1. Is Neutrality in Distribution Reasonable?
An Economic Perspective

2. 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

3. The Economic Scenario

4. 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 )

5. 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 )

6. 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 )

7. Profit Maximising Distribution

8. 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 )

9. Intra-brand competition𝒄
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 )

10. 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 )

11. The Per Se World

12. 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 )

13. 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 )

14. First Best

15. 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 )

16. 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 )

17. 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 )

18. Second Best

19. 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 )

20. 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

21. 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 )

22. 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 )

23. 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 )

24. Third Best

25. 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 )

26. 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

27. 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 )

28. 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!!!

29. Thank you! jpadilla@compasslexecon.com
Thank you very much for your attention!
View my research on my SSRN author page: