The Socialist Calculation Debate, with Prolegomena to Any Future Metamarkets. Part I: Really Hard Math.

The first in a series on socialist calculation, the work done by the price system, and some things we can already know about any future resource allocation strategies that might supplant the strategy of using markets.

The responses to this post surprised me.

As it turned out, the biggest objection seems to have been that markets don’t do much that couldn’t be accomplished by sufficiently intelligent and fair-minded people allocating resources according to scientific calculation: The price system adds little, if anything, to process of simply sharing ideas. Why, it probably shouldn’t even qualify as a different conceptual layer.[1]

I disagree. I think no matter how virtuous, intelligent, and well-informed the allocators are — and let us not doubt for a second that the very best people always serve in the federal government, incorruptibly and to the best of their abilities — still, the socialist calculation problem remains insoluble.

Not that we haven’t tried. On the contrary, lots of work has been done here. That work illuminates what markets actually accomplish (not always what we thought they did!), what economic science can know about them (not as much as we’d like!), and what institutions might eventually be able to replace them.[2] There are many facets to the socialist calculation debate, and in what follows I’ll talk about only some of the more relevant ones.

One problem in talking about this fascinating episode in economic history is that each of its lines of argument is often conflated with the others, and, at times, an author raising objections to the prospect of socialist calculation will veer from one problem to another with little in the way of transition. I’ve tried hard to sort out the threads as I see them, but it’s very possible that someone more well-read in Austrian economics will come along and disagree.[3]

Anyway, let’s begin looking at objections.

I. The Math Is Too Hard. This is by far the weakest objection to the prospect of socialist calculation. It’s also one that I still seem to find in all kinds of places, and still offered as if it mattered. It doesn’t, and it’s not an important objection anymore, but it’s necessary to go through it to get to the truly interesting stuff.

By the early 20th century, economists had shown that in theory, a socialist allocation of resources could match that of a market economy that was in a Walrasian general equilibrium—provided that the socialist economy’s planners solved a set of simultaneous differential equations, with the number of equations equaling the number of goods in the economy.

What’s a Walrasian general equilibrium? The economist Léon Walras proved mathematically that, under certain not obviously problematic assumptions, in an economy of many different goods, it was possible for the markets in all goods to clear simultaneously — that is, a multi-good market could still theoretically be efficient, with nothing about the simultaneous existence of many goods getting in the way. (Or the existence of money, for that matter.)[4]

That prospect has obvious appeal, and yet real-world economies never seemed to reach Walrasian equilibrium. We can know this for a fact because a Walrasian equilibrium would leave no goods or raw materials wasted — and yet in the real world, both are constantly wasted. Everywhere.

Walras himself emphasized that markets only approximated his theoretical equilibrium through a process he called tâtonnement—literally, groping. And they were therefore not terribly efficient when compared to the mathematical ideal. Which I think is true.

Scientific socialists, in part inspired by Enrico Barone, proposed to do better.[5] Solving the right system of equations would give planners the optimal allocations of all capital and consumption goods, allowing them to reach Walrasian equilibrium directly, even as markets could only grope about in the dark.

In the early twentieth century, theoretical economists — even folks like Lionel Robbins and F.A. Hayek — conceded that all of the above was true. But, they said, the math was just too hard. It’ll take forever to solve all those equations.[6]

But forever is a very long time, and today we have computers that can most certainly crack problems like this one. Even, as some have claimed, for an economy with millions of goods.

In 1993, Allin Cottrell and W. Paul Cockshott examined the calculations needed to very closely approximate market-clearing prices for all goods in the Soviet economy circa 1983. For this economy of around 10 million goods, and using only a commercially available supercomputer of mid-1980s vintage, they determined that market-clearing prices, denominated in hours of unskilled labor, could be roughly arrived at in just 17 minutes.

That’s a pretty impressive result. So impressive, in fact, that one gets the feeling that something else must almost certainly be going on here.

And indeed, something else is going on here, but what it is will have to wait for the next post in the series.

Notes

[1] Those who read me as excusing the tragedy of the commons made a different and less interesting mistake. It is certainly true that actors in a market will mistreat any resource whose ownership is not clearly assigned. But the remedy for that is to assign ownership, and thus to extend rather than contract the market order. Removing ownership assignments — because we fear that the market is to blame — only compounds the problem.

[2] My favorite objection — not really an objection at all — was that I seemed dangerously open to the prospect of something one day supplanting the market. Well, I am! Markets have been great for humanity. But if there’s something better, do let’s find it, shall we?

But only — and this is key — only after we understand what markets have been doing for us, and what pitfalls might await us if we abandon them. Some of these are wholly evitable, I think, and this is a matter that the socialist calculation debate does much to clarify.

My commitment is not to markets as an end in themselves, but only as a means to the end of human welfare. The same is true, if you would so much as bother to ask, of basically any other advocate of a market-driven social order. To be surprised at this is to be, frankly, more than a little condescending.

[3] Yes, Austrian, and not Chicago. The Chicago school of economics stands condemned in the eyes of the Austrians for making many of the same errors that the scientific socialists did. I think the Austrians are basically right, and while Chicago economists have done many interesting and worthwhile things, their claims about what we are capable of knowing about markets sometimes verge on hubristic to me. The reasons for this will become more apparent as the series goes on.

[4] There are many later objections to Walras’ model, including those of John Maynard Keynes. We don’t need to get into them here. It’s enough to say that if Keynes is right, then his work may pose a problem for both laissez-faire markets and for socialisms that try to emulate markets in Walrasian equilibrium.

[5] Marxists of course term themselves scientific socialists, in contrast to the utopians, but Marx did relatively little in the way of describing mathematically how industrial socialism would work. Still, though, this term is almost a necessity for labeling those who did. I can’t think of a better one.

[6] They raised other objections, too. Particularly Hayek, of whom we’ll have much more to say in future posts. Part of what I’m doing here is chunking the story into discrete analytical bits, and this one — sorry — is only about the Really Hard Math.