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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Find related papers by JEL classification: D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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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.
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