Abstract
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.
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Acknowledgements
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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Besada, M., García, J., Mirás, M. et al. Generalized marginal rate of substitution in multiconstraint consumer’s problems and their reciprocal expenditure problems. SERIEs 2, 401–421 (2011). https://doi.org/10.1007/s13209-011-0037-8
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DOI: https://doi.org/10.1007/s13209-011-0037-8
Keywords
- Quasi-concave programming
- Indirect utility function
- Marginal rates of substitution
- Multiple constraint optimization problems