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Who can make sense of this post by RedHughs on Optimal Control?

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ultraviolet's picture
ultraviolet
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Jan 20 2012 23:23
Who can make sense of this post by RedHughs on Optimal Control?

Can anyone make sense of this? RedHughs, can you clarify?

He's talking about production and allocation in a libertarian-communist / moneyless society. This is something I want to understand better and it seems like he's talking about really important stuff, but even after looking up some of these terms it's still not so clear to me what it all means.

Post link: http://libcom.org/forums/theory/eca-working-group-23032010#comment-369455

RedHughs wrote:
2) The large production processes can have their inputs and outputs balanced by using optimal control theory. Each large-scale work group would spend some time determining the production function of the group's production process and that function's partial derivatives. This would allow the direct calculation of each production process's Lagrange multipliers and thus allow a planning process to determine the optimal distribution of inputs for desired distribution of outputs (or the allocation of resources that was close to optimal as it is mathematically and computationally practical to find). This planning process wouldn't have to be done by a centralized group but could easily be run on PC of each group linked together.
-- It should be noted that this kind of calculation in optimal control theory is sometimes described as simulating the market (with the Lagrangian multipliers refered to as "shadow prices") but in fact such an algorithm is theoretically optimal in all cases whereas a market system is only optimal when actual prices correspond to the lagrangian multipliers/"shadow prices" of an optimal control system. And that is not really a very general case. It only happens the production function corresponds to the Cobb-Douglas function, a relatively special case despite the fact that Cobb-Douglas is touted by econ textbooks (as the Wikipedia link notes, the Cobb-Douglas model doesn't even have consistency between a micro-view and macro-view, quite a weakness for a function that's the foundation of the theory of markets as efficient allocators. The derivation of the Langrange multiplier in the latter Wikipedia Section can be reversed to show my assertion that Cobb-Douglas is essentially the only production function in which cost-prices and Lagrange multipliers are equal and thus any other production function would imply that a price-system is an inherently sub-optimal distribution system).