The Effects of Revenue-Sharing Contracts onWelfare in Vertically-Separated Markets:Evidence from the Home Video IndustryJulie Holland Mortimer1A Common Challenge in Vertically-SeparatedIndustries is the Presence of SuccessiveMonopolies or Double-Marginalization2PQZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZDrJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJMRr= DwBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBMRwMCPwPr3Possible Solutions:• Vertical Integration• Contracts (Two-Part Tariffs)Revenue-Sharing Contracts (Two-Part Tariffs)were recently adopted in the video rental indus-try.Research Question: What is the effect of thiscontractual change on welfare (firm profits andconsumer surplus), relative to linear pricing.4General Approach:• Examine the institutional setting• Develop a model of firm behavior that in-corporates industry details• Estimate the model and conduct counter-factual experiments to answer the researchquestion.5Results:• Total firm profits increase by 10 - 20 per-cent.• Consumer surplus increases.6Previous LiteratureTheoretical Papers on Revenue-Sharing in HomeVideo• Dana & Spier (2000)• Cachon & Lariviere (2000)Empirical Literature on Contracting and Vertically-Separated Markets• Franchising/Double-Marginalization:LaFontaine (1995)• Moral Hazard:Shepard (1993), Slade (1996)• Transaction Costs and Risk:Allen & Lueck (1993, 1992)7Industry Facts• Rentals and sales total $16 billion in 1999,55 percent of studios’ gross domestic movierevenue.• 20,000 retailers, split evenlybetween large chains and independents.• Contracting environment includes linear pricesand revenue sharing since 1998 (Blockbustercontracts differ from Rentrak’s).• Upstream firms must offer the samecontractual terms to all retailers(Robinson-Patman Act).• “Right of First Sale” Doctrine allowsresale of legally-owned tapes.8Two Important Features of the Contracts• Retailers have a choice between pricingcontracts.• Studios use inventory restrictionsunder revenue-sharing terms.9Data DescriptionWeekly transaction data for a panel of 6,594video retail stores for 1,114 titles for 104 weeks(1998-1999).• Store characteristics:– zip code location and demographics– measures of local competition– chain size, revenue size and product mix includ-ing adult, games and DVD rentals and sales– entry or exit from the database• Title information:– box office category– studio and studio size• Store-Title detail:– Contract choices (linear-pricing or revenue-sharing)by each store for each title.– Number of tapes purchased and contract termsfor each title.– All subsequent rentals and sales by week.10Model of Firm BehaviorMotivation:• Account for the endogeneity of retailers’contract choice.• Understand quantity restrictions.11Assumptions:• Monopolistic upstream firm (1 studio).• Symmetric downstream firms (N retailers).• Cournot competition.• Profits are additively separable across prod-ucts.12Intuition of the Model:• A Single Downstream Market– Revenue-Sharing Induces “Efficient” Inventory– No Role for Inventory Restrictions• Multiple Downstream Markets– Two types of heterogeneity: Demand cond.,Competitive cond.– Optimal Rev-Sharing Terms Differ by Market– Inventory Restrictions Fine-Tune Inventory Choices13One Downstream MarketDemand Equation:Q = V − ηPTechnological Constraint on Inventory:Q = τ C• Q is quantity of rentals• V is the intercept of demand• C is inventory (number of copies)• τ is the num ber of rentals produced fromeach tape14Retailers’ Profit MaximizationRetailers choose:• Pricing Contract (Ri)• Inventory (ci)• Retail Price (p)15Profits under linear-pricing contract:πF Fi(ci) =V τηci−τ2ηciNXk=1ck− F ci• F is the wholesale price per tape• N is number of firms in the downstream market16Profits under revenue-sharing contract:πRSi(ci) = yV τηci−τ2ηciNXk=1ck− uci• u is the upfront fee per tape• y is the share of revenue kept by the retailer• F >> u and y ∈ (0, 1)Choose linear pricing if:V∗>η(F − yu +√y(F − u))(1 − y)τ(When demand is going to be low, the retaileris happy to share. When demand is going tobe high, the retailer prefers to pay upfront andkeep all revenue.)17Supply Equation:Retailers’ inventory under each contract:c∗i,F F=1(N + 1)τV −F ητc∗i,RS=1(N + 1)τV −uητMarket inventory under each contract:C∗F F=N(N + 1)τV −F ητC∗RS=N(N + 1)τV −uητ18The Studio’s Profit MaximizationThe Studio chooses:• A single linear price for the linear-pricingcontract.• A single upfront fee and revenue-split forthe revenue-sharing contract.• Quantity minimums and maximums for therevenue-sharing contract.19Upstream Firm Profits Under a Linear PriceThe linear price that induces efficient (vertically-integrated) choice of inventory:FV I=(N − 1)τ V2Nη+(N + 1)l2NThe linear price that maximizes upstream firmprofits:F∗= (τ V2η+l2)Profit-miximizing choice leads to a double-marginalization problem when downstream firmsare not perfectly competitive.20Upstream Firm Profits Under Revenue SharinguV I=(N − 1)τ V2Nη+(N + 1)l2Ny is set so that downstream firms receive atleast as much profit as they did under fixedfee pricing. The use of u and y solves thedouble-marginalization problem with a singledownstream market if the terms are set opti-mally.21Recap:With a single downstream market, revenue-sharing terms can be set optimally to induce“efficient” inventories.Optimal terms are a function of Demand Con-ditions (V) and Competitive Conditions (N).Revenue-sharing solves a double-marginalizationor successive monopoly problem.22Multiple Downstream MarketsMarkets differ in two dimensions: size of de-mand (V) and the number of firms (N).Optimal Upfront Fee Under Revenue Sharingu∗=τPMm=1(Nm−1)VmNm2η+lPMm=1(Nm+1)Nm2u∗is a weighted average of the set of optimalu∗mthat would be charged in each market underperfect price discrimination.23With many downstream markets, revenue-sharingterms are set to induce efficient inventories inthe “average” market.Optimal terms are a function of Demand Con-ditions (V) and Competitive Conditions (N).Revenue-sharing does not induce efficient in-ventory holdings for all markets because of het-erogeneity in V and N.24→ Too much inventory may be held in somemarkets. Too little inventory may be held inother markets.For example:Low Value Markets (Average N, high V ):•