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

Hwan Lin and L.F. Shampine

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Patent Length; Innovation; Delay Differential Equation; Advance Differential Equation; Transitional Dynamics; Endogenous Growth (search for similar items in EconPapers)
JEL-codes: C63 O31 O34 (search for similar items in EconPapers)
Date: 2014-10
New Economics Papers: this item is included in nep-gro, nep-ino, nep-ipr and nep-pr~
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