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

• Manuel Besada ^[1] ; Javier García ^[1] ; Miguel Mirás ^[1] ; Carmen Vázquez ^[1]
  1. [1] Universidade de Vigo

     Universidade de Vigo

     Vigo, España

     
• Localización: SERIEs : Journal of the Spanish Economic Association, ISSN 1869-4195, Vol. 2, Nº. 3, 2011, págs. 401-421
• Idioma: inglés
• DOI: 10.1007/s13209-011-0037-8
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• Resumen

  • 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.