Home » Uncategorized » Matrix Redux. Start With Consumer Prices and Solve Mises’s Calculation Problem?

Matrix Redux. Start With Consumer Prices and Solve Mises’s Calculation Problem?

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We’ve written quite a few articles explaining Mises’s Calculation Problem, the problem he says any Socialist economy will have that will bring on its downfall.

Recently, we have discussed solving the problem with good old linear algebra. One Mabel suggested we just input all the costs of production in Column A of some gigantic matrix, other stuff in the other columns, and then solve the system of equations the matrix represents, using our sophisticated computers, and lo and behold, the solution will be exactly how much of everything we need to make, using what ingredients. She even linked to a sample matrix that does exactly that.

I explained that the heart of the calculation problem is that we don’t know what to put in Column A.

Devil’s Advocate: Felt pretty smug, didn’t you? Until you got that cryptic comment from Michele which left you scratching your head.

Here’s her comment:

hi Mabel,

just a fast reply

if you do have the explicit preference structure of all the individuals in an economy you can solve the calculation problem with a good matrix. that’s for sure.

but that’s also not the problem

the calculation problem lies in the impossibility to obtain the preference structure of the individuals which is only revealed through the market process.

Smiling Dave: I admit I was mystified. But reading around a bit, I think I know what she’s saying. Allow me to elaborate.

if you do have the explicit preference structure of all the individuals in an economy you can solve the calculation problem with a good matrix. that’s for sure.

The idea here is simple. We don’t know what numbers to put in Column A? Then we will work backwards. Austrian Economics says that costs of production are determined by the profits to be made.

DA: Say what?

SD: Why does steel, say, cost 40 cents a pound? In the old days, people thought it’s because of the amount of labor that went into making it, or some other reason inherent in the properties of steel. But Austrian Economics says it costs forty cents a pound because there is someone out there who has figured out that he can make a profit large enough to keep himself happy if he pays forty cents a pound for that steel, uses it to make steel mixing bowls, and sell the bowls at ten bucks each. His bid for the steel is the highest, and that’s what determines the price of steel.

DA: But his profit depends on what he can charge the customers.

SD: Exactly. That’s why the prices for factors of production depends on the prices of consumer goods, and not vice versa.

DA: So what Michele is saying is that if we know all prices consumers are willing to pay for consumer goods, we can work backwards to figure out costs of production, fill in column A of that matrix Mabel was talking about, and voila! Calculation problem solved.

So that’s what she meant in the first sentence. What did she mean in the second?

Here it is again:

but that’s also not the problem

the calculation problem lies in the impossibility to obtain the preference structure of the individuals which is only revealed through the market process.

DA: So what does that mean?

SD: I think what she’s saying is that there is no way to find out the prices people are willing to pay for consumer goods unless there is a market selling them.

DA: So what’s the problem? In a Socialist economy Mises was talking about, there are stores, there is money, there are consumer goods for sale. The only change from a free market economy is that the govt owns all the factors of production. What part of “the market process” is missing?

SD: Yep, I agree. That’s why I think she missed the boat.

DA: So is the calculation problem solved, at least in theory? I mean, I know that current estimates of how long it would take to solve such a matrix using existing computer power is about a quadrillion years. So it’s practically impossible. But I’m asking about in theory. Is Michele right? Has she solved the calculation problem “for sure”?

SD: I think not. And here we enter deep waters. The thing is, costs of production are not determined by actual market prices. They are determined by the estimate of some entrepreneur as to what market price will be.

In other words, steel is not forty cents a pound because somebody can make a nice profit buying it at forty cents a pound, making steel mixing bowls, and selling them for ten bucks apiece. It is forty cents a pound because somebody thinks that what will happen, and is willing to gamble his fortune on it.

DA: But isn’t that a quibble, really? All the Socialist planner has to do is see what mixing bowls are selling for now, and assume that’s what they will sell for when the next batch of bowls are made.

SD: Let’s begin with a dialog between J. K. Rowling and the Socialist Office of Book Publishing.

JKR: I have this wonderful new book, Harry Potter meets the Vampire. I bet the public will pay $25 a copy for it, just like my other books back in the day.

S. O. of Book P: I don’t like it. My mother in law has written a new book, Comrade Potter Defeats the Imperialist Bourgeoisie, and I think that is what will sell.

SD: You get the idea. It’s the nature of people that they get tired of the same old same old. On the one hand, you cannot keep making more copies of the old Harry Potter books and expect them to sell at the same price forever. On the other hand, the public wants reading material. On the third hand, who decides what new stuff to offer, what price to charge, and based on what criteria?

DA: So there will have to be entries for which the consumer price is unknown.

SD: Yep. Books, music, the latest fashion in clothing, new inventions, new ideas, [assuming the Socialist economy has a provision for that. I mean, imagine of the Socialist got their wish right after Marx wrote his book. Would we not have cars, computers, all the inventions that came after Marx, in a Socialist economy? Sounds pretty horrific already].

DA: But how does a free market know what prices to set for goods that have never been offered before? How does it know whether to publish Harry Potter or Boring Potter?

SD: The free market has something the Socialist economy, by definition, lacks, namely people who are willing to bet their fortunes that they have guessed right about these things.

DA: So you are saying that yes, costs of production are indeed determined by consumer prices, but by future consumer prices, [as estimated by the fellow buying the factors of production], not by present consumer prices. Because he might be planning on making something for which there is no precedent.

SD: Exactly. And once we understand that it’s future prices that determine the prices of factors of production, then it becomes obvious that we cannot know the price of any consumer good tomorrow, not just of unwritten Harry Potter books, but of anything. Who can foresee the future? Consumers are fickle. They change their minds all the time. Just because yesterday they paid ten dollars for the mixing bowl doesn’t mean they will pay ten dollars six months from now. They may decide to spend their money elsewhere. It takes an expert to know these things.

DA: So we cannot start with prices of consumer goods and work backwards, because that’s using actual consumer prices today. But the price of factors of production is determined, not by them, but by imaginary numbers in the mind of some aspiring entrepreneur, as he imagines himself making big bucks.

SD; Exactly

DA: But why not put him in charge?

SD: So already we are throwing away the matrix, and getting back to people making the decisions based on their understanding of the future.

DA: Yes, the matrix is dead. Long live the Planning Board of Experts.

SD: Well that old chestnut, the Planning Board pretending they are real businessmen, has been refuted long ago by Mises in Human Action.

DA: Dave, could you give a summary here?

SD: I’m glad you asked.

The calculation problem is that you do not know what numbers to fill in Column A of your matrix, costs of production.

And you cannot compute Column A from current consumer prices, because costs of production are not determined by them, but by totally unknowable future prices of consumer goods that exist in the imagination of someone thinking about going into business.

In a free market, there are people who can make good guesses what those prices will be. But such people can only exist in a free market. See Human Action Chapter 26, section 5.


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