into the above Taylor rule, the real wage gap, since we have in our model a dependence
of aggregate demand on income distribution and the real wage. The state of income
distribution matters for the dynamics of our model and thus should also play a role in
the decisions of the central bank. All of the employed gaps are measured relative to the
steady state of the model, in order to allow for an interest rate policy that is consistent
with balanced growth.
We note that the steady state of the considered Keynesian dynamics is basically the same
as the one considered in Asada, Chen, Chiarella and Flaschel (2004), with eo = 0, Voc =
Vc, Vl = Vl,∏m = ∏. The values of ωo, ro are in principle determined as in Asada, Chen,
Chiarella and Flaschel (2004), but are here just assumed as given, underlying the linear
approximation of the present model around the steady state of the original framework
(when adjusted to the considered modifications of the baseline model).
The steady state of the dynamics is locally asymptotically stable under certain sluggish-
ness conditions that are reasonable from a Keynesian perspective, loses its asymptotic
stability by way of cycles (by way of so-called Hopf-bifurcations) if the system becomes
too flexible, and becomes sooner or later globally unstable if (generally speaking) ad-
justment speeds become too high, as we shall show below. If the model is subject to
explosive forces, it requires extrinsic nonlinearities in economic behavior - like down-
ward wage rigidity - to come into being at least far off the steady state in order to
bound the dynamics to an economically meaningful domain in the considered 5D state
space. Asada, Chiarella, Flaschel and Hung (2004) provide details for such an approach
with extrinsically motivated nonlinearities and undertake its detailed numerical investi-
gation. In sum, therefore, our dynamic AS-AD growth model here and there will exhibit
a variety of features that are much more in line with a Keynesian understanding of
the characteristics of the trade cycle than is the case for the conventional modelling of
AS-AD growth dynamics or its reformulation by the New Keynesians.
Taken together the model of this section consists of the five laws of motion:
V Vc
V/l
r
ω
-αvc(Vc — Vc) ± αlω(ω — ωl) — α((r — p) — (rl — π)) (1)
βv1 ( Vc — Vc ) — βvi ( ω — ωl ) + βv3 Vc (2)
— Yr (r — ro) + Yp (p — π) + Yvc ( vc — Vc) + Yω (ω — ωo) (3)
κ [(1 — κp )( βw 1 ( V l — V l ) — βw 2 ( ω — ωo )) — (1 — κw )( βP 1 ( V c — V c ) + βP 2 ( ω — ωo ))]
where the following reduced form expression for the price inflation rate
βπm (p — ∏m) or
πm(t) = πm(to)e
-βπm (t-to) + βπm t eβπm (t-s)p^(s)ds
(4)
(5)
'p = κ [ βp 1 ( V c — V c ) + βp 2 ( ω — ωo ) + κp ( βw 1 ( V l — V l ) — βw 2 ( ω — ωo ))] + πm
has to be inserted into the third and fifth equation in order to get an autonomous system
of differential equations in the state variables: capacity utilization V c , the rate of em-
ployment V l , the rate of interest r, the real wage rate ω and the inflationary climate πm.