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A Theory of Bilateral Oligopolywith Applications to Vertical Mergers
Kenneth HendricksUBC and University of Texas
andR. Preston McAfee
University of Texas
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Exxon Mobil Merger
§Refining is concentrated in CA
§Retail Sales are concentrated too
§How to assess the impact of the merger?
§How to think about captive consumption?
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Other Applications
• Trade in spectrum licenses• BP/ARCO
• IBM’s captive chip production• Defense industry mergers
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Questions
• How to treat captive consumption?• What is the effect of vertical integration?
• With concentration upstream, can an increase in concentration downstream improve efficiency?
• How to generalize HHI to two-sided concentration?
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Literature
• Old literature on “bilateral oligopoly”
• Many, many papers with special assumptions about upstream and downstream configuration
– Foreclosure, raising rival’s costs, etc.
• Klemperer & Meyer
– Invented solution concept
– No applied results
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Review of Cournot
• Profits are• Manipulating the first order conditions:
• Where si is the market share of firm i and åis the elasticity of demand.
• Thus, the HHI measures price cost margins.
)()( iiij ji qcqqp −= ∑π
,)(
))(( 2
ε
∑∑ =
′− i ii
iis
QQp
qcQp
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Special Theory
• Ignore downstream competition• Firms have capacities ki, gi
• Capacities lead to payoffs from consumption qi and production xi of:
).( iii
ii
i
iii xqpxck
qvk −−
−
=
γγπ
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Special Theory, Cont’d
• Formulation facilitates consideration of mergers
• Merger if i and j produces a firm with capacities ki + kj, gi+gj.
• Net purchase at identical market price p• Value v, cost c exhibit CRS w.r.t. (q,k)
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Solution Concept
• Firms can pretend to have other k, g• Restricted to acting like a possible type
• Market maps the pretend levels to the efficient outcome (p,qi) given those levels
• Firm choice is full information equilibrium to the induced game
• Mirrors Cournot black box
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Special Theory Solution
• å, h are the elasticities of demand (v) and supply c, respectively. si and si are the shares of consumption and production.
• Theorem 1: In any interior equilibrium,
andii cv ′=′
.)1()1( ii
iiii
ss
ppc
ppv
σηε
σ
−+−
−=
−′=
−′
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Special Theory Solution
• Generalizes to incorporate boundaries• Yields Cournot as h Æ0 and buyers are
dispersed• More generally, value minus cost is:
( ) ( )∑∑∑ ===
−+−
−=′−′
n
iii
iin
i ii
n
i ii ss
cvsp 1
2
11.
)1()1(1
σηε
σσ
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Special Theory Conclusions
• Only net trades matter• Captive consumption can be safely ignored
• HHI generalizes to this intermediate good case
• Similar information requirements
• Quantity, not capacity, shares are relevant (true in Cournot, too)
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General Theory
• Add Cournot downstream• Retail price r(Q), elasticity a
• Selling cost ki w(qi/ki), elasticity b• Production cost gi c(xi/gi), elasticity h• q=p/r
• A=1/a; B=(1-q)/b; C=q/h
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General Theory
• Firms can pretend to have different capacities than they have
• Firms maximize given the behavior of others and the true capital levels
• Market prices, quantities are efficient given the pretend levels chosen by the firm.
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Main Theorem
• The quantity weighted difference between price and marginal cost, or modified herfindahl, is:
.)1()1()1)(1(
)1()1()(
1
222
∑ =
−+−+−−
−+−+−=
n
i iiii
iiiiii
sCBsA
sACABssBCMHI
σσσσσ
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Special Cases
• A=0: perfectly elastic demand, yields special theory.
• AÆ•:
∑ −+
−−=
ii
i
i
i
s
sMHI
)1()1()1(
22
σησ
θβ
θ
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Effect of Downstream
• The more elastic the downstream demand, the more only the HHI based on net trades matters.
• When downstream demand is very inelastic, MHI is a weighted sum of upstream and downstream HHIs, with weights given by the intermediate to final good price ratio.
– Captive consumption matters 100%
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Effect of Downstream
• Thus, paper helps resolve the debate about accounting for captive consumption
• Count captive consumption more the more inelastic is downstream demand
• Counts strongly in BP-Arco
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Special Cases, Cont’d
• B=0 is a constant marginal cost of retailing• Any retailer can expand easily
• Only the upstream matters.
∑ ==
+−
=n
ii
iB
MHI1
2
0 )1( θασηθσ
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The Exxon Mobil Merger
• In California, both gasoline refining and retailing are highly concentrated
• Seven firms account for 95% at each level• Retail demand is very inelastic
Exxon Mobil Merger
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The Exxon Mobil Merger
6.85.4Ultramar
8.97.0Exxon
9.77.0Mobil
20.413.8Arco
16.016.6Equilon
17.821.5Tosco
19.226.4Chevron
sisiCompany
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The Exxon Mobil Merger
• Small inaccuracies arise from relying on public data sources
• q= p/r is approximately 0.7• Estimate a=1/3, b=5, h=1/2.
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The Exxon Mobil Merger Results
94.394.694.394.6% Efficiency
21.220.121.320.0% Markup
Retail
Sale
Refinery Sale
Post-
merger
Pre-Merger
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The Exxon Mobil Merger Effects
• Small quantity effects• Significant (1%) retail price effects
• Markup increase• Virtually solved by refinery divestiture• Retail divestiture has little effect
• Approach based on naïve market shares mimics exact approach
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The Exxon Mobil Merger
• Sensible predictions:• Relatively elastic retaining means retail
merger is of little consequence• Inelastic downstream demand magnifies
effect of upstream concentration• 20% price/cost margin in line with CA vs.
gulf coast prices.
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Conclusions
• Generalize Cournot theory to case of intermediate goods
• Similar informational requirements to calculate price/cost margins
• Readily evaluate effects of mergers• Compute effects of divestitures
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Conclusions, Continued
• The more elastic the retail demand, the smaller the effect of captive consumption
• The price/cost margin is a weighted average of:
HHI of the intermediate good market
Weighted (by price ratio) average of the upstream and downstream HHIs (captive production included)
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Conclusions
• As the downstream production process gets more elastic, it figures less in price/cost margin
• Vanishing in the limit of perfectly elastic retailing costs.
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Conclusions
• Modest information requirements– Intermediate to final good price, q– Elasticity of retail demand, a– Elasticity of retailing costs, b– Elasticity of production cost, h– Upstream si and downstream si market shares
• Straightforward computations with exact predictions
• Available on my website
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Conclusions: Exxon-Mobil
• 20% price/cost margin, 95% efficient output• Merger increases retail price by 1%
• Retailing concentration less important• Refining concentration very important
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Robustness
• Ignores– Entry
– Collusion
– Product differentiation
– Dynamic considerations
• Static theory• Added competitive fringe to computation