Prepared with SEVI SLIDES Competition Policy - Spring 2005 Vertical Restraints Antonio Cabrales & Massimo Motta May 9, 2005 ➪ ➪ ➲
➟ ➪ Summary • Introduction ➟ • Types of vertical restraints ➟ • Intra-brand competition: The problem of double marginalization ➟ ➠ • Intra-brand competition: Horizontal externality ➟ ➠ • Other reasons for vertical restraints ➟ • The commitment problem ➟ ➠ ➪ ➲ ➪ ➟
➟ ➪ Introduction Vertical restraints (or agreements): clauses to control for the externalities arising between firms operating at successive stages of an industry. Plan 1. Different types of vertical restraints. 2. Intra-brand competition: (a) Double marginalization. (b) Horizontal externalities. 3. Inter-brand competition. 4. Welfare effects of vertical restraints. 5. Exclusive dealing and vertical foreclosure. ➪ ➪ ➟ ➲ 1 20
➟ ➠ ➪ Types of vertical restraints Different vertical restraints are used (according to observability, absence of arbitrage etc.): 1. Non-linear pricing: (a) Franchise fee (FF) contracts. (b) Quantity discounts. 2. Resale price maintenance (RPM). 3. Quantity fixing. 4. Exclusivity clauses: (a) Exclusive territories (ET). (b) Exclusive dealing (ED). (c) Selective distribution. ➟ ➪ ➪ ➟➠ ➲ 2 20
Intra-brand competition: The problem of dou- ➣➟ ➠ ➪ ble marginalization (1/6) Upstream firm (manufacturer) Downstream firm (retailer) Consumers • First proposed by Spengler (1950) (but even Cournot 1838 had something like this). • Consumer demand q = a − p, marginal cost of upstream firm c, c < a . • Marginal cost of downstream firm w, the wholesale price. ➟ ➪ ➪ ➟➠ ➣ ➥ ➲ 3 20
Intra-brand competition: The problem of dou- ➢ ➣➟ ➠ ➪ ble marginalization (2/6) Linear pricing • Upstream firm sets w, and after observing it, downstream firm sets p. • Solution to last stage max Π D = ( p − w )( a − p ) p Thus: ; Π D = ( a − w ) 2 p = a + w ; q = a − w 2 2 4 • Anticipating this, solution to first stage: Π U = ( w − c ) a − w max 2 w Thus: w = a + c 2 ➟ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 4 20
Intra-brand competition: The problem of dou- ➢ ➣➟ ➠ ➪ ble marginalization (3/6) • This implies that overall: = ( a − c ) 2 D = ( a − c ) 2 p sep = 3 a + c ; Π sep ; Π sep U 4 8 16 D ≡ PS sep = 3( a − c ) 2 Π sep + Π sep U 16 Merger - Vertical Integration max Π V I = ( p − c )( a − p ) p ; PS V I = ( a − c ) 2 p V I = a + c ; q V I = a − c 2 2 4 Comparison • p sep > p V I (since 3 a + c 2 , when a > c ). So CS sep < CS V I . > a + c 4 • PS sep < PS V I (since 3( a − c ) 2 < ( a − c ) 2 ). 16 4 • Total welfare increases with V I. ➟ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 5 20
Intra-brand competition: The problem of dou- ➢ ➣➟ ➠ ➪ ble marginalization (4/6) Vertical restraints If a vertical merger is not feasible (or very transaction -costly). • Resale price maintenance (RPM): • Imposing p = p V I = a + c maximizes PS. 2 • Then the firms bargain over w to distribute surplus PS (with w ∈ [ c, p V I ]). • Identical outcome is achieved with forcing p ≤ p = p V I (and again w determines surplus PS division). • Quantity fixing (QF) (mirror image) : • Imposing q = q V I = a − c maximizes PS. 2 • Then the firms bargain over w to distribute surplus PS (with w ∈ [ c, p V I ]). • Identical outcome is achieved with forcing q ≤ q = q V I ( w determines surplus PS division). ➟ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 6 20
Intra-brand competition: The problem of dou- ➢ ➣➟ ➠ ➪ ble marginalization (5/6) • Franchise fee (FF): • Nonlinear pricing. Downstream firm is charged: F + wq, with w = c. • Then downstream maximizes: Π ff max D = ( p − c )( a − p ) − F p • So that p ff = a + c ; q ff = a − c 2 2 and = ( a − c ) 2 − F ; Π ff Π FF U = F D 4 • Then bargaining is done over F. ➟ ➪ ➪ ➟➠ ➥ ➢ ➣ ➥ ➲ 7 20
Intra-brand competition: The problem of dou- ➢ ➟ ➠ ➪ ble marginalization (6/6) Risk aversion (Rey-Tirole - AER 1986): • Risk neutral manufacturer (upstream), risk averse retailer (downstream). • Under demand uncertainty: π U RPM > π U FF and SW RPM > SW FF . • Under cost uncertainty: π U FF > π U RPM and SW FF > SW RPM . ➟ ➪ ➪ ➟➠ ➥ ➢ ➲ 8 20
Intra-brand competition: Horizontal externality ➣➟ ➪ (1/9) Upstream firm (manufacturer) Downstream firm Downstream firm (retailer) (retailer) Consumers • First proposed by Telser (1960):. • Good shopkeepers/advertising help to sell the brand, but not at that store. • Free riding by other stores. ➟ ➠ ➪ ➪ ➟ ➣ ➥ ➲ 9 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (2/9) • Model • Perceived quality: u = u + e, where e = e 1 + e 2 . • Costs: C ( q, e i ) = wq + µe 2 i / 2 , with µ > 1 • Demand: q = ( v + e ) − p (competition in prices avoids double marginalization). Separation • Equilibrium (downstream): p 1 = p 2 = w ; and e 1 = e 2 = 0 . • Equilibrium (upstream): Anticipating p = w Π sep max = ( w − c )( v − w ) U w Thus w = w + c 2 . • = ( v − c ) 2 ; CS sep = ( v − c ) 2 ; W sep = 3( v − c ) 2 PS sep = Π sep U 4 8 8 ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 10 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (3/9) Vertical integration • Maximization: p,e 1 ,e 2 Π V I = ( p − c )( v + e 1 + e 2 − p ) − µe 2 2 − µe 2 1 2 max 2 • Solving: � ∂ Π V I ∂e i = p − c − µe i = 0 ∂ Π V I ∂p = v + e 1 + e 2 − 2 p + c = 0 . • Equilibrium: 2( µ − 1); p V I = µ ( v + c ) − 2 c v − c ; q V I = µ ( v − c ) e 1 = e 2 = e V I = 2( µ − 1) 4( µ − 1) PS V I = Π V I = µ ( v − c ) 2 4( µ − 1) ; CS V I = µ 2 ( v − c ) 2 8( µ − 1) 2 ; W V I = µ (3 µ − 2)( v − c ) 2 8( µ − 1) 2 Welfare comparison W sep < W V I since 3( v − c ) 2 < µ (3 µ − 2)( v − c ) 2 8( µ − 1) 2 8 ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 11 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (4/9) Vertical restraints. If a vertical merger is not feasible (or very transaction -costly). • Exclusive territories and franchise fee: • Non-linear contract T = wq + F, with w = c. • Maximization (if perceived level of quality is still e = e 1 + e 2 ): − µe 2 p,e i Π ET = ( p i − c )( v + e 1 + e 2 − p i ) i max 2 − F 2 � ∂ Π ET ∂e i = p i − c − µe i = 0 2 • Solving: ∂ Π ET ∂p i = v + e 1 + e 2 − 2 p i + c = 0 • For any e i price p i is as in first best. Effort is not first best , but it is closer . • Retailer maximization if perceived quality is e = e i : − µe 2 p,e i Π ET = ( p i − c )( v + e i − p i ) i max 2 − F 2 � ∂ Π ET ∂e i = p i − c − µe i = 0 2 • Solving: ∂ Π ET ∂p i = v + e i − 2 p i + c = 0 • Still not first best , as fixed/convex cost of quality spread over smaller market. ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 12 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (5/9) • Resale price maintenance and franchise fee: • Forcing price to p = p V I , and non-linear contract, ( w, F ) . • Maximization (if perceived level of quality is still e = e 1 + e 2 ): − µe 2 Π RPM = ( p V I − w )( v + e 1 + e 2 − p V I ) i max 2 − F. 2 e i = e V I = ∂ Π ET ∂e i = p V I − w − µe i = 0 . e i = p V I − w v − c • Solving: 2( µ − 1) . 2 2 µ • Thus, we must have w < c as otherwise we cannot have e V I (each retailer takes into account its effect into its own profit): Π V I w RPM = 3 µc − 2 c − µv < c ; F = 2 + ( c − w ) q V I . 2( µ − 1) ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 13 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (6/9) • Resale price maintenance and quantity forcing: • Forcing price to p = p V I , and q ≥ q V I . • Maximization (if perceived level of quality is still e = e 1 + e 2 ): ( p V I − w )( v + e 1 + e 2 − p V I ) − µe 2 Π QF i max = 2 − F 2 e i ( v + e 1 + e 2 − p V I ) ≥ q V I subject to : 2 • Solving is simply choosing: e i = 2 q V I + p V I − v = e V I . 2 • This contract already achieves efficiency. Rent allocation with w (zero profits under no bargaining power for retailer): w )( v + 2 e V I − p V I ) − µ ( e V I ) 2 ( p V I − � = 0 2 2 • Thus: w = v + c . � 2 ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 14 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (7/9) Vertical integration can reduce welfare • Example with two types of consumers, different willingness to pay for quality, no price discrimination. • Vertical integration: oversupply of quality, distortion used to extract some rents from high quality types. • Vertical integration between competing integrated firms does not harm welfare. ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 15 20
Intra-brand competition: Horizontal externality ➢ ➣➟ ➪ (8/9) More general treatment: 1. Downstream firms compete in quantities: double marginalization → Prices too high. 2. Free-riding in services → Quality too low. 3. Free-riding in prices → Prices too low (from point of view of competitors). 4. Effect number 1 is stronger than number 3. ➟ ➠ ➪ ➪ ➟ ➥ ➢ ➣ ➥ ➲ 16 20
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