The Solow-Swan model with a bounded population growth rate

The paper analyzes the dynamic of the Solow-Swan growth model when the labor growth rate is non-constant but variable and bounded over time. Per capita capital is seen to stabilize to the non-trivial steady state of the Solow-Swan model with a particular constant labor growth rate. The solution of the model is proved to be asymptotically stable. In case of a Cobb-Douglas production function and a generalized logistic population growth law, the solution is shown to have a closed-form expression via Hypergeometric functions.