In 1993 two Marxist economists, Allin Cottrell and W. Paul Cockshott, proposed a problem for calculating the plausibility of calculating the labour values in a planned economy. Their benchmark was the amount of time it would take a computer to calculate an economy of ten million goods, which would require 10^21 multiplication operations. With a multiprocessor of that time it would take 30,000 years to calculate this economy using a simple model like the one they suggested.
However I was wondering how long it would take with a modest example of super-processing from today’s computers. I chose the SETI@Home distributed supercomputing system, which has an average computing capacity of 505 TFLOPS or 505*10^12. So my math went like this:
(10^21)/(505*10^12) = 1980198.01980198 seconds
1980198.01980198/60 = 33003.300330033 minutes
33003.300330033/60 = 550.055005501 hours
550.055005501/24 = 22.918958563 days
22.918958563/7 = 3.274136938 weeks
Using a more sophisticated formula developed by Cottrell and Cockshott (An^1.4 where A is a constant assumed to be 10, n is the number of units, and 1.4 is a modifier to account for the number of components in the units sold) we arrive at this time cost:
6.3*10^10/(505*10^12) = 0.000124752 seconds
Which is clearly not a significant obstruction.
But what about a more realistic measure of units in the economy? I decided to use one of the largest unit sales volume figures I could find, which was Wal-Mart’s annual worldwide sales for 2010 of 7820 million units (3708 million units domestic + 4112 million units international).
Plugging this into the economists’ formula for estimating the number of calculations required we arrive at:
10(7820×10^6)^1.4 = 1.780284679×10¹⁵ calculations
7.238929522×10¹⁴/(505*10^12) = 3.525316196 seconds
Clearly based on this data, labour value calculations are a plausible basis for economic planning from a technological standpoint. If SETI@Home calculating the entire volume of Wal-Mart’s enormous worldwide sales in 2010 would only require 3.5 seconds, the rest of a national, or even international economy could quite easily be accommodated. While the objection is often raised that planned economies are unable to keep track of fluctuations in supply, demand, and within their own supply chains, this problem has already been largely addressed through Wal-Mart’s development of the world’s most sophisticated supply chain management system (Which is described in some detail in Thomas Friedman’s The World is Flat). Clearly we have the technology required for a post-capitalist economy. What is needed is the political will to implement it, and the sophistication to ensure that it is sufficiently democratic.
NOTE: I am not an economist by training, nor am I particularly skilled at math. While these are very simple calculations, there is still the possibility that I made a mistake somewhere. If anyone notices something amiss please let me know.