Endogenous Innovation in a Growth Model à la Solow

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.