A Modified Arrow Learning-by-Doing Growth Model in a Ramsey-Cass-Koopmans Optimal Control Framework

Abstract

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, population growth, and public policies affecting the degree of learning by doing associated with the economy’s stock of capital per efficient worker. Numerical simulations indicate the model’s faster adjustment to equilibrium from an initial disequilibrium position.