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R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type

Author

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  • Hwan C. Lin

    (University of North Carolina at Charlotte)

  • L. F. Shampine

    (Southern Methodist University)

Abstract

The statutory patent length is 20 years in most countries. R&D-based growth models, however, often presume an infinite patent length. In this paper, finite-length patents are embedded in a non-scale R&D-based growth model, while allowing any patent’s effective life to be terminated prematurely, subject to two idiosyncratic hazards from imitation and creative destruction. This gives rise to an autonomous system of mixed-type functional differential equations (FDEs) that had never been encountered in the growth literature. Its dynamics are driven by current, delayed and advanced states. We present a relaxation algorithm to solve these FDEs by solving a sequence of standard boundary value problems for systems of ordinary differential equations. We use this algorithm to simulate a calibrated U.S. economy’s transitional dynamics by making discrete changes from the baseline 20 years patent length. We find that if transitional impacts are taken into account, the switch to the long-run optimal patent length can incur a welfare loss, albeit rather small.

Suggested Citation

  • Hwan C. Lin & L. F. Shampine, 2018. "R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type," Computational Economics, Springer;Society for Computational Economics, vol. 51(1), pages 123-158, January.
  • Handle: RePEc:kap:compec:v:51:y:2018:i:1:d:10.1007_s10614-016-9597-9
    DOI: 10.1007/s10614-016-9597-9
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    3. Hu, Mei-Ying & Lu, You-Xun & Lai, Ching-Chong, 2022. "Patent term extensions and commercialization lags in the pharmaceutical industry: A growth-theoretic analysis," MPRA Paper 113923, University Library of Munich, Germany.

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    More about this item

    Keywords

    Patent length; Innovation; Delay differential equation; Advance differential equation; Dynamics; Endogenous growth; Relaxation algorithm;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O34 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Intellectual Property and Intellectual Capital

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