Re: [OPE] classical macro dynamics and the labor theory of value

From: Anders Ekeland <>
Date: Mon Feb 07 2011 - 14:32:15 EST

Thanks to Ian for an informative answer.

I do not feel that we really disagree fundamentally here. I am
looking forward to what models and insights Ian can come up with. We
have to look at actual models and their use in order to advance the


At 21:16 04.02.2011, Ian Wright wrote:
>Yes agreed. Allow me to widen the discussion a little. We have been
>discussing "equilibrium" and "equilibrium point" but of course these
>are natural language echoes of a highly developed mathematical theory
>of deterministic dynamical systems (systems of ordinary differential
>equations) in which "equilibrium points" play a small part. Some of
>this theory reappears in economics. In other fields -- such as physics
>-- there is a much longer and more intimate connection between the
>domain of application and the mathematics.
>It's commonplace in physical models and control theory to "stitch
>together" a model that keeps some input constant with another model
>that then drives that constant and makes it variable. In fact, many
>stability theorems exploit our ability to analytically separate the
>dynamics of the complete system in this manner. For example,
>dissipativity theory, a generalization of Lyapunov theory to systems
>which are "open" to inputs, works this way. We can prove stability
>properties for the base system assuming the inputs are zero. Then we
>can take another system that is also "open" to inputs and prove the
>same. Then we can join those systems together via their input/output
>ports. We then use the stability proofs for the separate systems to
>construct a stability proof for the joined systems.
>My point is this -- the "counterfactual" approach of assuming some
>things constant (when factually they are not) is an *essential* tool
>for understanding the causality of complex dynamic systems. The
>mathematicians exploit this analytical procedure. It is really after
>all simply "divide and conquer". I feel that critics of this
>methodological approach must either be ignorant or naive.

In general I have no problems with such an approach.

> > Ian:
> >>This is semantic. I take "natural prices" to refer to those prices
> >>that obtain when there is no profit incentive to reallocate capital in
> >>circumstances of constant technique and final demand.
> >
> > The problem that Jurriaan points to here is that the same forces that
> > drives you towards eq. - the forces of competition also continuously
> > changes the technique and the preferences.
>Yes of course they do. I want to understand these kinds of dynamics.
>My approach is to take one step at a time. You can't enjoy the full
>scientific meal at one sitting, that is all.
> > The problem here is that the value of the thermostat is continuously
> > changing. The thermostat might change in an orderly way so that you
> > can have a theory of the moving attractor. Given that we can estimate
> > the *reaction speed* we could get - if not an equilibrium theory, so
> > at least a theory of "non-crisis" path of development - like the
> > golden decades after the 2nd WW.
>I agree with your general point. But my example was constructed to
>show that -- even if the reference temperature of the thermostat is
>constant -- it is not the case that the whole system will reach its
>equilibrium point; nonetheless the attractor is real and causally
>efficacious. In other words, it is wrong-headed to deny the importance
>of theorizing equilibrium points and their stability properties simply
>because empirical reality seems not to exhibit such properties.
> > You are right - capitalism still exist - it reproduces itself - but
> > on a ever expanding diseq. path with periodic crisis (not regular,
> > not repetitive) - so the meaning of non-constant technology
> > equilibrium and corresponding prices is not still clear to me.
>It is an analytical abstraction to hold some things constant, just as
>a physical experiment is designed to isolate a particular mechanism
>from the interference of other causes.
>I cannot expand on this now, but I am deeply influenced by early Roy
>Bhaskar (i.e., critical realism). So I view the empirical stream of
>events as jointly determined by multiple "hidden" causal mechanisms in
>"open systems". Part of the work of science is to discover the laws
>that describe how those mechanisms operate in isolation or "closed
>systems". How those mechanisms work in isolation may be very different
>from how they manifest in open systems. Once you've done that, put the
>mechanisms back together again and you'll have a good explanation of
>the empirical. The abstraction of natural price is a "moment" in this
>scientific project.
>I also think this is essentially Marx's method, for what it's worth.
> >>Having said that, I do think there are important sources of
> >>instability in capitalist economies.
> >
> > Problem is not that there are "sources" of instability - but that
> > they are the same as the equilibrating forces, i.e. the un-cordinated
> > - not mutually consistent from the outset - actions of individual firms.
>I am not sure they are the same. For instance, I think that price and
>quantity adjustment by firms is connected to but quite different from
>sources of technical change.
> > I agree that to hold things still might be useful, but we have been
> > waiting for the full story for more than hundred years - so one might
> > ask if not economic modelling should start with modelling real
> > competition, real change of technology - because it has shown itself
> > extremely difficult to modify these models to make them dynamic afterwards.
>I can't speak to the poor progress of economic science, although of
>course the obsession with static, Walrasian equilibrium models is
>largely to blame.
>But I can say that "modeling everything at once" is easy to do --
>especially with computational agent-based models -- but this approach
>has the danger of creating a proxy object that is almost as complex as
>the real world. You don't get insight.
> > The problem between Cap. vol 1 and 3 - the transformation problem has
> > shown itself very resistant - although Farjoun and Machower,
> > your work, the TSSI - points to another and hopefully more fruitful
> > research agenda - but I think Jurriaan is correct in stressing that
> > using static models to model "moving attractor systems" with slow
> > reaction speeds for the eqilibr. processes compared to technological
> > development is a real problem.
>My model is not a static model. There's lots of interesting dynamics
>in there. I do (unapologetically) assume a constant technique, because
>my current (short-term) aim is to formally analyze some outstanding
>conceptual problems in value theory (rather than "model the economy").
> >From my reading of the classical authors they too assumed a constant
>technique; that's part of the meaning of "natural price".
> >From a mathematical perspective, I also know that it is easy to add
>technical change to this kind of cross-dual model. I have already done
>this in simulation. But developing a good understanding of the
>resultant system requires a lot of time and effort. Again, as a
>practical "working scientist", it pays dividends to analyze simpler
>models first.
>Best wishes,
>ope mailing list

ope mailing list
Received on Mon Feb 7 14:35:26 2011

This archive was generated by hypermail 2.1.8 : Mon Feb 28 2011 - 00:00:02 EST