Diminishing Marginal Rates of Substitution and Quasi-concavity

Stephen Layson

No 15-6, UNCG Economics Working Papers from University of North Carolina at Greensboro, Department of Economics

Abstract: Only in the 2-good case is a diminishing marginal rate of substitution equivalent to quasi-concavity of the utility function. When there are more than 2 goods, the conditions for quasi-concavity, expressed in terms of bordered hessians, are very unintuitive and tedious to implement. This paper demonstrates, however, that a constant or diminishing marginal rate of substitution between any good and a composite good, consisting of all other goods, is equivalent to quasi-concavity. A new method for checking quasi-concavity is demonstrated that is sometimes easier to use than the traditional method of checking the signs of the bordered hessians.

Keywords: Marginal Rates; Substitution; Quasi-concavity (search for similar items in EconPapers)
JEL-codes: D01 D11 (search for similar items in EconPapers)
Pages: 12 pages
Date: 2015-07-17
New Economics Papers: this item is included in nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:ris:uncgec:2015_006

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