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May 2013

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

The socialist calculation debate is an important episode in the history of economic thought in part because it revealed some of the previously underappreciated things that markets accomplish. It did so by supposing the existence of a socialist planning agency that would have to do all of those things instead - a thing that many socialists of course wanted, but that supporters of the free market have also found very useful to examine. It turned out that the planning agency would face a large number of previously unanticipated problems. Many of them now appear 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, if any, might ever be able to improve on them.[1] 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 the history of economic thought 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.[2]

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 a terribly important objection anymore, but it’s necessary to go through it to get to the interesting stuff.

By the early 20th century, economists had shown that in theory, a centrally directed socialist allocation of resources could match that of a market economy that was in a Walrasian general equilibrium.

What’s a Walrasian general equilibrium? The economist Léon Walras had earlier shown mathematically that, under certain not obviously problematic assumptions it was possible for the markets in many different goods to clear simultaneously – that is, a multi-good market could theoretically adjust all of its prices so that supply and demand were in balance for all goods at the same time. Producers could theoretically make the exact amounts needed to fill consumer demand, and consumers who were willing to pay the market price could always get what they wanted. Most importantly, Walras showed that nothing about the simultaneous existence of many different goods in his model would get the way of the process, and the existence money wouldn’t either.[3]

General equilibrium has obvious appeal, and yet real-world economies never seem to reach it. 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.[4] Solving the right system of equations would in theory 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 in part, the math was just too hard. It’ll take forever to solve all those equations.[5]

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.


  1. Do I seem perhaps dangerously open to the prospect of something one day supplanting the market? Well, I am! My commitment is not to markets as an end in themselves, but only as a means to the end of human well-being. The same is true, I think, of basically any other reflective advocate of a market-driven social order.  ↩

    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 actually been doing for us, and thus 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.

  2. Yes, Austrian, and not Chicago. The Chicago school of economics stands condemned in the eyes of 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.  ↩

  3. 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 those calculating socialisms that try to emulate markets in Walrasian equilibrium.  ↩

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

  5. 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.  ↩

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