Constant population growth rate and time to build: the Solow model case

We analyze the Solow model with constant population growth rate, where production occurs with a time delay while new capital is installed (time to build). Taking time delay as a bifurcation parameter, we discuss the stability and the existence of the Hopf bifurcation occurring at the equilibrium. It is proved that the equilibrium is locally asymptotically stable for any delay if population is increasing, whereas there are stability switches if population is decreasing. In this case, a steady state bifurcation and a Hopf bifurcation occur. Contrary to the Solow model, a different scenario arises.