On Tue, 23 Jul 1996, Duncan K Foley wrote:
> > Paul:
> > How would the shadow prices be calculated?
>
> Well, they are implicit in the optimization of a social welfare function
> subject to constraints on the availability of resources.
Shadow prices emerge from, for instance, the solution of the
allocation problem as a linear programming exercise. But Paul and
I have argued that this is not feasible for the economy as a whole.
The complexity is just too high. On the other hand we've argued
that the balancing of a disaggregated plan for a multi-million
product economy (by finding the Leontieff inverse) is computationally
feasible. And we are in effect saying (I think) that the
embodied labour coefficients are a good first approximation to
shadow prices. We have spelled this out, with some reference to
the modes of calculation used in the USSR, in an article in the
Revue Europeene des Sciences Sociales (which is also available on
the Web in postscript of pdf at
gopher://csf.colorado.edu:70/11/econ/authors/Cottrell.Allin
> > In what units would the social priorities be measured in order to
> > comensurate them with the shadow prices?
>
> This is, of course, very abstract and theoretical, but the idea would be
> to measure relevant aspects of the allocation, including average levels of
> consumption, provision for the future, and distribution (a la Marx's
> remarks in his comments on the Gotha program), and establish a social
> ranking among the goals that compete. Then maximizing the social welfare
> function would yield shadow prices on whatever resources one regarded as
> scarce (including human time and energy).
Our suggestion is that consumer goods are marked with their 'value'
(embodied labour-time), and also a (roughly) market-clearing price
expressed in Owen-style labour-tokens (with which people are paid
for their work, at an average rate of one per hour). Then the
plan can be amended according to the algorithm, if P > V, order
more of the good; if P < V order less. If P > V that says that
people are willing to pay, in their own time, more time than it
costs society to produce the thing. When I say the plan is
'amended' I mean that a new target vector of final outputs is
generated, and the required vector of gross outputs is computed.
All this is -- we argue -- computationally feasible. On the
other hand "maximizing a social welfare function" directly is
not. A lot of effort went into the latter in the USSR, and I
think it was basically wasted. It was too "abstract and
theoretical" to be of any practical utility to GOSPLAN.
Allin Cottrell
Department of Economics
Wake Forest University