OPE-L message, Re: [OPE-L] Koopmans versus Kantorovich

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Dear Paul:

I can’t say anything about simplex method, but I should warn you about the efficiency losses in case of maximum utilization of equipment when there are other lines of production highly valued from consumers’ point of view. Kantorovich was right when observing that the majority of firms under Capitalism work at half capacity, but he was wrong when thinking that efficiency is mostly a thing of reaching the full capacity of production.

The relevant issue is the allocation of capacity to lines of production according to the marginal subjective valuation of the output this obtained. And this is not only the case in market economies but when a Planned Economy accepts as a primary input consumers’ preferences, you would be pushed to open several line of production even to obtain differentiated goods of the same basic product. This would impede the Planner to expand a single line of production till saving per unit of investment is the optimum.

As Ludwig von Mises wrote:

“As long as there is a more profitable employment available for the capital required for the expansion of production, it is reasonable for the entrepreneur to abstain from such a further expansion. It is at the same time reasonable from the viewpoint of the consumer […] If the additional capital required for this full capacity production can yield a higher return when used for another kind of production, it would be wasteful –both from he viewpoint of the entrepreneur and from that of the consumer as a totality– to use the plant’s full capacity. This would withdraw capital and labour from other lines of production for the products of which the demand is more intense […] It is the consumer who orders him not to use the “full capacity” of one design up to the limit at which the profit must disappear […] Standardization of products can go as far as the public is ready to buy the cheaper article rather than a more expensive article of another pattern.” Monopoly Prices, The Quarterly Journal of Austrian Economics, vol. 1, nº 2, 1998, pp. 14-15.

Best regards,

Alejandro Agafonow

----- Mensaje original ----
De: Paul Cockshott <clyder@xxxxxxxxxx>
Para: OPE-L@xxxxxxxxxxxxxxxx
Enviado: sábado, 19 de mayo, 2007 14:40:13
Asunto: [OPE-L] Koopmans versus Kantorovich

I have just been re-reading Kantorovich's 1939 paper on mathematical
methods of organising and planning production, and was struck by the
way in which his formulation of linear programming is significantly different
from that in standard western presentations.

Kantorovich himself says:

" I want to emphasize again that the greater part of the problems of which I
shall speak, relating to the organization and planning of production, are con-
nected specifically with the Soviet system of economy and in the majority of
cases do not arise in the economy of a capitalist society. There the choice of
output is determined not by the plan but by the interests and profits of indi-
vidual capitalists. The owner of the enterprise chooses for production those
goods which at a given moment have the highest price, can most easily be sold,
and therefore give the largest profit. The raw material used is not that of
which
there are huge supplies in the country, but that which the entrepreneur can buy
most cheaply. The question of the maximum utilization of equipment is not
raised; in any case, the majority of enterprises work at half capacity."

Recent Russian commentaries on his work make out that this is nothing
but a token bit of marxist ideology to cloak a work that actually is
quite independent of or non marxist. At first sight this would be
reinforced by the fact that 10 years later linear programming or linear
optimisation techniques were developed in the west as well.
But the approach taken by Kantorovich seems significantly different.
Western texts emphasise that the objective function being maximised is
a linear combination of the outputs aX_1+ bX_2+ cX_3
this makes sense if you view a,b,c as prices at which the outputs
X_i will be sold.

Kantorovich on the other hand assumes that the outputs must in
fixed ratios so that x_1 = a m, x_2= b m, x_3 = c m
where m is the scale of production and a,b,c are multipliers

In the western form the combination of outputs is a matter
of indifference since they take commodity production for granted,
and all they are concerned with is maximising money income.
For Kantorovich the proportions of outputs are taken as given
as he takes planned production for granted. Kantorovich optimises
along a ray, but the western version attempts to reach a maximal
hyperplane.

I get the impression that there is some way of translating
Kantorvich's ray formulation into the Planar formulation of Koopmans
and Danzig, but I have not found a source explaining how to do it,
and it looks to me as if a simplex solution would not actually
meet Kantorovich's requirement.

Does anyone know how one utilizes the simplex method to solve
Kantorovich's problem?

Paul Cockshott

www.dcs.gla.ac.uk/~wpc
reality.gn.apc.org

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