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Hicks Neutrality and Homotheticity in Technologies with Multiple Inputs and Multiple Outputs

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Abstract

We analyse two popular notions in production theory: the notion of Hicks neutral technical change and the notion of homothetic technology. Both of these notions are characterized by the radial expansions or contractions of the relevant isoquants, yet in different ways. In the case of multiple-input and multiple-output, an isoquant is characterized by either the input or output combinations. Thus, for each of these notions, there are two types of conditions: one is based on the input isoquants and the other is based on the output isoquants. We show that for each notion, these two conditions are equivalent under the ð ›¼-returns to scale technology. From this result, we also derive several implications for the properties of well-known productivity indexes, such as the Malmquist productivity index and the Hicks-Moorsteen productivity index.

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  • Rolf Färe & Hideyuki Mizobuchi & Valentin Zelenyuk, 2019. "Hicks Neutrality and Homotheticity in Technologies with Multiple Inputs and Multiple Outputs," CEPA Working Papers Series WP092019, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:139
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    File URL: https://economics.uq.edu.au/files/15436/WP092019.pdf
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    Cited by:

    1. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.
    2. Yunguo Lu & Lin Zhang, 2023. "Environmental information disclosure and firm production: evidence from the estimated efficiency of publicly listed firms in China," Journal of Productivity Analysis, Springer, vol. 59(1), pages 99-119, February.
    3. Léopold Simar & Valentin Zelenyuk & Shirong Zhao, 2025. "Statistical inference for Hicks–Moorsteen productivity indices," Annals of Operations Research, Springer, vol. 351(2), pages 1675-1703, August.
    4. Walter Briec & Marc Dubois & Stéphane Mussard, 2021. "Technical efficiency in firm games with constant returns to scale and $$\alpha $$ α -returns to scale," Annals of Operations Research, Springer, vol. 304(1), pages 35-62, September.
    5. Mergoni, Anna & Emrouznejad, Ali & De Witte, Kristof, 2025. "Fifty years of Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 326(3), pages 389-412.
    6. Rolf Färe & Valentin Zelenyuk, 2020. "POn Fisher Aggregation of Multi-factor Productivity Indexes," CEPA Working Papers Series WP082020, School of Economics, University of Queensland, Australia.

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    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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