P8475423 at vmsuser.acsu.unsw.EDU.AU P8475423 at vmsuser.acsu.unsw.EDU.AU
Thu Aug 24 16:53:40 MDT 1995

John R Ernst recently posted:

|I do not see how the "post-Keynesian" growth models are, on the one hand,
|related to Marxian theory or, on the other hand, connected to Minsky's
|efforts.  Can you be more explicit about these matters?  Here,
|on this list, I think the manner in which Marx's ideas are captured in the
|models would be of interest.

John's question requires a detailed and somewhat technical reply, so
I apologise to those who don't like this approach.

The particular Post Keynesian growth model that I have in mind is
Goodwin's 1967 predator-prey model (I don't particularly like Kaldor's
or other approaches which work in terms of equilibrium growth).

This model is very well detailed in Blatt, _Dynamic Economic Systems_,
ME Sharpe, 1983. I also outline it, and simulate it numerically,
in my paper in the current issue of the Journal of Post Keynesian
Economics (Vol. 17, No. 4). But to do it brief injustice here:

* It is is a one-commodity, no-prices model with exogenous constant
technical change, but I believe it can be generalised to a 3
commodity, prices model (though this may involve changing from an
ODE approach to difference equations).

* It has fixed capital (something I note you criticise Grossman for
omitting). Goodwin didn't incorporate depreciation, but I added that
very easily in my JPKE paper.

* In the form Goodwin presented it, he had capitalists investing
all their surplus; I have generalised it to include a investment
function, where investment ceases at zero profit and increases
non-linearly above it.

* Capitalist investment decisions output, which in turn determines

* Workers wage demands are a nonlinear function of the rate of
employment: high employment generates demands for higher wages,
high unemployment forces workers to accept pay cuts (though there
is a maximum rate of fall of wages in the system).

* Population growth is constant, hence the available workforce
grows at a constant rate.

The cycle it generates goes as follows:

If the system starts with high employment, investment will be low
while demands for increased wages are high. Depreciation reduces
the capital stock, which reduces employment (workers are hired
to "tend the machines"), and simultaneously population growth
increases the workforce. Unemployment rises, slackening wage
demands at first, and later leading to wage cuts. This increases
the amount available for investment, leading to higher growth
and rising employment, which eventually grows faster than
population growth, cutting unemployment and leading to demands
for higher wages. The cycle then repeats.

To explain why I see this as Marxian in spirit, I need only cite
the following from Ch 25 of Capital:

"accumulation slackens in consequence of the rise in the price of labor,
because the stimulus of gain is blunted. The rate of accumulation
lessens; but with its lessening, the primary cause of that lessening
vanishes, i.e. the disproportion between capital and exploitable labor
power. The mechanism of the process of capitalist production removes the
very obstacles that it temporarily creates. The price of labor falls
again to a level corresponding with the needs of the self-expansion of
capital, whether the level be below, the same as, or above the one which
was normal before the rise in wages took place... To put it
mathematically, the rate of accumulation is the independent, not the
dependent variable; the rate of wages the dependent, not the independent
variable." (Ibid., pp. 580-581.)

I have written to Goodwin asking whether this was the specific
inspiration for his model, but I haven't yet heard back.

As for the link to Minsky, that was built simply by acknowledging the
fact that banks lend money to capitalists to finance investment.
With this incorporated into Goodwin's 2-equation limit cycle model
(by the simple equation dD/dt = rD + I - P, where D is debt, I
investment, and P profits), what eventuated was a 3 equation,
chaotic model, whose long term stability was a function of the
rate of interest. If that rate was below a certain level, then
the growth in debt eventually tapered, leading to constant economic
growth without cycles and with constant income shares.

Above that level, growth of debt appeared to taper but never stopped
rising, leading eventually to a debt blowout and complete collapse
of output.

I extended it one step more by incorporating government counter-
cyclical policies, to establish Minsky's claim that a capitalist
economy with big government cannot fall into a depression. The
result there was a 6 equation model which generated a true limit
cycle--in that no matter where the system began, it converged to
a cyclical growth path, but never broke down.

I hope this is sufficient: to do anymore would go beyond what can
be done with email; graphs and equations are needed. Both exist
in the JPKE paper, if you are interested in pursuing it.

Steve Keen
PS To Lisa and Chris--the above model is of course a chaotic

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