A Modified Arrow Learning-by-Doing Growth Model in a Ramsey-Cass-Koopmans Optimal Control Framework
Delano Villanueva · Theoretical Economics Letters · 2026
The Solow-Swan or S-S growth model has been, and still is, the workhorse of standard neoclassical growth theory. The S-S growth model has two distinguishing features-the saving rate is an exogenously fixed constant, and all technical change is exogenous. The present paper's growth model relaxes both features by modifying Arrow's learning-by-doing model with endogenous technical change and embedding it in a Ramsey-Cass-Koopmans growth setup that derives an endogenously determined optimal saving rate. This optimizing framework produces empirically plausible and testable predictions about the per capita output growth effects of changes in consumer preferences-discount rate and coefficient of relative risk aversion (inverse of intertemporal elasticity of substitution or IES)-population growth and public policies that raise the equilibrium capital intensity and the learning by doing coefficient. Holding the learning-by-doing coefficient constant, adjustment to the steady state is faster as IES increases. Numerical simulations indicate the model's faster adjustment to equilibrium from an initial disequilibrium position.