[PEN-L:9373] Re: Walras vs. Sraffa

[Gil Skillman <gskillman@xxxxxxxxxxxx>]

Jim writes:

>A long time ago, someone (Gil Skillman, I believe) argued on pen-l that the
>Sraffa system was simply a special case of the Arrow-Debreu general
>equilibrium model.

I confess I made a claim similar to this, but the details of the argument
are important.  Noting that the Sraffian system imposes remarkably stringent
conditions on economic outcomes (i.e. the "law of one price" for all
commodities, including labor power, and equalization of profit rates across
sectors), I argued that such a configuration could only be coherently
conceived as emerging from the sort of mutually consistent optimization
conditions under complete markets and price-taking behavior that are assumed
in the Arrow-Debreu framework.  Thus, although the Sraffian system does not
incorporate such conditions explicitly, they, or something like them, must
be part of any attempt to justify the potential relevance, even on purely
theoretical grounds, of the Sraffian construct.  The equal-price-and
profit-rate conditions aren't guaranteed by "nature", and they surely don't
describe capitalist reality.  So what microeconomic process could
*conceivably* generate them?  And if the answer is "none", why should we
study the Sraffian model?

Two corollaries:

Any valid claim deduced from the Sraffian system could emerge from a
corresponding Arrow-Debreu model configured to yield the particular price
and profit rate conditions of the Sraffian model.

Suppose somehow the Sraffian model were used to criticize an analytical
result of the Arrow-Debreu model, say by deriving a contrary conclusion.
Such a criticism would necessarily beg a central question, since there's no
way of telling whether the contrary result is consistent with the (unstated)
conditions required to ensure that the (highly specialized and empirically
undescriptive) Sraffian assumptions are not mere chimera.

To put it another way, it's not obvious what to make of a proof that horses
can't fly
(purple horses, if you insist) on the basis that unicorns can't fly.

Anyway, from Jim's description Dumenil and Levy's (please excuse the lack of
accent marks) book sounds quite interesting.  It's not in our library so
I'll have to hunt up a copy.  One side comment on Jim's summary below.

 Anybody interested in this issue will want to look at
>Dumenil & Levy THE ECONOMICS OF THE PROFIT RATE, ch. 4. It suggests that
>this "special case" theory is wrong. However, not being an expert on (or an
>advocate of) either system, I can't say that D & L are right or wrong.
>
>They also have a useful passage on formalism, abstract model-building:
>
>"It is true that a model is always based on simplifying assumptions, but
>the construction of the model has the advantage that it requires, at least,
>that assumptions be made explicit. The purpose of a model is not to 'prove'
>a theory or to provide it 'scientific' foundations, but rather to test its
>internal consistency, i.e., to detect obscurities or internal
>contradictions. In addition, models often reveal properties which were not
>obvious initially.
>
>"There is also no denying the fact that modeling is not neutral and,
>actually, was not neutral in the development of economic theory. A model is
>based on a specific set of mathmeatical tools, such as linear equations, or
>dynamic systems. Here, it is obvious that there is a feedback effect from
>mathematics on economic theory. For example, the development of the
>so-called 'method of equilibrium' [that dominates mainstream economics],
>paralleled the progress of mathematics, from linear equations to complex
>fixed-point theorems. It is also clear that the lack of interest in
>dynamics can be partially explained by the comparative difficulty and late
>maturity of the mathematical field of dynamic systems. [I would also
>mention the ideological attractiveness of equilibrium conceptions. -- JD]

Attractiveness to which ideology?  Austrian economists also firmly reject
the notion of equilibrium.  On the other hand, Marx's assessment of
capitalism as an exploitative system would apply even if it were somehow in
equilibrium, understood statically or dynamically.  His assessment of
capitalism as a self-destructive system would obtain if the steady-state
equilibrium involved (near) zero profits.

>"Mathematics are also responsible for a kind of fetishism among economists,
>who may believe that the progress of economic analysis is a function of the
>sophistication of its models, [even though] the simultaneous consideration
>of various simple [non-sophisticated] models ... is often more telling than
>the construction of [such] complicated frameworks."

>I recommend this book. It is very lucid and deals with a lot of interesting
>economic issues.

In solidarity, Gil Skillman