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Factor-specific technology choice

Author

Listed:
  • 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.
    • Handle: RePEc:nbp:nbpmis:265
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    References listed on IDEAS

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    Cited by:

    1. Armando Sánchez-Vargas & José Manuel Márquez-Estrada & Eric Hernández-Ramírez, 2023. "Uncovering the Link Between the Theoretical and Probabilistic Models of the Global Production Function: A Copula Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 289-315, June.
    2. Guimarães, Luís & Mazeda Gil, Pedro, 2022. "Explaining the Labor Share: Automation Vs Labor Market Institutions," Labour Economics, Elsevier, vol. 75(C).
    3. Irmen Andreas, 2020. "Endogenous task-based technical change—factor scarcity and factor prices," Economics and Business Review, Sciendo, vol. 6(2), pages 81-118, June.
    4. Michael Knoblach & Fabian Stöckl, 2020. "What Determines The Elasticity Of Substitution Between Capital And Labor? A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 847-875, September.
    5. Jakub Growiec, 2019. "The Hardware–Software Model: A New Conceptual Framework of Production, R&D, and Growth with AI," Working Paper series 19-18, Rimini Centre for Economic Analysis.
    6. Kemnitz, Alexander & Knoblach, Michael, 2020. "Endogenous sigma-augmenting technological change: An R&D-based approach," CEPIE Working Papers 02/20, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    7. Lin, Justin Yifu & Liu, Zhengwen & Zhang, Bo, 2023. "Endowment, technology choice, and industrial upgrading," Structural Change and Economic Dynamics, Elsevier, vol. 65(C), pages 364-381.

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    More about this item

    Keywords

    technology choice; technology menu; production function; utility function; duality; envelope; homotheticity.;
    All these keywords.

    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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