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Distribution contracts to support optimal inventory holdings under demand uncertainty

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  • Marvel, Howard P.
  • Wang, Hao

Abstract

When suppliers produce products for which demand is uncertain, they face a problem of inducing downstream distributors to stock inventory levels that the suppliers prefer. This paper considers a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that linear supply contracts specifying any combination of two of these three instruments can implement the vertical integrated outcome for a monopoly, thereby generating the supplier's preferred inventory configuration and price distribution. We extend our results to differentiated product oligopoly, demonstrating that each supplier obtains its preferred inventory configuration and price distribution, given the choices of its rival. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. Thus, suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion.

Suggested Citation

  • Marvel, Howard P. & Wang, Hao, 2009. "Distribution contracts to support optimal inventory holdings under demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 27(5), pages 625-631, September.
  • Handle: RePEc:eee:indorg:v:27:y:2009:i:5:p:625-631
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    References listed on IDEAS

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    1. Deneckere, Raymond & Marvel, Howard P & Peck, James, 1997. "Demand Uncertainty and Price Maintenance: Markdowns as Destructive Competition," American Economic Review, American Economic Association, vol. 87(4), pages 619-641, September.
    2. Dana, James D, Jr & Spier, Kathryn E, 2001. "Revenue Sharing and Vertical Control in the Video Rental Industry," Journal of Industrial Economics, Wiley Blackwell, vol. 49(3), pages 223-245, September.
    3. Raymond Deneckere & Howard P. Marvel & James Peck, 1996. "Demand Uncertainty, Inventories, and Resale Price Maintenance," The Quarterly Journal of Economics, Oxford University Press, vol. 111(3), pages 885-913.
    4. Howard P. Marvel & Hao Wang, 2007. "Inventories, Manufacturer Returns Policies, and Equilibrium Price Dispersion under Demand Uncertainty," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(4), pages 1031-1051, December.
    5. Bousquet, Alain & Cremer, Helmuth & Ivaldi, Marc & Wolkowicz, Michel, 1998. "Risk sharing in licensing," International Journal of Industrial Organization, Elsevier, vol. 16(5), pages 535-554, September.
    6. Prescott, Edward C, 1975. "Efficiency of the Natural Rate," Journal of Political Economy, University of Chicago Press, vol. 83(6), pages 1229-1236, December.
    7. Raymond Deneckere & James Peck, 1995. "Competition Over Price and Service Rate When Demand is Stochastic: A Strategic Analysis," RAND Journal of Economics, The RAND Corporation, vol. 26(1), pages 148-162, Spring.
    8. Marvel, Howard P & Peck, James, 1995. "Demand Uncertainty and Returns Policies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(3), pages 691-714, August.
    9. Eden, Benjamin, 1990. "Marginal Cost Pricing When Spot Markets Are Complete," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1293-1306, December.
    10. Carlton, Dennis W, 1978. "Market Behavior with Demand Uncertainty and Price Inflexibility," American Economic Review, American Economic Association, vol. 68(4), pages 571-587, September.
    11. GĂ©rard P. Cachon & Martin A. Lariviere, 2005. "Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations," Management Science, INFORMS, vol. 51(1), pages 30-44, January.
    12. Howard P. Marvel & James Peck, 2008. "Inventory Turnover and Product Variety," Journal of Law and Economics, University of Chicago Press, vol. 51(3), pages 461-478, August.
    13. James D. Dana Jr., 1999. "Equilibrium Price Dispersion Under Demand Uncertainty: The Roles of Costly Capacity and Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 30(4), pages 632-660, Winter.
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