Generalized marginal rate of substitution in multiconstraint consumer’s problems and their reciprocal expenditure problems
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The aim of this paper is to explore several features concerning the generalized marginal rate of substitution (GMRS) when the consumers utility maximization problem with several constraints is formulated as a quasi-concave programming problem. We show that a point satisfying the first order sufficient conditions for the consumer’s problem minimizes the associated quasi-convex reciprocal cost minimization problems. We define the GMRS between endowments and show how it can be computed using the reciprocal expenditure multipliers. Additionally, GMRS is proved to be a rate of change between different proportion bundles of initial endowments. Finally, conditions are provided to guarantee a decreasing GMRS along a curve of initial endowments while keeping the consumer’s utility level constant.
KeywordsQuasi-concave programming Indirect utility function Marginal rates of substitution Multiple constraint optimization problems
JEL ClassificationC61 D11
We thank an anonymous referee for his/her comments on a previous version of this work. We have benefited from the financial support of the Spanish Ministry of Education through DGICYT grants ECO2008-03004 and SEJ2006-15401-C04-01/ECON.
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