Is Neutrality in Distribution Reasonable? An Economic Perspective

1 The Economic Scenario 2 Profit Maximising Distribution 6 3 The Per Se World 10 4 First Best 13 5 Second Best 17 Third Best 23 7 In Conclusion 27

The Economic Scenario

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) The economic scenario 𝒄 Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) The economic scenario 𝒒 𝑩 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 + 𝒒 𝑶 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 =𝑸 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 𝒄 𝒒 𝑩 𝒑 𝑩 , 𝒑 𝑶 ,𝟎 = 𝒒 𝑶 𝒑 𝑩 , 𝒑 𝑶 ,𝟎 =𝟎 Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) The economic scenario Neutrality in preferences: consumers are indifferent across distribution channels 𝒄 Upstream firm 𝒒 𝑩 𝒑,𝒑, 𝒆 𝑩 = 𝑸(𝒑, 𝒆 𝑩 ) 𝟐 𝒄 𝑩 𝒄 𝑶 𝒑 𝑩 > 𝒑 𝑶 𝒒 𝑩 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 =𝟎 𝒑 𝑩 < 𝒑 𝑶 𝒒 𝑩 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 =𝑸( 𝒑 𝑩 , 𝒆 𝑩 ) B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

Profit Maximising Distribution

Intra-brand competition Profit maximising company sets wholesale prices for B&M and online distributors B&M distributor selects the end-price and the level of effort that maximises its profits, taking as given the wholesale prices set by the vertically integrated firm Online distributor selects the end-price that maximises its profits, taking as given the wholesale prices set by the vertically integrated firm 𝒄 Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

Intra-brand competition 𝒄 𝒆 𝑩 =𝒎𝒂𝒙 𝒑 𝑩 − 𝒄 𝑩 𝒒 𝑩 −𝒄( 𝒆 𝑩 ) Upstream firm 𝒘(𝒒 𝑩 )=( 𝒑 𝑩 − 𝒄 𝑩 ) 𝒒 𝑩 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

Intra-brand competition Non-neutrality in distribution since B&M distributor’s effort is indispensable Low 𝑐 𝐵 Upstream firm wants to limit the ability of online distributor to undercut B&M distributor; High 𝑝 𝐵 Possible need to foreclose online distribution High 𝑞 𝐵 𝒄 Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

The Per Se World

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) The per se world 𝒄 Neutrality in distribution No restrictions of intra-brand competition Upstream firm 𝒄 𝑶 = 𝒄 𝑩 𝒄 𝑩 𝒄 𝑶 𝒑 𝑩 ≠ 𝒑 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

Intra-brand competition Non-neutrality in distribution since B&M distributor’s effort is indispensable Low 𝑐 𝐵 Upstream firm wants to limit the ability of online distributor to undercut B&M distributor; High 𝑝 𝐵 Possible need to foreclose online distribution High 𝑞 𝐵 𝒄 Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

First Best

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) FIRST BEST 𝒄 Social planner maximises total welfare It sets wholesale and final prices and it also determines the level of effort of the B&M distributor The social planner needs to respect the participation constraints of the upstream firm and the B&M and online distributors Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) first best (cont.) 𝒑 𝑩 = 𝒑 𝑶 =𝒑 𝒄 𝒄 𝑶 =𝒑− 𝒘 Upstream firm 𝒄 𝑩 =𝒑−𝒘( 𝒆 𝑩 ) 𝒄 𝑩 𝒄 𝑶 𝒘 𝒆 𝑩 =𝒄 𝒆 𝑩 + 𝒘 B&M distributor Online distributor 𝒆 𝑩 =𝒎𝒂𝒙 𝒒 𝑩 + 𝒒 𝑶 (𝟏−𝒄)−𝒄( 𝒆 𝑩 ) 𝒑 𝑩 𝒑 𝑶 𝒑−𝒄 𝒒 𝑩 + 𝒒 𝑶 =𝒘 𝒆 𝑩 𝒒 𝑩 + 𝒘 𝒒 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) first best (cont.) 𝒄 Non-neutrality in distribution Consumers pay the same price across distribution channels Upstream firm 𝒘 𝒆 𝑩 > 𝒘 𝒄 𝑩 =𝒑−𝒘 𝒆 𝑩 <𝒑− 𝒘 = 𝒄 𝑶 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 = 𝒑 𝑶 =𝒑 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

Second Best

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) Second BEST 𝒄 Social planner sets wholesale and final prices to maximise social welfare B&M distributor selects the level of effort that maximises its well-being, taking as given the prices set by the social planner Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) second best (CONT.) 𝒑 𝑩 = 𝒑 𝑶 =𝒑 𝒄 𝒄 𝑶 =𝒑− 𝒘 Upstream firm 𝒄 𝑩 =𝒑−𝒘( 𝒒 𝑩 + 𝒒 𝑶 ) 𝒄 𝑩 𝒄 𝑶 𝒘 𝒒 𝑩 + 𝒒 𝑶 ∥ 𝒆 𝑩 =𝒎𝒂𝒙 𝒘( 𝒒 𝑩 + 𝒒 𝑶 )−𝒄( 𝒆 𝑩 ) B&M distributor Online distributor 𝒆 𝑩 =𝒎𝒂𝒙 𝒒 𝑩 + 𝒒 𝑶 (𝟏−𝒄)−𝒄( 𝒆 𝑩 ) 𝒑 𝑩 𝒑 𝑶 𝒑−𝒄 𝒒 𝑩 + 𝒒 𝑶 =𝒘( 𝒒 𝑩 + 𝒒 𝑶 )+ 𝒘 𝒒 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) Incentive Compatibility

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) second best (Cont.) 𝒑 𝑩 = 𝒑 𝑶 =𝒑 𝒑 𝑩 =𝒑< 𝒑 𝑶 𝒄 𝒄 𝑶 =𝒑− 𝒘 Upstream firm 𝒄 𝑩 =𝒑−𝒘( 𝒒 𝑩 + 𝒒 𝑶 ) 𝒄 𝑩 𝒄 𝑶 𝒘 𝒒 𝑩 + 𝒒 𝑶 ∥ 𝒆 𝑩 =𝒎𝒂𝒙 𝒘( 𝒒 𝑩 + 𝒒 𝑶 )−𝒄( 𝒆 𝑩 ) B&M distributor Online distributor 𝒆 𝑩 =𝒎𝒂𝒙 𝒒 𝑩 + 𝒒 𝑶 (𝟏−𝒄)−𝒄( 𝒆 𝑩 ) 𝒑 𝑩 𝒑 𝑶 𝒑−𝒄 𝒒 𝑩 + 𝒒 𝑶 =𝒘( 𝒒 𝑩 + 𝒒 𝑶 )+ 𝒘 𝒒 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

second best versus first best Informational rents Possible foreclosure of online distribution Higher prices Lower output Lower consumer welfare Lower total welfare 𝒄 𝒘 𝒒 𝑩 + 𝒒 𝑶 >𝒘( 𝒆 𝑩 ) Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) second best (cont.) 𝒄 Non-neutrality in distribution Consumers pay the same price across distribution channels or online is foreclosed Upstream firm 𝒘 𝒒 𝑩 , 𝒒 𝑶 > 𝒘 𝒄 𝑩 = 𝒑 𝑩 −𝒘 𝒒 𝑩 , 𝒒 𝑶 < 𝒑 𝑶 − 𝒘 = 𝒄 𝑶 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 =𝒑≤ 𝒑 𝑶 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

Third Best

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) Vertical integration 𝒄 Profit maximising company sets compensation levels for B&M and online agents B&M distributor (agent) selects the level of effort that maximises its well- being, taking as given the prices set by the vertically integrated firm Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) Vertical integration 𝒑 𝑩 =𝒑≤ 𝒑 𝑶 𝒄 𝒄 𝑶 = 𝒑 𝑶 − 𝒘 Upstream firm 𝒄 𝑩 =𝒑−𝒘( 𝒒 𝑩 + 𝒒 𝑶 ) 𝒄 𝑩 𝒄 𝑶 𝒘 𝒒 𝑩 + 𝒒 𝑶 ∥ 𝒆 𝑩 =𝒎𝒂𝒙 𝒘( 𝒒 𝑩 + 𝒒 𝑶 )−𝒄( 𝒆 𝑩 ) B&M distributor Online distributor 𝒑, 𝒆 𝑩 =𝒎𝒂𝒙 𝒑−𝒄 𝒒 𝑩 + 𝒒 𝑶 −𝒘 𝒒 𝑩 + 𝒒 𝑶 − 𝒘 𝒒 𝑶 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 ) Profit maximization

Vertical integration versus second best Higher prices Lower output Lower consumer welfare Lower total welfare But, as in first and second best, non-neutrality in distribution Vertical price restraints And, as in second best, possible foreclosure of online distribution 𝒄 Upstream firm 𝒄 𝑩 𝒄 𝑶 B&M distributor Online distributor 𝒑 𝑩 𝒑 𝑶 𝒒 𝑩 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )+ 𝒒 𝑶 ( 𝒑 𝑩 , 𝒑 𝑶 , 𝒆 𝑩 )

In Conclusion The Per Se World Needs to Reconsider its Vertical Restraints Policy because it is not a First Best, nor a Second Best, not even a Third Best World!!!

Thank you! jpadilla@compasslexecon.com Thank you very much for your attention! View my research on my SSRN author page: http://ssrn.com/author=47132