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Managerial Delegation of Competing Vertical Chains with Vertical Externality

  • Kangsik Choi ORCID logo , Ki-Dong Lee und Seonyoung Lim EMAIL logo
Veröffentlicht/Copyright: 1. Februar 2020
The B.E. Journal of Theoretical Economics
Aus der Zeitschrift The B.E. Journal of Theoretical Economics Band 20 Heft 2

Abstract

We examine that the bilateral supplier affects the incentive contracts that owners of retailers offer their managers, assuming that the manufacturer sets the input price after observing the terms of the incentive contracts offered to management in the downstream market. Thus, we compare the two models: (1) decentralized bargaining between manufacturers and retailers including two-part tariff contract (2) linear input pricing without bargaining. Contrast to previous studies, we find that in equilibrium, the owners of retailers offer delegation contracts to managers for output restriction regardless of competition modes when offering linear input pricing, which implies that owners do not face a prisoners’ dilemma situation and Pareto superior profit is obtained for retailer. Thus, managerial delegation of retailer is not socially desirable due to the output restriction. Furthermore, decentralized bargaining allows to equalize all the equilibrium outcomes in the different delegation structure under both Bertrand and Cournot competition and leads no delegation for the endogenous delegation problem.

Keywords: delegation; linear input pricing; Nash bargaining; Bertrand; Cournot
JEL Classification: D43; L13; M21

Appendix

A Appendix

πiddC−πiddB=−d2Θ121+dΔ248+8d−16d2−d3+d42Δ2<0ifd<d∗=0.96368,
uiddC−uiddB=−(a−c)2d24−d2Θ221−d48+8d−16d2−d3+d42Δ2<0,
πiddB−πinnB=a−c1−d2−d232−32d2+7d4Θ32−d221+d4−d−2d22Δ2>0,
πiddC−πinnC=32−16d2+d4192+192d−64d2−56d3+14d4+4d5−d624−d22+d248+8d−16d2−d3+d42>0,
uiddB−uinnB=−(a−c)21−d22+d2−d232−32d2+7d4Θ42−d1+d4−d−2d22Δ2<0,
uiddC−uinnC=(a−c)22−d32−16d2+d4160+32d−48d2−4d3+3d44−d22+d48+8d−16d2−d3+d42<0,
SWnnC−SWddC=(a−c)232−16d2+d4608+128d−304d2−44d3+45d4+3d5−2d64−d22+d248+8d−16d2−d3+d42>0,
SWnnB−SWddB=a−c)21−d2(2−d232−32d2+7d4Θ52−d21+d4−d−2d22Δ2>0,

where

Θ1=1179648−1179648d−3670016d2+3629056d3+4784128d4−4664320d5−3432192d6+3289472d7+1495488d8−1405968d9−408876d10+378136d11+70330d12−63930d13−7191d14+6521d15+388d16−360d17−8d18∓8d19,
Θ2=98304−131072d−270336d2+376832d3+300544d4−440832d5−178048d6+274944d7+63360d8−101256d9−14518d10+22902d11+2189d12−3155d13−200d14+244d15+8d16−8d17,
Θ3=192−192d−320d2+328d3+178d4−184d5−46d6+44d7+5d8−4d9.
Θ4=160−128d−224d2+172d3+93d4−67d5−12d6+8d7,
Θ5=1216−960d−2016d2+1544d3+1158d4−852d5−279d6+196d7+24d8−16d9.

Acknowledgements

We are especially indebted to the editor, Jan Wenzelburger for his constructive suggestions to improve the paper, as well as to two anonymous referees for their valuable comments. An earlier version of this paper was presented at the meeting of Japan Association for Applied Economics in 2019. We benefited from discussant Kosuke Hirose and participants for their valuable comments as well as Yoshihiro Tomaru.

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Published Online: 2020-02-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Research Articles
  2. The Effects of Entry when Monopolistic Competition and Oligopoly Coexist
  3. Managerial Delegation of Competing Vertical Chains with Vertical Externality
  4. Fiat Money as a Public Signal, Medium of Exchange, and Punishment
  5. Education Spending, Fertility Shocks and Generational Consumption Risk
  6. Should the Talk be Cheap in Contribution Games?
  7. College Assignment Problems Under Constrained Choice, Private Preferences, and Risk Aversion
  8. Competition with Nonexclusive Contracts: Tackling the Hold-Up Problem
  9. Endogenous Authority and Enforcement in Public Goods Games
  10. Disequilibrium Trade in a Large Market for an Indivisible Good
  11. Pretrial Beliefs and Verdict Accuracy: Costly Juror Effort and Free Riding
  12. Product R&D Coopetition and Firm Performance
  13. A Model of Inequality Aversion and Private Provision of Public Goods
  14. Managerial Accountability Under Yardstick Competition
  15. On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty
https://doi.org/10.1515/bejte-2019-0029
Schlagwörter für diesen Artikel
delegation; linear input pricing; Nash bargaining; Bertrand; Cournot

Artikel in diesem Heft

  1. Research Articles
  2. The Effects of Entry when Monopolistic Competition and Oligopoly Coexist
  3. Managerial Delegation of Competing Vertical Chains with Vertical Externality
  4. Fiat Money as a Public Signal, Medium of Exchange, and Punishment
  5. Education Spending, Fertility Shocks and Generational Consumption Risk
  6. Should the Talk be Cheap in Contribution Games?
  7. College Assignment Problems Under Constrained Choice, Private Preferences, and Risk Aversion
  8. Competition with Nonexclusive Contracts: Tackling the Hold-Up Problem
  9. Endogenous Authority and Enforcement in Public Goods Games
  10. Disequilibrium Trade in a Large Market for an Indivisible Good
  11. Pretrial Beliefs and Verdict Accuracy: Costly Juror Effort and Free Riding
  12. Product R&D Coopetition and Firm Performance
  13. A Model of Inequality Aversion and Private Provision of Public Goods
  14. Managerial Accountability Under Yardstick Competition
  15. On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty
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