chapter  4
Viability and corridor stability in Keynesian supply driven growth
Pages 18

We show in Section 4.2 that this 2D dynamical model produces local convergence to the steady state for sluggish output adjustment (with respect to profitability) and gives rise to degenerate Hopf bifurcations thereafter if behavior is linear (in terms of rates of growth) close to the steady state. This conclusion indeed applies to all such linear growth rate systems which therefore cannot exhibit isolated periodic orbits.3 After the bifurcation point has been passed, the dynamics become purely explosive and are thus not yet completely specified. Full capacity limits are therefore added and lead (in Section 4.3) to meaningfully bounded economic behavior that converges globally to the steady-state solution for adjustment speeds below the Hopf bifurcation point and to persistent fluctuations in a certain “corridor” or compact domain around the steady state for adjustment speeds above this point, where the dynamics are not asymptotically stable. There is thus always an economically meaningful subdomain in the positive part of the phase space 2, determined by global arguments, that is closed and invariant under the flow generated by the dynamics and is thus “viable” from the

economic point of view, so that the state variables of the dynamics always stay in this domain and cannot approach zero.4