Central Planning's Computation Problem

0:00In the paper that I'd like to present, I call Central Planning's computation problem, or perhaps more whimsically, Sorry Jacques, computers can't run an economy. My inspiration really comes from four sources. Two of those would be the great Mises and Hayek. The other two would be the much less great Venus project. It's a vision by Jacques Fresco of how we can run an economy without money. I'll give more detail later on. And the fourth being my experiences with MATLAB. It's something of a love-but-mostly-hate relationship that I have with Matlab, which is more or less a glorified calculator that you can use to solve computational problems. The Venus Project's vision for how we should run society, they imagine we have a computer-run, resource-based economy. This is what we should shoot for, they claim, where consumers just enter what they want into terminals they have there in their homes.

0:49systems. Computers then arrange delivery to some local pickup location. If production is necessary, computers arrange that as well. There's no money in the system, there are no profits, and therefore there is no corruption. It's their claim, not mine. Now essentially we'll notice this is really a form of central planning just run by computers. After all, it's perfectly possible that people are going to enter things that they want and will have have conflicting desires, so the computers will have to figure out who gets what. That means we're going to run into the standard problems that central planning runs into. Information problems that Hayek points out, calculation problems that Mises points out. Unfortunately, when you try to tell the Venus Project people that they run into these problems, they have dodges already prepared.

1:35First, against the information problem, they say, well, computers are just so good, they're They're going to track all the information, transfer it instantaneously, no problem at all. For the calculation problem, they say, well, it's easy, we just have experts, our experts decide the best way to produce everything, no problem whatsoever. And naturally we recognize these are dodges, not answers, but it suggested to me that maybe there are other problems that also might show up that might be more convincing that they don't have prepared answers for. So I thought of the computational problem. Some of my background, when I was working on my dissertation, I was using computational models to solve an inventory problem. This involved lots of time with MATLAB. This is a very simplified model. Homogeneous households, homogeneous labor, just labor in the abstract to use a Marxist term, two stages of production, just two types of capital, it's very, very simple compared to a real economy.

2:28The only complications are that when we invest in capital, we're forward-looking, looking, we have different firms hold different levels of inventories, and we have delivery costs for these goods we hold in inventory. Those are the only complications in this model. Yet, despite those being the only complications, it took two weeks for MATLAB to converge on a solution. Maybe there's a time problem here with trying to use computers to solve a problem. And that's after I corrected a small programming error. Actually, I hear the story is circulating about this thing running for months, that's true. That's because I'm not the best programmer in the world. Once I fixed that problem, it still took two weeks. So the lesson being that computers are bad at solving certain types of problems. And it so happens those problems are the kind that show up in the economy all the time.

3:17In this case, it was delivery costs that really made this process extremely slow from the computational standpoint. So the computation problem, just to present it, I'm going to make a number of unreasonable assumptions. I recognize these are unreasonable, so don't rake me over the coals for those. I just want to make computation possible and as easy as possible for the computer. We don't wanna make it too hard, too fast. Let's make it as easy as possible and see what it's gonna take for the computer to solve the problem. At the same time, I want to hold to a small number of touchstones with reality. The end result, though, is going to be the computers are just too slow to run a consumer-oriented economy. My unreasonable assumptions. First, we have a benevolent omniscient computer. Any fan of science fiction knows that this is obviously false.

4:05Any computer that comes close to omniscient is never benevolent. It always turns against humanity. Setting that aside, let's assume the computer is in fact interested in satisfying our preferences and that it does actually know all the available resources. Computers have solved the information problem and want to actually satisfy our preferences. Preferences. I'm going to assume, moving away from science, back toward fiction, that preferences have a cardinal utility function representation. All that really means is I want the computer to actually solve a mathematical equation, so I have to give it an equation to solve. So I'm assuming a cardinal utility functions, specifically a quadratic form just because that makes it as easy as possible for the computer to solve the problem. If we go to anything more complicated, it's going to be slower. So let's make it as easy I also have to assume that interpersonal comparisons of utility are okay. If I have to figure out whether Bob or Jerry is going to get this root beer, I have to be able to know what's the effect on utility for each of these, and be able to compare across them.

5:09I'm also going to assume away from all production. Production is really, really ugly computationally, so we're just going to assume it away. Say we just have the set of goods, the number of different goods, we're just figuring out who gets what and how much. Production also is inherently dynamic. That makes it even worse. We need certain inputs at certain times. That makes it very, very difficult to solve. Just three touchstones with reality. First, heterogeneous preferences. Different people actually want different things. For example, some people have gluten allergies, some people love bread. We want to make sure we get bread to the right people. We also have heterogeneous consumer goods. I care very much whether you have just given me a pair of shoes or a belt. These serve different purposes, so I'll keep those heterogeneous as well.

5:56Finally, I'm going to assume that we're limited to the current supercomputer processing power of the top 500 supercomputers in the world. Now, this may not really be reality. Would they let me use all of the top 500 supercomputers to solve the problem? Probably not, but this is a limitation. We're not going to get any more than that, certainly. My method, I'm not going to go into too much detail, it's not particularly interesting, but basically the computer runs a maximization routine to figure out how to distribute this set of goods. This really boils down to solving a system of linear equations. Now, just as a note, solving systems of linear equations are what computers are good at. Give them anything non-linear, they hate it, they slow down, give it to them in a linear form, and they can actually solve it and do so relatively efficiently.

6:45Relatively efficiently compared to other methods. Now, the number of equations is going to depend on the number of people and the number of goods. Now, how we can interpret these processing times I'm going to talk about here in a couple slides, we can really think of this as when we need to start the computation if we want to solve the problem at a particular point in time. So, I know it's going to take 10 minutes to solve the problem. I want to make sure that I start solving the problem 10 minutes before the problem actually arises so I get the solution at the right point in time. So here we can actually see a parallel. Entrepreneurs have to foresee needs before they arise because you have to have time to produce. So we need to foresee the need before it arises. We also need, apparently here, an entrepreneurial computer that can foresee the need before it arises just so it has time to compute what the solution to the problem is.

7:37Just as an example, a very small problem. Suppose we have a hundred people and a thousand different goods, trying to figure out who gets what. By the top 500 supercomputers, that takes about 11 seconds to solve. That's not too bad, right? We could even wait until we find out what these needs are and what goods are available and people will walk away not too dissatisfied. If I wait 11 seconds in a line at a store, that's pretty good, right? But then when we scale the problem up, the problem is that computation time increases This is very, very quickly as the problem grows in size. So, suppose we have 300 million people, a little bit less than is in the US. Suppose we just have 100 different goods. Now, if you go to the bookstore downstairs, you'll see more than 100 different goods for sale here, so that's assuming way, way less than is actually true.

8:23But keep it simple. Let the computer solve the problem. And how long does it take? Just 9.7 million years. Okay, so let's build a timeline. What does this look like? Well, here we are, 9.7 million years ago, all the way on the left. We start computation. Here in the present, we complete it. In the meantime, about six million years ago, the Himalayas begin to rise. They're no longer the plains of Nepal. They're now the foothills. About two and a half million years ago, the homogenous appears. It takes longer for Homo sapiens to appear. I think that's roughly 50,000 years ago, right? I think we see the problem, right? We need a computer that pre-exists humanity by 20, 200 times, roughly, in order to solve the problem for the U.S. today with far, far fewer goods than actually exist.

9:12That's even ignoring production, once again. Now let's scale it up some more, to a more realistic global problem. After all, the Venus Project, what they really want to do, they want all the globe's resources to be available for what they're doing. They want to serve all of the world's people. So, it's only fair to scale this up to the problem they want to solve. So, suppose 6 billion people, and I know I'm ignoring a billion, but oh well. So, just 6 billion people, 80,000 goods. 80,000 was not arbitrary. That's the number that we track for the consumer price index. So, naturally it's also underestimating. The average grocery store actually has about 40,000 goods in it. So, 80,000 is not too, too bad. 6 billion people, 80,000 goods. How long does it take to solve?

9:57It takes 39.7 quintillion years. If you're like me, you're not clear what a quintillion is. Macroeconomists, we deal with trillions on a regular basis. That's natural. Quintillions are not. It's 39.7 billion billion years. I'm using the top 500 again. So here's our timeline. 39.7 quintillion years ago, we start computation. We finish now. In the meantime, the Big Bang happens. You'll notice it happens on roughly the same pixel as we finish computation. We don't divide pixels enough to actually make those two different pixels in my timeline. We notice a problem.

10:44We need a computer that can pre-exist the Big Bang and survive the Big Bang to give us the result. This is going to be difficult. Now naturally, then we can start throwing in real world complications. I didn't bother doing the math. I was convinced by the 40 quintillion years. But we can think about production. What does this do? Production takes time. That pushes back our computation even further because we want to make sure we finish the problem in time to actually produce the stuff. Although, in terms of production time, it's going to be far less than some of these computation times, I hope. Or we also have a choice of methods. That makes things difficult. And it's largely the point of the calculation problem that Mises points out. We have lots of different ways to produce things. What is the best way? How do we compare it without any kind of common denominator that is provided by prices and money?

11:33We also have the fact that preferences in reality are inescapably ordinal. I don't have these numbers sitting around in my head of, oh, I get this many utils from that thing, that many from that thing. So the fact they're inescapably ordinal preferences, that makes this hard. I can't even get off the ground with the type of computation methods I've used. Now, there are ways around it. These ways are much, much slower though, making the problem even worse. Similarly, the impossibility of interpersonal comparisons of utility. If I can't actually compare how much better off I'm making one person another, that really puts the kibosh on the whole thing. I really can't do this figure out how much to give each person if we don't know how to compare across So again, we could think of ways around this, imagine some random distribution, see if we can improve people's outcomes, but computationally that's much, much worse than what I've done here.

12:27We also have the problem of dispersed information. In reality, information is not all in this omniscient, benevolent computer, it's actually spread out as Hayek pointed out. So just in conclusion, here we ignored the information problem. Set that aside, let all the information be central. Here we ignored production and therefore the calculation problem fell to the wayside. Yet at the same time, we found that limited processing power itself is enough to make large-scale consumer-oriented central planning absolutely impossible. We just cannot do it. Now just kind of a side note, in terms of how, do we just not have powerful enough computers yet? That's a natural question. Computers are much better now than they were 20, 30 years ago. I actually did some looking and there were a couple of physicists, I believe, at Boston University that suggested that there is actually a maximum to how fast computers can compute.

13:25It ends up information can only travel so fast and it has to travel within a processor. So that puts a maximum on it and that's about 10 billion times faster than what we do now. Okay, that's pretty good, but if we look back, our 39.7 billion billion years, okay, so we can divide that by 10 billion, right? We're still looking at 4 billion years in this process, even at the fastest possible, theoretically fastest possible computer that we could possibly have, right? Making it, once again, completely impossible for us to have computers run an economy that actually takes account of the fact that different people have different preferences over goods. Thank you very much.