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Diminishing Marginal Rates of Substitution and Quasi-concavity


  • Layson, Stephen

    () (University of North Carolina at Greensboro, Department of Economics)


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.

Suggested Citation

  • Layson, Stephen, 2015. "Diminishing Marginal Rates of Substitution and Quasi-concavity," UNCG Economics Working Papers 15-6, University of North Carolina at Greensboro, Department of Economics.
  • Handle: RePEc:ris:uncgec:2015_006

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    More about this item


    Marginal Rates; Substitution; Quasi-concavity;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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