligopoly model
Suppose each firm gets representative sample, symmetric
Profits P(Q)qi − QE [c|u ≥ P(Q)]
Let AC ≡ E [c|u ≥ P(Q)] and MC ≡ E [c|u = P(Q)]
What is first-order condition?
P−[θMC+(1−θ)AC]
P
=
θ
=⇒ Weighted average of demand and MR, AC and MC
What is optimal market structure?
1
2
With adverse selection? Competition as before!
With advantageous selection? do at home: θ? =
Weyl Summer Course
Oligopoly
MC−AC
MS+MC−AC
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Optimal market structure with selection
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Cream-skimming and market collapse
Now design distortions: differentiated Bertrand
Cost same, given ρ; symmetric utility distribution
Symmetric equilibrium/optimum in ρ, P
Two margins: switching S between, each expansion X
By symmetry, same for each, size M S and M X
By symmetry, social optimum just change uniformly:
NE [u 0 − c 0 |Θ] = M X Cov (u 0 , c|X )
Competition applies profit maximization to both margins




0 |X ∪S] −E[c 0 |Θ]=M X Cov(u 0 ,c|X )+
N
 E[u

| {z }
Spence distortion
M S Cov(u 0 ,c|S)
|
{z
}
Rothschild-Stiglitz cream-skimming
“Skim cream” from competitor; blows up as M S → ∞
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Incidence in symmetric oligopoly
Is market power all bad?
Cream-skimming and selection
Applications of cream-skimming
This distortion may be important in some contexts
1
Erodes coverage in insurance markets
Skim off the best customers
2
Inefficient hazing and workplace regulation
Finance firms work long hours to skim from competitors
Potential reason for workplace regulations
I don’t think anyone has ever measured!
3
Informational racing in financial markets
Try to get out ahead on buying stocks
Wasteful tunnel from New York to Chicago
4
Competitive price-discrimination (Holmes 1989)
Grandma’s and student may not stay home, just search
This is just cream-skimming; general issue in discrimination
Important and neglected downside of competition!
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
A simple case of Cournot’s theorem
So competition perhaps not so great...
But return to world where competition good
Think about Cournot’s model: n → ∞ =⇒ θ → 0
P−MC
→ 0; efficient marginal cost pricing
P
=⇒ As long as bounded above 0 at P = MC
Cournot’s Theorem
As the number of competing firms grow arbitrarily large, price
converges to marginal cost.
One of the most fundamental results in economics
Foundation of perfect competition
Basis of most antitrust/competition policy
When not Cournot, other definitions of θ → 0
Differentiated Bertrand: things become very substitutable...
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Entry with a distribution of costs
Or with distribution of marginal costs ci
May represent Bertrand competition or auction
Optimal prices pi ≈ E [c2 |c1 = ci ]
I “bid” my guess of second bid, conditional on me winning
Exactly for inelastic demand, but lower with elastic
I won’t go through proof, but pretty intuitive
I “just try to beat” the next guy
As the number of firms grow, what happens?
Lots of firms near the lowest cost
Thus lots of firms close to lowest-cost firm
=⇒ E[c2 |c1 = ci ] → ci , c1 → c, lowest cost
Thus price converges to lowest constant marginal cost
Intuitive, as more firms, I am less necessary
=⇒ As firms increase, again price to lowest cost
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Cournot’s theorem with Bertrand competition
So again, in different setting, we obtain:
Cournot’s Theorem with Bertrand competition
As firms increase, prices gradually converge to lowest constant
marginal cost.
If all costs were not constant marginal...
Then we would need everyone with different quantities
This becomes efficient too, with competition
=⇒ In very different model, same basic result
Thus we can take this general rule about competition
1
2
Eventually, but not immediately, competition drives to cost
With “enough” firms, price should be efficient
=⇒ Natural question: how much is enough?
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Empirical study of the effect of entry
Bresnahan and Reiss (1991) proposed clever way to study
As market grows larger, can support more firms
Call number of people to support N firms SN , sN = SNN
Represents customers per firm at different numbers
If prices same, only fixed cost, constant in N
If price falls, then should decline, more for second guy
s3 < s2 < s1 , etc.
Could be other reasons as well: heterogeneity
But pretty smart first pass, easy to implement
1
2
3
Found 5 professions in many rural towns
How many people and professionals in each town?
When does s start to level out?
Interpret as convergence to perfect competition
Around 3-5 professionals
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Bresnahan
and Reiss (1991)’s data
996
JOURNAL
OF POLITICAL
ECONOMY
to-
v
*
(N
co
z
Druggists
Tire Dealers
*
Doctors
*
Dentists
+
Plumbers
_N
U)
L0
C/
0
4
5
12
Number
of Firms
FIG. 4.-Industry
ratios Of S5 to
sN by N
Weyl Summer Course
Oligopoly
56
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Other arguments for and against competition policy
This theory and empirical findings basis of competition policy
Tries to make sure enough competition in markets
We’ll talk a lot about this, but first arguments pro/con
Pro:
1
2
3
Stop from assembling too much political, cultural power
Screening out real externalities: don’t with competition and
close substitutes; like screening willingness-to-pay
“Too big to fail” in financial markets
Con:
1
2
3
4
Cream-skimming and adverse selection
Impedes economies of scale, profits from innovation
Complementarities and coordination (Monday)
Dynamic entry prevents problems; policy too late/slow
Usually policy ignores other factors
Lots of work to be done to include!
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Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
The Clayton Act and the US infrastructure
In US, authority from Clayton Antitrust Act
Sherman prevented illegal combinations (cartels)
Clayton regulates legal combinations
Why not block all mergers?
Economies of scale! Efficient, may even benefit consumers
Growing the ATT network may make reception better
Thus agencies have to weigh v. anticompetitive effect
Several agencies, but two primary share by industry?
1
2
Department of Justice Antitrust Division
Federal Trade Commission
Merging companies must pre-notify of intentions
1
2
3
Agencies subpoena data in several stages
Analyze with team of ≈ 150 PhD economists
Most survive, some settle and a few go to court
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Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Comparative international infrastructure
Perhaps most sophisticated economic regulation in world
Has been copied by most developed countries
1
2
European Commission now a major leader
Also commonwealth: UK, Australia, New Zealand, etc.
Much more primitive, unstructured in developing world
1
In many, no law against mergers even exists!
2
In others, law, but minimal infrastructure
Perú is leading example
Effectively no control, ineffective without cartel enforcement
3
Others have structure, but limited economics
Colombia still writing guidelines, institution-building
4
A few aspire to developed sophistication
China, Brazil, Chile, etc.
Very heterogeneous across world
Much to be gained by improving quality where weak
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Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Market definition and industry concentration
Traditional evaluation based on “industry concentration”
1
Treat industry as single product; how?
Requires “defining” boundaries of industry: which products?
Start with merging products, adds closest substitutes?
Both geographic and type of product
Stop when a monopolist would raise prices by 5% for 1 year
SSNIP: “Small but Significant and Nontransitory Increase in Price”
2
Measure industry concentration?
Classic measure is Herfindahl-Hirschmann
Index (HHI)
P
Let σi ≡ qQi , then H = i σi2 , sometimes multiply by 1000
1
H approximate number of firms; from above < 3 − 5 danger
Also related to collusion (Stigler) and Cournot performance
P − MCi = P 0 qi =
3
P
σ
i
=⇒
P
i
i
σi P−MC
=
P
H
Mergers causing H > 1800 and/or raising by > 300 flagged
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Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Current real-world merger policy
Unfortunately this approach has proved very cumbersome:
1
Market definition often quite cumbersome: totally 0-1
2
Relevance of concentration somewhat ambiguous
In Cournot, mergers increasing most the best (reduce cost)
Thus merger guidelines issued by agencies moved away
Represent official policy, guide to merging businesses
Issued roughly each 10 years since 1980, latest in 2010
I was closely involved with this, similar in UK and EU
1992 all based on HHI and market definition
New ones emphasize logic above (no need for definition!)
Explicitly us differentiated products model
Designed by Carl Shapiro and Joe Farrell, creators of UPP
Progress on-going, new guidelines may reflect ideas above
UK report on conjectural variations for merger review
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Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
A merger between differentiated products firms
Let’s look at the approach from these reforms
Idea: competition often between differentiated products
=⇒ Merger doesn’t eliminate product, just consolidates
Does competition help (merger hinder) in this case?
Simplest case just focus on two merging firms
A bit like monopoly: minimum of moving parts possible
Other firms later; also assume Nash-in-Prices
Demand Q i (pi , pj ), profits pi Q i pi , pj − C i Q i pi , pj
Denote partial derivatives wrt own price by Q1i other Q2i
0
0
FOC pi Q1i + Q i − C i Q1i = 0; let MC i ≡ C i , divide by Q1i :
pi = MC i +
Qi
:
−Q1i
price = MC + Cournot distortion
If now merge, profits p1 Q 1 + p2 Q 2 + C 1 Q 1 + C 2 Q 2
FOC for p1 : Q 1 + p1 − MC 1 Q11 + p2 − MC 2 Q22 = 0
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Cournot’s theorem and other rationales
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Upward Pricing Pressure and intuition
Divide by Q11 , obtain: p1 = MC 1 +
Q1
−Q11
+ p2 − MC 2
Q22
−Q11
First two terms on right-hand side exactly as before
Third term is new (effect of merger) so let’s focus on that:
UPP2→1 ≡
p2 − MC 2
| {z }
×
mark-up on partner’s product:M 2
Q22
−Q 1
| {z 1}
“diversion ratio” from 1 to 2:D12
Called the “Upward Pricing Pressure” from product 1 to 2
Always positive if substitutes: Q22 is positive if substitutes
D: every burger BK sells, how many sales does MD lose?
If they merge, BK internalizes the profits lost: M 2 D12
Exactly UPP: new opportunity cost created by merger
Like any other cost, passed-through to prices!
=⇒ All else equal, merger of competitors raises prices
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The institutions of competition policy
Merger analysis
A general model of oligopoly
This gives us basic flavor but we left out:
Other firms in the industry, conjectures (non-NiP)
Adding these is relatively simple given our work:
Define my residual demand taking into account conjectures
Qii ≡
dQ i
dpi
=
∂Q i
∂pi
+
j
∂Q i dp
j6=i ∂pj dpi
P
Qi
Qii
Then pre-merger optimum just like before: pi = MC i +
Post-merger, though, we want to hold fixed other price
If FOC’s for price, partial derivative makes us hold fixed
But conjectures don’t allow this; need to define to shut down
ei, Q
e j hold fixed pj ; skip messy math
=⇒ If i and j merger, let Q
i
i
Then FOC as above: pi = MC i +
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Oligopoly
Qi
ei
−Q
i
+ pj − MC j
ej
Q
i
ei
−Q
i
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Generalized pricing pressure
What are differences now? Well, two rather than one?
1
1 i
i
j
j
i
e
−
− i p
g ≡ Dj p − MC
e
i
{z
}
|
{z
}
|
generalized UPP (GUPP)
end of accommodating reactions (EAR)
Two changes:
e i holds fixed
e i pj − MC j where D
1
GUPP: D
j
j
Merging prices pj and whatever firm believes for others
2
EAR: merger partner reaction no longer anticipated
More accommodating reactions =⇒ offsets GUPP more
First term larger with reactions, but second more negative
Different from (simplifies to) UPP: GUPP - EAR but...
Result relatively robust to conjectures because offset
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Oligopoly
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Measuring pricing pressure
How can we actually measure all this? Several approaches:
1
Internal company documents
If we can get access, may discuss reactions, diversion
Companies have to think about these things
2
Surveys and internet data
Ask consumers about their second choice; like diversion
Better: data from online, what other people bought etc.
3
Win-loss studies for auctions
Who are most common first and second in auction?
4
Econometrics
Estimate demand using changes in cost
Difficult under NiP: need changes to all firms’ costs
5
Consistent conjectures (Baker and Bresnahan 1986)
With consistent conjectures, residual demand for partners
Thus only need changes in merging firm costs
Weyl Summer Course
Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
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Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Pass-through and price impact
We may want not just opportunity cost, but also price change
But we know very well how to translate!
If only one firm raised price, just multiply by pass-through
This is basically right, but two (small) complications
1
2
Merger pushes up both merging firms’ prices
Rise (strategically or otherwise) affects other firms’ prices
All this covered by pass-through matrix ρ
Each element is effect of one firm’s cost on another’s price
Then if g is GePP for merging firms, 0 elsewhere:
∆p ≈ g> × ρ
Don’t worry, you don’t really need to follow these matrices
Key point is pass-through can be used to covert here
This is lucky, because we use it for everything else
Makes easy to measure: same cost shocks as for diversion
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Oligopoly
Oligopoly and Solution Concepts
Incidence and the Downside of Competition
Competition Policy
Cournot’s theorem and other rationales
The institutions of competition policy
Merger analysis
Prices and welfare impact
How much do these changes in price hurt consumers?
As always, by envelope, just multiply by quantity
∆CS ≈ −g> × ρ × Q
Quantities particularly easy to measure
Price index (percent increase) by dividing by p × Q
How about social welfare?
Need to find quantity changes: ∆Q ≈ g> × ρ × ∂Q
∂p
Then multiply by mark-ups: ∆SS ≈ g> × ρ × ∂Q
∂p × M
Longer, but all stuff we had from before (demand, etc.)
Just like monopoly comparative statics, simple principles
Benefit of normative: can incorporate other effects:
1
2
Platforms, quality and Spence distortion
Selection and cream-skimming distortions
Very active area of research
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Oligopoly