Re: [ox-en] Re: What is value?
- From: Paul Cockshott <wpc dcs.gla.ac.uk>
- Date: Fri, 28 Nov 2008 09:42:45 +0000
graham wrote:
Thanks, that makes a lot more sense to me! (three more questions below)
Paul:
They are all the distinct products along one axis and all the
technologies to produce products along the other.
This notation was introduced by von Neumann in the late 20s, but was
also being pioneered by GOSPLAN at the same time
I take it when you say 'technologies' you mean something more like
'means of production' than 'steam power, nuclear power, integrated
circuits, biotechnology' stuck on one axis?
In the literature on this a technology is a particular way of producing
a specific good.
So a specific production process producing an ASUS eee PC would count as
a technology.
It takes as input a whole set of components and a set of labour powers
of different skill levels.
Paul:
Kantorovich's claim is that it can be found by a process of linear
optimisation. Prior to that Remak and Von Neumann has proved
that there is a solution but not come up with an algorithm for it.
There are presumably lots of different things you could optimize for;
I guess you have to fix what you want and optimize for one? eg. from
possible things you might optimize for, like:
- maximum production of consumer goods
- minimum number of hours worked
- minimum energy usage
- minimum physical resources consumed
You are correct there are lots of different things you could optimize for.
There are two distinct approaches to this: the approach of Dorfman which
is predicated on capitalist economic relations, and the
approach of Kantorovich which is predicated on Soviet socialist style
economies.
In Dorfmans case he was concerned with optimising in a market economy,
so he simply translated all the inputs and all the
sales into money at current prices and looked for the profit maximising
solution.
In Kantorovichs case he assumed that the national plan had set targets
for final consumption in particular proportions
this set of proportions defined what he called a 'ray', a straight line
along the path of the vector of outputs nominally
provided for in the plan.
He then tried to find the use of machinery, labour, energy etc that
maximised the final output in this mix.
In Kantorovichs case there is in principle no need for prices or
commodity exchanges, though he himself was
very concerned with deriving what he called Objective Valuations, which
were a set of numbers associated
with each product which would allow decentralised optimsation, so that
if each factory knew these objective
valuations they could use them in a decentralised algorithm to adopt the
production technology which would
be best from the point of view of society as a whole. He had had
extensive experience in various industries :
plywood and timber boarding, railway engine manufacture etc, and had
realised that there was a general
class of problems faced in industrial production : given that many
machine tools have multiple uses, and
given that multiple materials may be used in a process, how do you
decide which is the most efficient
combination of machine tools and materials to use in a given factory?
I have an article, originally drafted as a chapter for an introductory
economics textbook, showing
how Kantorovichs methods can be used to address issues of environmental
constraints as well:
http://www.dcs.gla.ac.uk/~wpc/reports/index.html#econ
It deals with issues like suppose you can produce electricity either by
windmills, or by hydro power, and you
have a particular amount of river valleys and mountain land available
for this. How do you
chose the best combination?
If you build hydro power stations, the problem is that they flood
valleys in which you could
grow food. On the other hand they produce a lot more electricity than
windmills.
- what does it mean to say that 'value is a potential or scalar
field'? (To my non-mathematical ears that sounds like an odd mixture
of physics and mathematical usages of 'field').
A potential associates a real number with every point in some set.
Consider the set to be the set of all bundles of goods. Value
associates a real number to all members of this set.
I'm still not getting this one. This is a single number associated
with each *bundle* of goods? The bundle being say the actual total
annual product of a country? So 'value' (as opposed to 'exchange
value') doesn't measure single commodities, but might measure
(randomly) output of Nigeria versus output of Canada?
Yes in principle you are right.
What value does is enable you to take two arbitrary combinations of
goods and compare them along one dimension.
This is true of any system of valuation, be it in terms of money, labour
time, energy use, or Kantorovich's ODVs.
This enables a relatively autonomous unit of decision to select which
combination of inputs is best in order to
minimise the use of what the valuation system measures.
However because all systems of valuation are simply scalar measures,
whereas the real world in which we live
imposes much more complex vector constraints on us, valuations are a
***degenerate*** representation of
the constraints. They are only locally valid as a guide to optimisation,
and the valuations themselves arise from the
projection of a much more complex structure down onto the space of values.
It is becoming more and more important to realise this as society runs
up against the physical limits set by
the planet on which we live.
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