Steve Reads

At some point in my education, I will need to find the collection of papers that encapsulated the socialist calculation debate between Oscar Lange and Friedrich von Hayek. The story, as I understand it, is that Lange believed a sufficiently large computer could rationally allocate resources just as well as the market could.

Somewhere along the line, someone noted that this computer would have to be massive indeed. Assume there are markets for n products (wheat, bread, rubber, tires, etc., each in manifold variations). The problem of assigning prices to all n commodities seems at least as difficult as solving a linear-programming problem with an n-by-n matrix: in a perfectly competitive market, the price of each commodity would be driven down to its marginal cost, which means that the price of the nth commodity could be written like so:

p_n = p₁q₁ + p₂q₂ + … + p_nq_n-1

where p_i is the per-unit price of the ith commodity and q_i is the amount of the ith commodity that goes into the nth commodity. To solve for the prices of all n quantities simultaneously, you would need to solve n such equations at once (one for commodity 1, one for commodity 2, etc.).

Stopping here for a moment: I’m curious how far people took this challenge in practice. For one thing, this matrix would be extremely sparse: most commodities don’t take most other commodities as ingredients. Wheat is not a constituent part of an automobile, for instance. Even assuming that the average commodity has 100 parts — which seems implausibly large — you still have a matrix with millions of rows, most of whose columns are zeroes.

In short, then, the mythical socialist computer would need to solve linear-programming problems that were well beyond the capacities of computers at the time, and may well be beyond today’s computers. (What size linear program can be solved very quickly on a modern computer? If we want the computer to set prices as quickly as a financial market does, the time scale would have to be as small as the smallest scale on which prices typically change.)

In any case, I need to read more.

The question I came here with, though, is about market failures. If we envision a market as a distributed computer, whose many distributed parallel processors are all solving subproblems of the overall price-setting problem, then we have to ask how that distributed computer can screw up. In particular: under what conditions does the computer optimize all its subproblems, yet fail to optimize the overall problem? This is what happens in any number of economic paradoxes — the paradox of thrift, for instance. If we all do what we think is in our best interest, sock away money in the bank and eat only beans and rice, then we all suffer: no money is circulating in the economy, our companies have no money to pay us, and we all end up on the bread line. Individually rational behavior leads to globally suboptimal behavior (specifically, a Pareto-inferior allocation).

I guess what I’m asking is some form of a question about dynamic programming, and how far the analogy between computers and economies can reach.

And then very specifically: does anyone know of papers that tackle this sort of analogy? Does it contribute anything to either field that that field didn’t already know?