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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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  • Leung, Siu Fai, 2009. "Cake eating, exhaustible resource extraction, life-cycle saving, and non-atomic games: Existence theorems for a class of optimal allocation problems," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1345-1360, June.
  • Handle: RePEc:eee:dyncon:v:33:y:2009:i:6:p:1345-1360
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    References listed on IDEAS

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    1. 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.
    2. Heal, Geoffrey M., 1993. "The optimal use of exhaustible resources," Handbook of Natural Resource and Energy Economics, in: A. V. Kneese† & J. L. Sweeney (ed.), Handbook of Natural Resource and Energy Economics, edition 1, volume 3, chapter 18, pages 855-880, Elsevier.
    3. Daron Acemoglu, 1998. "Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality," The Quarterly Journal of Economics, Oxford University Press, vol. 113(4), pages 1055-1089.
    4. Kumar, T Krishna, 1969. "The Existence of an Optimal Economic Policy," Econometrica, Econometric Society, vol. 37(4), pages 600-610, October.
    5. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    6. Leung, Siu Fai, 1994. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," Econometrica, Econometric Society, vol. 62(5), pages 1233-1239, September.
    7. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39, pages 137-137.
    8. ABRHAM, Jaromir, 1970. "An approximate method for solving a continuous time allocation problem," LIDAM Reprints CORE 73, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 1-18.
    10. Abrham, Jaromir, 1970. "An Approximate Method for Solving a Continuous Time Allocation Problem," Econometrica, Econometric Society, vol. 38(3), pages 473-481, May.
    11. 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.
    12. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," Review of Economic Studies, Oxford University Press, vol. 32(2), pages 137-150.
    13. Artstein, Zvi, 1980. "Generalized Solutions to Continuous-Time Allocation Processes," Econometrica, Econometric Society, vol. 48(4), pages 899-922, May.
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    Cited by:

    1. Tatyana Balas & Anna Tur, 2023. "The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon," Mathematics, MDPI, vol. 11(2), pages 1-13, January.

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