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Diminishing marginal value of income without apology


  • Christian E. Weber


This paper considers value functions for maximization problems where the objective function is maximized subject to several constraints. I show that such value functions exhibit diminishing marginal rates of substitution (MRS) between the resource endowments which define the constraints. For the household, this implies that an ordinally defined marginal value of income falls as income rises. I also derive conditions under which the value function is homothetic in the endowments, so that the MRS between two resources is a monotone function of the ratio of the endowments of those resources and under which the MRS between two resources declines when one resource is increased with the other held constant, i.e., under which the marginal rate of substitution declines when the households moves from one indirect indifference curve to another. I apply these results to a model with two linear constraints and to a model of asset choice under uncertainty. Copyright 2005, Oxford University Press.

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  • Christian E. Weber, 2005. "Diminishing marginal value of income without apology," Oxford Economic Papers, Oxford University Press, vol. 57(4), pages 586-609, October.
  • Handle: RePEc:oup:oxecpp:v:57:y:2005:i:4:p:586-609

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    References listed on IDEAS

    1. Marion, Nancy P., 1984. "Nontraded goods, oil price increases and the current account," Journal of International Economics, Elsevier, vol. 16(1-2), pages 29-44, February.
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    Cited by:

    1. Manuel Besada & Javier García & Miguel Mirás & Carmen Vázquez, 2011. "Generalized marginal rate of substitution in multiconstraint consumer’s problems and their reciprocal expenditure problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(3), pages 401-421, September.
    2. Courard-Hauri David & Lauer Stephen A., 2012. "Taking "All Men Are Created Equal" Seriously: Toward a Metric for the Intergroup Comparison of Utility Functions Through Life Values," Journal of Benefit-Cost Analysis, De Gruyter, vol. 3(3), pages 1-30, August.

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