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Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model

Author

Listed:
  • Lin, Hwan C.
  • Shampine, L.F.

Abstract

The statutory patent length is 20 years in most countries. R&D-based endogenous 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, but any patent’s effective life may be terminated prematurely at any moment, subject to two idiosyncratic hazards of imitation and innovation. This gives rise to an autonomous system of mixed-type functional differential equations (FDEs). Its dynamics are driven by current, delayed and advanced states. We present an algorithm to solve the FDEs by solving a sequence of standard BVPs (boundary value problems) for systems of ODEs (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, optimizing the patent length incurs a welfare loss, albeit rather small. This suggests that fine-tuning the world’s patent systems may not be a worthwhile effort.

Suggested Citation

  • Lin, Hwan C. & Shampine, L.F., 2014. "Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model," MPRA Paper 61603, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:61603
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    References listed on IDEAS

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    More about this item

    Keywords

    Patent Length; Innovation; Delay Differential Equation; Advance Differential Equation; Transitional Dynamics; Endogenous Growth;
    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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