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A Note on the Dual Approach to the Existence and Characterization of Optimal Consumption Decisions Under Uncertainty and Liquidity Constraints

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Abstract

This paper considers a dual approach to the problem of maximizing lifetime utility subject to liquidity constraints in a discrete time setting. These constraints prohibit the decision maker from borrowing against future endowment income. The dual approach allows us to exploit directly the supermartingale property of the marginal utility of expenditure and to establish existence and uniqueness of the optimal solution. The optimal solution is interpreted as deriving from a version of the problem that is subject to a single lifetime budget constraint, where expenditures and incomes are discounted to the beginning of the horizon by means of individualized Arrow-Debreu prices.

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File URL: http://cowles.econ.yale.edu/P/cd/d10a/d1018.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1018.

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Length: 24 pages
Date of creation: May 1992
Date of revision:
Handle: RePEc:cwl:cwldpp:1018

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Consumer choice; duality theory;

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  1. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
  2. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 1 McMaster University Archive for the History of Economic Thought.
  3. Zeldes, Stephen P, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 275-98, May.
  4. Zeldes, Stephen P, 1989. "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 305-46, April.
  5. repec:fth:banfra:12 is not listed on IDEAS
  6. Richard H. Clarida, 1984. "Consumption, Liquidity Constraints and Asset Accumulation in the Presence of Random Income Fluctuations," Cowles Foundation Discussion Papers 705R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1985.
  7. Hua He and Henri F. Pag�s., 1990. "Consumption and Portfolio Decisions with Labor Income and Borrowing Constraints," Research Program in Finance Working Papers RPF-200, University of California at Berkeley.
  8. Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
  9. Pissarides, Christopher A, 1978. "Liquidity Considerations in the Theory of Consumption," The Quarterly Journal of Economics, MIT Press, vol. 92(2), pages 279-96, May.
  10. Deaton, A., 1989. "Saving And Liquidity Constraints," Papers 153, Princeton, Woodrow Wilson School - Public and International Affairs.
  11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  12. Bewley, Truman, 1977. "The permanent income hypothesis: A theoretical formulation," Journal of Economic Theory, Elsevier, vol. 16(2), pages 252-292, December.
  13. Jackman, Richard & Sutton, John, 1982. "Imperfect Capital Markets and the Monetarist Black Box: Liquidity Constraints, Inflation and the Asymmetric Effects of Interest Rate Policy," Economic Journal, Royal Economic Society, vol. 92(365), pages 108-28, March.
  14. Browning, Martin & Deaton, Angus & Irish, Margaret, 1985. "A Profitable Approach to Labor Supply and Commodity Demands over the Life-Cycle," Econometrica, Econometric Society, vol. 53(3), pages 503-43, May.
  15. Artle, Roland & Varaiya, Pravin, 1978. "Life cycle consumption and homeownership," Journal of Economic Theory, Elsevier, vol. 18(1), pages 38-58, June.
  16. Sumru Altug & Robert A. Miller, 1987. "Household choices in equilibrium," Working Papers 341, Federal Reserve Bank of Minneapolis.
  17. Philip H. Dybvig & Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," Cowles Foundation Discussion Papers 860, Cowles Foundation for Research in Economics, Yale University.
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