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From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scale


  • Pierre Ouellette

    (Economics - UQAM - Université du Québec à Montréal)

  • Stephane Vigeant

    () (Institut des sciences economiques et de management - Université de Lille, Sciences et Technologies, LEM - Lille économie management - LEM - UMR 9221 - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)


The characterization of a technology, from an economic point of view, often uses the first derivatives of either the transformation or the production function. In a parametric setting, these quantities are readily available as they can be easily deduced from the first derivatives of the specified function. In the standard framework of data envelopment analysis (DEA) models these quantities are not so easily obtained. The difficulty resides in the fact that marginal changes of inputs and outputs might affect the position of the frontier itself while the calculation of first derivatives for economic purposes assumes that the frontier is held constant. We develop here a procedure to recover first derivatives of transformation functions in DEA models and we show how we can evacuate the problem of the (marginal) shift of the frontier. We show how the knowledge of the first derivatives of the frontier estimated by DEA can be used to deduce and compute marginal products, marginal rates of substitution, and returns to scale for each decision making unit (DMU) in the sample.

Suggested Citation

  • Pierre Ouellette & Stephane Vigeant, 2016. "From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scale," Post-Print hal-01533531, HAL.
  • Handle: RePEc:hal:journl:hal-01533531
    DOI: 10.1016/j.ejor.2016.02.036
    Note: View the original document on HAL open archive server:

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    Cited by:

    1. Lin, Winston T. & Chen, Yueh H. & Hung, TingShu, 2019. "A partial adjustment valuation approach with stochastic and dynamic speeds of partial adjustment to measuring and evaluating the business value of information technology," European Journal of Operational Research, Elsevier, vol. 272(2), pages 766-779.


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