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Comparing Sunspot Equilibrium and Lottery Equilibrium Allocations: The Finite Case

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  • Garratt, Rod

    (U of California, Santa Barbara)

  • Keister, Todd

    (Instituto Tecnologico Autonomo de Mexico)

  • Shell, Karl

    (Cornell U)

Abstract

Sunspot equilibrium and lottery equilibrium are two stochastic solution concepts for nonstochastic economies. Recent work by Garratt, Keister, Qin, and Shell (in press) and Kehoe, Levine, and Prescott (in press) on nonconvex exchange economies has shown that when the randomizing device is continuous, applying the two concepts to the same fundamental economy yields the same set of equilibrium allocations. In the present paper, we examine economies based on a discrete randomizing device. We extend the lottery model so that it can constrain the randomization possibilities available to agents in the same way that the sunspots model can. Every equilibrium allocation of our generalized lottery model has a corresponding sunspot equilibrium allocation. For almost all discrete randomizing devices, the converse is also true. There are exceptions, however: for some randomizing devices, there exist sunspot equilibrium allocations with no lottery equilibrium counterpart.

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Bibliographic Info

Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 02-07.

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Date of creation: Jul 2002
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Handle: RePEc:ecl:corcae:02-07

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  1. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
  2. Richard Rogerson, 2010. "Indivisible Labor, Lotteries and Equilibrium," Levine's Working Paper Archive 250, David K. Levine.
  3. Kehoe, Timothy J. & Levine, David K. & Prescott, Edward C., 2002. "Lotteries, Sunspots, and Incentive Constraints," Journal of Economic Theory, Elsevier, vol. 107(1), pages 39-69, November.
  4. Garratt, Rod, 1995. "Decentralizing Lottery Allocations in Markets with Indivisible Commodities," Economic Theory, Springer, vol. 5(2), pages 295-313, March.
  5. Edward Simpson Prescott & Robert M. Townsend, 2006. "Firms as Clubs in Walrasian Markets with Private Information," Journal of Political Economy, University of Chicago Press, vol. 114(4), pages 644-671, August.
  6. Garratt, Rod & Keister, Todd & Qin, Cheng-Zhong & Shell, Karl, 2002. "Equilibrium Prices When the Sunspot Variable Is Continuous," Journal of Economic Theory, Elsevier, vol. 107(1), pages 11-38, November.
  7. Shell, Karl & Wright, Randall, 1993. "Indivisibilities, Lotteries, and Sunspot Equilibria," Economic Theory, Springer, vol. 3(1), pages 1-17, January.
  8. Berentsen, Aleksander & Molico, Miguel & Wright, Randall, 2002. "Indivisibilities, Lotteries, and Monetary Exchange," Journal of Economic Theory, Elsevier, vol. 107(1), pages 70-94, November.
  9. Balasko, Yves, 1983. "Extrinsic uncertainty revisited," Journal of Economic Theory, Elsevier, vol. 31(2), pages 203-210, December.
  10. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
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Cited by:
  1. Rocheteau, Guillaume & Rupert, Peter & Shell, Karl & Wright, Randall, 2005. "General Equilibrium with Nonconvexities, Sunspots, and Money," Working Papers 05-16, Cornell University, Center for Analytic Economics.
  2. Prescott, Edward & Shell, Karl, 2002. "Introduction to Sunspots and Lotteries," Working Papers 02-08, Cornell University, Center for Analytic Economics.
  3. Rocheteau, Guillaume & Rupert, Peter & Wright, Randall, 2007. "Inflation and Unemployment in General Equilibrium," University of California at Santa Barbara, Economics Working Paper Series qt2fq1855f, Department of Economics, UC Santa Barbara.
  4. Hoelle, Matthew, 2014. "The relation between sunspot effects and multiplicity in incomplete markets models with numeraire assets," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 119-127.
  5. Rocheteau, Guillaume & Rupert, Peter & Shell, Karl & Wright, Randall, 2008. "General equilibrium with nonconvexities and money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 294-317, September.
  6. Jinpeng Ma & Fusheng Nie, 2002. "Walrasian Equilibrium in an Exchange Economy with Indivisibilities," Departmental Working Papers 200207, Rutgers University, Department of Economics.

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