, Volume 2, Issue 3, pp 401–421 | Cite as

Generalized marginal rate of substitution in multiconstraint consumer’s problems and their reciprocal expenditure problems

  • Manuel Besada
  • Javier García
  • Miguel Mirás
  • Carmen Vázquez
Open Access
Original Article


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.


Quasi-concave programming Indirect utility function Marginal rates of substitution Multiple constraint optimization problems 

JEL Classification

C61 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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Copyright information

© The Author(s) 2011

This article is published under license to BioMed Central Ltd. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Manuel Besada
    • 1
  • Javier García
    • 1
  • Miguel Mirás
    • 1
  • Carmen Vázquez
    • 1
  1. 1.Departamento de MatemáticasUniversidade de VigoVigoSpain

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