From Ordients to Optimization: Substitution Effects without Differentiability
AbstractThis paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradients for functions (utilities). The lexicographic order, albeit not representable, has an ordient. Not only binary relations representable by differentiable functions have an ordient, but also preferences representable by non-differentiable functions might. We characterize the constrained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem. Ordients have a natural economic interpretation as marginal rates of substitution. We apply our results to the classic problem of maximizing preferences over budget sets.
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Bibliographic InfoPaper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number 09/6.
Date of creation: Feb 2009
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Find related papers by JEL classification:
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-03-14 (All new papers)
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