Endogenous Innovation in a Growth Model à la Solow

Thi Kim Cuong Pham, Ngoc-Sang Pham (), Cuong Le Van () and Tin Nguyen-Trong
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Thi Kim Cuong Pham: CNRS, EconomiX, Université Paris Nanterre, 92001 Nanterre
Ngoc-Sang Pham: EM Normandie - École de Management de Normandie = EM Normandie Business School, CNRS, EconomiX, Université Paris Nanterre, 92001 Nanterre
Cuong Le Van: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, TIMAS, Thang Long University, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne
Tin Nguyen-Trong: CNRS, EconomiX, Université Paris Nanterre, 92001 Nanterre

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Abstract: We develop a dynamic endogenous-growth model with an R&D sector in which the elasticity of innovation with respect to existing knowledge can be negative. We prove the existence and uniqueness of a balanced growth path (BGP) and derive closed-form growth factors, showing that productivity and output growth are semi-endogenous and population-driven. We also establish the global stability under general production function. Under testable parameter restrictions, the economy converges to the BGP. When the knowledge elasticity is sufficiently low, a Jacobian-based condition implies instability, and an N-period innovation cycle can emerge. Comparative statics are conducted to show the role of several factors, including research efficiency, elasticity of inputs and population growth. Calibrated simulations map out transitions and mark the points at which stability is lost. They make clear when innovation frictions endanger balanced growth and provide practical guidance for R&D and demographic policy.

Keywords: endogenous growth; population-driven growth; balanced growth path; stability; instability; innovation; monotone dynamical system (search for similar items in EconPapers)
Date: 2025-11-29
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