Differential models of production the single product firm
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Differential Models of Production: The Single Product Firm. Lecture XXV. Overview of the Differential Approach. Until this point we have mostly been concerned with envelopes or variations of deviations from envelopes in the case of stochastic frontier models.

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Overview of the differential approach
Overview of the Differential Approach

  • Until this point we have mostly been concerned with envelopes or variations of deviations from envelopes in the case of stochastic frontier models.

    • The production function was defined as an envelope of the maximum output level that could be obtained from a given quantity of inputs.


  • The differential approach departs from this basic formulation by examining changes in optimizing behavior.


    • Starting from consumption theory we have bundle of outputs based on a vector of input costs.

      • We assume that consumers choose the levels of consumption so that these first-order conditions are satisfied.







    Differential model of production
    Differential Model of Production fundamental matrix equation:

    • Theil writes the production function in logarithmic space

      • The Cobb-Douglas function then becomes


















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