A Theory of Bilateral Oligopoly with Applications to Vertical Mergers

Transcription

1 A Theory of Blateral Olgopoly wth Applcatons to Vertcal Mergers Kenneth Hendrcks UBC and Unversty of Texas and R. Preston McAfee Unversty of Texas

2 Exxon Mobl Merger Refnng s concentrated n CA Retal Sales are concentrated too How to assess the mpact of the merger? How to thnk about captve consumpton?

3 Other Applcatons Trade n spectrum lcenses BP/ARCO IBM s captve chp producton Defense ndustry mergers

4 Questons How to treat captve consumpton? What s the effect of vertcal ntegraton? Wth concentraton upstream, can an ncrease n concentraton downstream mprove effcency? How to generalze HHI to two-sded concentraton?

5 Lterature Old lterature on blateral olgopoly Many, many papers wth specal assumptons about upstream and downstream confguraton Foreclosure, rasng rval s costs, etc. Klemperer & Meyer Invented soluton concept No appled results

6 Revew of Cournot Profts are π ( ) ( ) = p q q j j c q Manpulatng the frst order condtons: ( p ( Q ) 2 c ) q = p ( Q ) Q Where s s the market share of frm and å s the elastcty of demand. Thus, the HHI measures prce cost margns. ε s,

7 Specal Theory Ignore downstream competton Frms have capactes k, g Capactes lead to payoffs from consumpton q and producton x of: ). ( x q p x c k q v k = γ γ π

8 Specal Theory, Cont d Formulaton facltates consderaton of mergers Merger f and j produces a frm wth capactes k + k j, g +g j. Net purchase at dentcal market prce p Value v, cost c exhbt CRS w.r.t. (q,k)

9 Soluton Concept Frms can pretend to have other k, g Restrcted to actng lke a possble type Market maps the pretend levels to the effcent outcome (p,q ) gven those levels Frm choce s full nformaton equlbrum to the nduced game Mrrors Cournot black box

10 Specal Theory Soluton å, h are the elastctes of demand (v) and supply c, respectvely. s and s are the shares of consumpton and producton. Theorem 1: In any nteror equlbrum, and c v =. ) (1 ) 1 ( s s p p c p p v σ η ε σ + = =

11 Specal Theory Soluton Generalzes to ncorporate boundares Yelds Cournot as h Æ0 and buyers are dspersed More generally, value mnus cost s: 1 ( n n ) n ( s ) = σ sv σ c = = = 1 1 ε (1 s ) + η(1 σ ) 1 p 2.

12 Specal Theory Conclusons Only net trades matter Captve consumpton can be safely gnored HHI generalzes to ths ntermedate good case Smlar nformaton requrements Quantty, not capacty, shares are relevant (true n Cournot, too)

13 General Theory Add Cournot downstream Retal prce r(q), elastcty a Sellng cost k w(q /k ), elastcty b Producton cost g c(x /g ), elastcty h q=p/r A=1/a; B=(1-q)/b; C=q/h

14 General Theory Frms can pretend to have dfferent capactes than they have Frms maxmze gven the behavor of others and the true captal levels Market prces, quanttes are effcent gven the pretend levels chosen by the frm.

15 Man Theorem The quantty weghted dfference between prce and margnal cost, or modfed herfndahl, s: MHI = n = 1 BC( s A(1 σ s ) 2 )(1 + ABs σ ) 2 + (1 σ B(1 ) σ + ) AC + σ C(1 2 (1 s ) s ).

16 Specal Cases A=0: perfectly elastc demand, yelds specal theory. AÆ : MHI = (1 θ ) β s (1 2 s ) + θ η σ (1 2 σ )

17 Effect of Downstream The more elastc the downstream demand, the more only the HHI based on net trades matters. When downstream demand s very nelastc, MHI s a weghted sum of upstream and downstream HHIs, wth weghts gven by the ntermedate to fnal good prce rato. Captve consumpton matters 100%

18 Effect of Downstream Thus, paper helps resolve the debate about accountng for captve consumpton Count captve consumpton more the more nelastc s downstream demand Counts strongly n BP-Arco

19 Specal Cases, Cont d B=0 s a constant margnal cost of retalng Any retaler can expand easly MHI B n θσ = = 0 = 1 η( 1 σ ) + θα 2 Only the upstream matters.

20 The Exxon Exxon Mobl Mobl Merger In Calforna, both gasolne refnng and retalng are hghly concentrated Seven frms account for 95% at each level Retal demand s very nelastc

21 The Exxon Mobl Merger Company Chevron Tosco Equlon Arco Mobl Exxon Ultramar s s

22 The Exxon Mobl Merger Small naccuraces arse from relyng on publc data sources q= p/r s approxmately 0.7 Estmate a=1/3, b=5, h=1/2.

23 The Exxon Mobl Merger Results merger Pre- Merger Post- Refnery Sale Retal Sale % Markup % Effcency

24 The Exxon Mobl Merger Effects Small quantty effects Sgnfcant (1%) retal prce effects Markup ncrease Vrtually solved by refnery dvestture Retal dvestture has lttle effect Approach based on naïve market shares mmcs exact approach

25 The Exxon Mobl Merger Sensble predctons: Relatvely elastc retanng means retal merger s of lttle consequence Inelastc downstream demand magnfes effect of upstream concentraton 20% prce/cost margn n lne wth CA vs. gulf coast prces.

26 Conclusons Generalze Cournot theory to case of ntermedate goods Smlar nformatonal requrements to calculate prce/cost margns Readly evaluate effects of mergers Compute effects of dvesttures

27 Conclusons, Contnued The more elastc the retal demand, the smaller the effect of captve consumpton The prce/cost margn s a weghted average of: HHI of the ntermedate good market Weghted (by prce rato) average of the upstream and downstream HHIs (captve producton ncluded)

28 Conclusons As the downstream producton process gets more elastc, t fgures less n prce/cost margn Vanshng n the lmt of perfectly elastc retalng costs.

29 Conclusons Modest nformaton requrements Intermedate to fnal good prce, q Elastcty of retal demand, a Elastcty of retalng costs, b Elastcty of producton cost, h Upstream s and downstream s market shares Straghtforward computatons wth exact predctons Avalable on my webste

30 Conclusons: Exxon-Mobl 20% prce/cost margn, 95% effcent output Merger ncreases retal prce by 1% Retalng concentraton less mportant Refnng concentraton very mportant

31 Robustness Ignores Entry Colluson Product dfferentaton Dynamc consderatons Statc theory Added compettve frnge to computaton