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Key result:As long asw>c,p>pVIandq
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![Searches related to double marginalisation définition filetype:pdf Searches related to double marginalisation définition filetype:pdf](https://pdfprof.com/Listes/18/23721-18vertical_slides-uk4jj7.pdf.pdf.jpg)
Vertical Relations: Double Marginalization, Price
Negotiation and Integration
Jean-Francois Houde
Cornell University & NBER
October 17, 2016
Vertical Relations1 / 41
Introduction: Vertical Contracting
Goal:Solve an externality problem between downstream and upstream rms IAgency problem:Unmeasurable service quality
IPricing:Double marginalization
IUpstream competition:Exclusion of rival suppliersIUnder-investment:Incomplete contractingDouble marginalization:Retailer does not internalize the loss in
revenue from setting prices above cost.Legal restrictions: I Resale-price maintenance(RPM) is illegal in the U.S. IWholesale price discriminationis illegal only if judged anticompetitive (almost never prosecuted) ITie-inandexclusive territoriesare judge by a rule of reason (technically illegal)IVertical mergersare rarely prosecuted by the federal agenciesVertical RelationsDouble Marginalization2 / 41
Double Marginalization: Basic Model
Linear pricing contract:Manufacturer sets wholesale pricew IDownstream rm (with market-power):
max p(pw)D(p)$D(p) +D0(p)(pw) = 0 IUpstream rm (monopolist):
max w(wc)D(p(w))$D(p(w)) +D0(p(w))(wc)p0(w) = 0 IKey result:As long asw>c,p>pVIandq F Downstream rm fails to internalize the prot loss to the manufacturer associated with selling fewer units thanqVI.Remedies: I Two-part tari contract (i.e. franchising)
w=candF= (pVIc)qVI I Resale-price maintenance
IMinimum quantity contracts
IVertical integrationVertical RelationsDouble Marginalization3 / 41 Testing for Double Marginalization
Source:Villas-Boas (2007)Data:The market for Yogurt in a Midwestern city I Source:IRI
IMarket-structure:5 Manufacturers3 Retailers = 43 products ISample:Product characteristics and sales over 104 weeksMixed-logit demand (omitting time dimension):
u ij=xjiipj+j+ij;i i +Di +i wherej2 f0;1;:::;Ng,Nis the number of brandsstores, andDi is a vector of demographic characteristics (age and income), and iN(0;1).The demand parameters are estimated as in Nevo (2001). I Instruments:Aggregate cost-shocksproduct FEs (pretty weak...)Vertical RelationsDouble Marginalization4 / 41
Vertical Pricing
Assumption:Manufacturers are allowed to charge dierent wholesale prices for each retailer/product combination (i.e.wj)Notation:(again omitting the time dimension) I r: Ownership matrix at the retail level I w: Manufacturer ownership matrix (i.e. brands) Ir: Retail demand own and cross price derivative (i.e. rjk=@sk=@pj) Iw: Wholesale demand own and cross derivative (i.e. wjk=@sk=@wj) I: Retail equilibrium pass-through matrix (i.e. kj=dpk=dwj)Identity:Manufacturer perceived demand slope depends on the
retailers' anticipated pricing decision wjk=@sk=@wj=NX l=1@sk@pldp ldw j;or w= TrTiming:Manufacturers set wholesale prices, and retailers determine retail prices knowing the entire vector of wholesale price Vertical RelationsDouble Marginalization5 / 41
Vertical Contract 1: Linear Pricing
Retail supply relation:
(pj) :sj+X k rjk@sk@pj(pkwkcrj) = 0$pj=crj+wj+ ( rr)1 j;:sWholesale supply relation: (wj) :sj+X k wjk@sk@wj(wkcwk) = 0;where@sk@wj=NX l=1@sk@pldp ldw j $wj=cwj+ wTr1 j;:sEquilibrium pass-through (dierentiating retailers' FOC): (wf) :NX l=1" @sj@pl+X k rjk@2sk@pj@pl(pkwk) + rjk@sl@pj# |{z}quotesdbs_dbs2.pdfusesText_3
Two-part tari contract (i.e. franchising)
w=candF= (pVIc)qVI IResale-price maintenance
IMinimum quantity contracts
IVertical integrationVertical RelationsDouble Marginalization3 / 41Testing for Double Marginalization
Source:Villas-Boas (2007)Data:The market for Yogurt in a Midwestern city ISource:IRI
IMarket-structure:5 Manufacturers3 Retailers = 43 productsISample:Product characteristics and sales over 104 weeksMixed-logit demand (omitting time dimension):
u ij=xjiipj+j+ij;i i +Di +i wherej2 f0;1;:::;Ng,Nis the number of brandsstores, andDi is a vector of demographic characteristics (age and income), and iN(0;1).The demand parameters are estimated as in Nevo (2001). IInstruments:Aggregate cost-shocksproduct FEs (pretty weak...)Vertical RelationsDouble Marginalization4 / 41
Vertical Pricing
Assumption:Manufacturers are allowed to charge dierent wholesale prices for each retailer/product combination (i.e.wj)Notation:(again omitting the time dimension) I r: Ownership matrix at the retail level I w: Manufacturer ownership matrix (i.e. brands) Ir: Retail demand own and cross price derivative (i.e. rjk=@sk=@pj) Iw: Wholesale demand own and cross derivative (i.e. wjk=@sk=@wj)I: Retail equilibrium pass-through matrix (i.e. kj=dpk=dwj)Identity:Manufacturer perceived demand slope depends on the
retailers' anticipated pricing decision wjk=@sk=@wj=NX l=1@sk@pldp ldw j;or w= TrTiming:Manufacturers set wholesale prices, and retailers determine retail prices knowing the entire vector of wholesale price