Economic Theory

, Volume 5, Issue 2, pp 295–313 | Cite as

Decentralizing lottery allocations in markets with indivisible commodities

  • Rod Garratt
Research Articles


In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common “sunspot device” as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.


Economic Theory Potential Mechanism Welfare Gain Walrasian Equilibrium Sunspot Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Besley, T., Coate, S., Loury, G.: The economics of rotating savings and credit associations. Amer. Econ. Assoc.83, 792–810 (1993)Google Scholar
  2. 2.
    Broome, J.: Approximate equilibrium in economies with indivisible commodities. J. Econ. Theory5, 224–249 (1972)Google Scholar
  3. 3.
    Cass, D., Shell, K.: Do sunspots matter? J. Pol. Econ.91, 193–227 (1983).Google Scholar
  4. 4.
    Cooley, T.F., Smith, B.D.: A theory of optimal denominations for government liabilities. Econ. Theory3, 597–623 (1993)Google Scholar
  5. 5.
    Dierker, E.: Equilibrium analysis of exchange economies with indivisible commodities. Econometrica39, 997–1008 (1971)Google Scholar
  6. 6.
    Fenchel, W.: Convex cones, sets, and functions. Mimeo, Department of Mathematics, Princeton University 1953Google Scholar
  7. 7.
    Garratt, R., Marshall, J.: Public finance of private goods: the case of higher education. J. Pol. Econ., forthcomingGoogle Scholar
  8. 8.
    Greenwood, J., Huffman, G.: A dynamic equilibrium model of inflation and unemployment. J. Mon. Econ.19, 203–228 (1987)Google Scholar
  9. 9.
    Hansen, G.D.: Indivisible labor and the business cycle. J. Mon. Econ.16, 309–327 (1985)Google Scholar
  10. 10.
    Henry, C.: Indivisibilities dan une economie d'echanges. Econometrica38, 542–558 (1970)Google Scholar
  11. 11.
    Ichiishi, T.: In: Shell, K. (ed.) Game theory for economic analysis. New York: Academic Press 1983Google Scholar
  12. 12.
    Marshall, J.M.: Gambles and the shadow price of death. Amer. Econ. Rev.74, 73–86 (1984)Google Scholar
  13. 13.
    Mas-Colell, A.: Indivisible commodities and general equilibrium theory. J. Econ. Theory16, 443–456 (1977)Google Scholar
  14. 14.
    Ng, Y.K.: Why do people buy lottery tickets? Choices Involving Risk and the Indivisibility of Expenditure, J. Pol. Econ.73, 530–535 (1965)Google Scholar
  15. 15.
    Peck, J., Shell, K.: Market uncertainty: correlated and sunspot equilibria in imperfectly competitive economies. Rev. Econ. Stud.58, 1011–1029 (1991)Google Scholar
  16. 16.
    Prescott, E., Rios-Rull, J.-V.: Classical competitive analysis of economies with islands. J. Econ. Theory57, 73–98 (1992)Google Scholar
  17. 17.
    Prescott, E., Townsend, R.: Pareto optima and competitive equilibria with adverse selection and moral hazard. Econometrica52, 21–45 (1984)Google Scholar
  18. 18.
    Prescott, E., Townsend, R.: General competitive analysis in an economy with private information. Int. Econ. Rev.25, 1–20 (1984)Google Scholar
  19. 19.
    Rogerson, R.: Indivisible labor, lotteries and equilibrium. J. Mon. Econ.21, 3–16 (1988)Google Scholar
  20. 20.
    Rogreson, R., Wright, R.: Involuntary unemployment in economies with efficient risk sharing. J. Mon. Econ.22, 510–515 (1988)Google Scholar
  21. 21.
    Shell, K.: Monnaie et allocation intertemporelle. Mimeo, 1977Google Scholar
  22. 22.
    Shell, K., Wright, R.: Indivisibilities, lotteries, and sunspot equilibria. Econ. Theory2, 1–17 (1992)Google Scholar
  23. 23.
    Shubik, M.: The ‘bridge game’ economy: an example of indivisibilities. J. Pol. Econ.79, 909–912 (1971)Google Scholar
  24. 24.
    Smith, B.D., Villamil, A.P.: Efficiency, randomization, and commitment in government borrowing. Mimeo, 1993Google Scholar
  25. 25.
    Townsend, R.: Arrow-Debreu programs as microfoundations of macroeconomics. In: Bewley, T. (ed.) Advances in economic theory. Cambridge: Cambridge Univerisity Press 1987Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Rod Garratt
    • 1
  1. 1.Department of EconomicsUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations