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Factor-specific technology choice

Author

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  • Jakub Growiec

    (Narodowy Bank Polski and SGH Warsaw School of Economics)

Abstract

We analyze the properties of a two-dimensional problem of factor-specific technology choice subject to a technology menu – understood as the choice of the degree of factor augmentation by a producing firm or the choice of quality of goods demanded by a consumer. By considering the problem in its generality, we are able to reach beyond the known results for Cobb–Douglas, CES, Leontief (minimum) and maximum functions. We demonstrate that the technology menu and the global function (envelope of local functions) are dual objects, in a well-defined generalized sense of duality. In the optimum, partial elasticities of (i) the local function, (ii) the technology menu and (iii) the global function are all equal and there exists a clear-cut, economically interpretable relationship between their curvatures. Invoking Bergson’s theorem, we also comment on the consequences of assuming homotheticity of the three objects, with a particular focus on technology menus constructed as level curves of idea (unit factor productivity) distributions.

Suggested Citation

  • Jakub Growiec, 2017. "Factor-specific technology choice," NBP Working Papers 265, Narodowy Bank Polski, Economic Research Department.
  • Handle: RePEc:nbp:nbpmis:265
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    File URL: http://www.nbp.pl/publikacje/materialy_i_studia/265_en.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Michael Knoblach & Fabian Stöckl, 2019. "What Determines the Elasticity of Substitution between Capital and Labor? A Literature Review," Discussion Papers of DIW Berlin 1784, DIW Berlin, German Institute for Economic Research.

    More about this item

    Keywords

    technology choice; technology menu; production function; utility function; duality; envelope; homotheticity.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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