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Optimal Public Rationing and Price Response

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  • Simona Grassi

    ()
    (Max Weber Fellow, European University Institute)

  • Ching-to Albert Ma

    ()
    (Department of Economics, Boston University)

Abstract

We study optimal public rationing of an indivisible good and private sector price responses. Consumers differ in their wealth and costs of provisions. Due to a limited budget, some consumers must be rationed. Public rationing determines the characteristics of consumers who seek supply from the private sector, where a firm sets prices based on consumers’ cost information and in response to the rationing rule. We consider two information regimes. In the first, the public supplier rations consumers according to their wealth information. In equilibrium, the public supplier must ration both rich and poor consumers. Supplying all poor consumers would leave only rich consumers in the private market, and the firm would react by setting a high price. Rationing some poor consumers is optimal, and implements price reduction in the private market. In the second information regime, the public supplier rations consumers according to consumers’ wealth and cost information. In equilibrium, consumers are allocated the good if and only if their costs are below a threshold. Wealth information is not used. Rationing based on cost results in higher equilibrium total consumer surplus than rationing based on wealth.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2009-008.

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Length: 32
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Handle: RePEc:bos:wpaper:wp2009-008

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  1. Hugh Gravelle & Luigi Siciliani, 2009. "Third degree waiting time discrimination: optimal allocation of a public sector healthcare treatment under rationing by waiting," Health Economics, John Wiley & Sons, Ltd., vol. 18(8), pages 977-986.
  2. Pedro Pita Barros & Pau Olivella, 2005. "Waiting Lists and Patient Selection," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 14(3), pages 623-646, 09.
  3. Hugh Gravelle & Luigi Siciliani, 2007. "Ramsey Waits: Allocating Public Health Service Resources when there is Rationing by Waiting," Discussion Papers 07/15, Department of Economics, University of York.
  4. Epple, Dennis & Romano, Richard E, 1996. "Public Provision of Private Goods," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 57-84, February.
  5. Besley, Timothy & Coate, Stephen, 1991. "Public Provision of Private Goods and the Redistribution of Income," American Economic Review, American Economic Association, vol. 81(4), pages 979-84, September.
  6. Simona Grassi & Ching‐To Albert Ma, 2012. "Public Sector Rationing and Private Sector Selection," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(1), pages 1-34, 02.
  7. Grassi, Simona & Ma, Ching-to Albert, 2011. "Optimal public rationing and price response," Journal of Health Economics, Elsevier, vol. 30(6), pages 1197-1206.
  8. Cremer, Helmuth & Marchand, Maurice & Thisse, Jacques-Francois, 1991. "Mixed oligopoly with differentiated products," International Journal of Industrial Organization, Elsevier, vol. 9(1), pages 43-53, March.
  9. David M. Cutler & Jonathan Gruber, 1995. "Does Public Insurance Crowd Out Private Insurance?," NBER Working Papers 5082, National Bureau of Economic Research, Inc.
  10. Ellis, Randall P., 1998. "Creaming, skimping and dumping: provider competition on the intensive and extensive margins1," Journal of Health Economics, Elsevier, vol. 17(5), pages 537-555, October.
  11. Iversen, Tor, 1997. "The effect of a private sector on the waiting time in a national health service," Journal of Health Economics, Elsevier, vol. 16(4), pages 381-396, August.
  12. Hoel, Michael & Saether, Erik Magnus, 2003. "Public health care with waiting time: the role of supplementary private health care," Journal of Health Economics, Elsevier, vol. 22(4), pages 599-616, July.
  13. Garber, Alan M. & Phelps, Charles E., 1997. "Economic foundations of cost-effectiveness analysis," Journal of Health Economics, Elsevier, vol. 16(1), pages 1-31, February.
  14. de Fraja, Giovanni & Delbono, Flavio, 1990. " Game Theoretic Models of Mixed Oligopoly," Journal of Economic Surveys, Wiley Blackwell, vol. 4(1), pages 1-17.
  15. Hoel, Michael, 2007. "What should (public) health insurance cover?," Journal of Health Economics, Elsevier, vol. 26(2), pages 251-262, March.
  16. Gruber, Jonathan & Simon, Kosali, 2008. "Crowd-out 10 years later: Have recent public insurance expansions crowded out private health insurance?," Journal of Health Economics, Elsevier, vol. 27(2), pages 201-217, March.
  17. Weinstein, Milton & Zeckhauser, Richard, 1973. "Critical ratios and efficient allocation," Journal of Public Economics, Elsevier, vol. 2(2), pages 147-157, April.
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Cited by:
  1. CANTA, Chiara, 2011. "Efficiency, access and the mixed delivery of health care services," CORE Discussion Papers 2011046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Simona Grassi & Ching-to Albert Ma, . "Optimal Public Rationing and Price Response," Boston University - Department of Economics - Working Papers Series wp2009-008, Boston University - Department of Economics.
  3. Simona Grassi & Ching‐To Albert Ma, 2012. "Public Sector Rationing and Private Sector Selection," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(1), pages 1-34, 02.

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