A growth-cycle model of Solow–Swan type, I

We construct an endogenous growth-cycle model of the Solow–Swan type. The equilibrium point of the growth-cycle model is the same as the steady state of the Solow–Swan growth model. Unlike in the Solow–Swan growth model, the representative household in the growth-cycle model, however, adaptively estimates his/her average income and determines his/her consumption in proportion to average income. We prove that if the steady state is unstable, any non-equilibrium path converges to a limit cycle. However, even if the steady state is stable, growth cycles can emerge. In fact, we prove that the growth-cycle model generates corridor stability. As a result, we prove that there exists an unstable cyclic path such that any path in the interior of the cyclic path converges to the steady state and any path in the exterior of the cyclic path tends toward a limit cycle (growth cycle). We also prove that a high economic growth rate is not compatible with a stable economy.