[OPE-L] how much information is there in value

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Mon Feb 21 2005 - 18:21:19 EST

A question about the information in prices

I have a question about how much information in a price
is value and how much is noise generated by market disequilibria.

Start out with Farjoun and Machovers Psi variable. This is 
a random variable defined as the price of a randomly selected
hours worth of embodied labour. They measure the price not
in terms of what has more recently been called the Melt
but in terms of the hourly wage. 

Thus psi = price in hourly wages/ hours embodied labour 
since they expect s/v = 100% they argue that psi will
be normally distributed with a mean of 2. They argue
that it is very unlikely that the price will be too low
to cover all of the labour costs, thus assume that if
e= s/v , then the standard deviation of psi must be
no more than e/3 as otherwise too many firms
will be making a loss. When one translates the results
that Allin and I have published fo the the UK PSI
into F&Ms formulation one finds that, adjusting
for the difference in e between the UK and their
assumed 100%, the observed standard deviation of
psi of approx 0.15 almost exactly fits their predictions
for the measured rate of exploitation we got for 1984 of

I then ask the question, how much information is
encoded in the random variable PSI. If we perform
numerical integration of the Shannon entropy formula
on a normal distribution with sigma = 0.15 we get
and entropy of just under 6 bits, for the F&M case
we would have an entropy of 7. 

If the deviation of price from value represents around
6 to 7 bits of information. The next question is how
much information is there in a randomly selected price.

Generally prices are given to about 3 figures, but they
can range from around 10pence to 1billion pounds, say
for a large ship. This is about 10 orders of magnitude.
Thus you might need 3 digits to encode a price and one
digit to give the order of magnitude, since a digit encodes
3.3 bits roughly, this means that the entropy of the
original prices is unlikely to exceed 14 bits. This
implies that the value of a commodity probably represents
something between 6 and 8 bits of an actual price.

My question is if anyone can think of a realistic
functional form for the statistical distribution
of prices, if one had that one could in principle
integrate the Shannon formula

H = - p Log p

over the pdf of prices and work out the likely 
entropy of prices slightly more accurately than
the rough and ready estimate of <14 bits.

I would suspect that some sort of gamma distribution
may do it, but one has to take into account 
what sort of weighting to use. Should the pdf
of prices be value weighted, so that a purchase
of an aircraft carrier embodying perhaps 100 million hours
of labour counts for more than a packet of crisps embodying
perhaps 4 mins labour.

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