# [OPE-L:2022] Re: money and circulating capital models

Steve Keen (s.keen@uws.edu.au)
Sun, 28 Apr 1996 22:55:34 -0700

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Jerry asks me to explain the relevance of my assumptions of...
>>a circulating capital only, no technical change,
>> no population growth, no stocks, three class model (workers, bankers,
>> capitalists) with multiple commodities and hence input-output relations.

The relevance is the progressive construction of a more relevant model. Even
with this extremely simple basis, the resulting system had 5 vector and 1
scalar third order difference equations! Increasing the realism will
undoubtedly increase the complexity of the model, but I simply wanted to be
sure that a determinate system could be derived before introducing technical
change, population growth, and fixed capital.

>By assuming a circulating-capital-only model, isn't the distinction
>between money capital and industrial capital effectively obliterated?

No. Money capital in this model is the number recorded in the bank balances
of capitalists. Industrial capital are the columns in the input-output
matrix which are used as inputs to produce other commodities (basic
commodities, in Sraffa's terminology).

>How can a model without technical change or capital stocks be a model
>that has relevance for capitalism? (except, via analogy, in the formal sense
>that a model of simple reproduction has relevance for explaining extended
>reproduction).

This model has little relevance, agreed; hopefully its more complete
successors will have more. But even at this level, one clarifying result
(the endogeneity of credit money) occurs. And contrary to your next comment:

>Of course, it is much easier to get results, in a determinate
>mathematical sense, with such models (and linear economic models
>generally)

the model is *not* linear. This is for two reasons: one "non-essential"
nonlinearity is a nonlinear wages function; but when you have a model with
quantity, markup and price dynamics, that model is necessarily nonlinear.
This was the starting point for my work, in fact: Steedman had criticised
Kaleckian mark-up pricing models on the basis of the proposition that prices
should obey the formula:

p = (u+pA)(I+M)

where u is a vector of exogenous costs, A the input-output matrix, I the
identity matrix, and M a diagonal matrix of sectoral mark-ups. He then
derived a number of limitations on the values in M using traditional linear
algebra arguments, to make the case that markups cannot be based solely on
competitive conditions for each industry (the Kaleckian approach), but are
constrained by the pattern of prices, p.

I argued that this is true if equilibrium reigns, and/or if M is fixed. If,
however, M is a variable, then the function for prices is nonlinear, and the
setting of prices and markups can be nonlinear systems occurring at
non-equilibrium values. Taking the (utterly unrealistic but one would think
stability-inducing) position that markups are a function of price:

p[t+1]=(u+p[t]A)(I+M[t+1])
m[t+1] = m(t) - a(p[t]-p[t-1])

you get "chaos", using Steedman's numerical example, when a> .943.

This model is "just" a generalisation of this approach to multi-sectoral
analysis, and a first step at that. But you've got to start somewhere!

Re the "mind picture" that matches this model:

>Even in a rural economy, fixed capital is required for production.
>
>Even in a corn model, aren't means of production required to plant and
>harvest corn?

Yep, but it's feasible to imagine that harvesting is done using, for
example, bamboo tools which wear out each season. Circulating capital, after
all, can be viewed as fixed capital which has 100 0epreciation in the first
period (I think Allin or Paul C made this point earlier on, in reverse).

Cheers,
Steve
Steve Keen
Senior Lecturer
Economics & Finance
University of Western Sydney
PO Box 555 Campbelltown NSW 2560
Australia
s.keen@uws.edu.au (046) 20-3016 Fax (046) 26-6683
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