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Cake eating, exhaustible resource extraction, life-cycle saving, and non-atomic games: Existence theorems for a class of optimal allocation problems

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  • Leung, Siu Fai

Abstract

This paper investigates the problem concerning the existence of a solution to a diverse class of optimal allocation problems which include models of cake eating, exhaustible resource extraction, life-cycle saving, and non-atomic games. A new formulation that encompasses all these diverse models is provided. Examples of these models for which a solution does not exist and the causes of the non-existence are studied. Two theorems are provided to tackle the existence problem under different conditions. Several analytical examples with a closed-form solution are offered to illustrate the usefulness of the existence theorems.

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File URL: http://www.sciencedirect.com/science/article/B6V85-4VK6N5T-1/2/0fe14515a97cdd1db76b6f16a7da4621
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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 33 (2009)
Issue (Month): 6 (June)
Pages: 1345-1360

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Handle: RePEc:eee:dyncon:v:33:y:2009:i:6:p:1345-1360

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Cake eating Exhaustible resource extraction Life-cycle saving Non-atomic games Optimal allocation Existence;

References

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  1. Acemoglu, Daron, 1997. "Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality," CEPR Discussion Papers 1707, C.E.P.R. Discussion Papers.
  2. Artstein, Zvi, 1980. "Generalized Solutions to Continuous-Time Allocation Processes," Econometrica, Econometric Society, vol. 48(4), pages 899-922, May.
  3. Kumar, T Krishna, 1969. "The Existence of an Optimal Economic Policy," Econometrica, Econometric Society, vol. 37(4), pages 600-610, October.
  4. Olivier J. Blanchard, 1984. "Debt, Deficits and Finite Horizons," NBER Working Papers 1389, National Bureau of Economic Research, Inc.
  5. Hart, Sergiu, 2002. "Values of perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 57, pages 2169-2184 Elsevier.
  6. Abrham, Jaromir, 1970. "An Approximate Method for Solving a Continuous Time Allocation Problem," Econometrica, Econometric Society, vol. 38(3), pages 473-81, May.
  7. Leung, S.F., 1992. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," RCER Working Papers 323, University of Rochester - Center for Economic Research (RCER).
  8. Leung, Siu Fai, 2007. "The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint," Journal of Economic Theory, Elsevier, vol. 134(1), pages 470-493, May.
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