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The Matrix Solves Mises’s Calculation Problem. Or Does It?

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One lovely young lady named Mabel
Placed a comment on my Calculation Problem Article, saying it’s a fable.
I took no offense,
Did not say, “Get thee hence”,
But laid all my cards on the table.

Mabel claimed the Calculation Problem was solved by 1970, and linked to a matrix that apparently solves it.

I think that matrix is a wonderful tool, not to refute the Calculation Problem, but to give a nice visual of where the problem actually is. That neat little matrix shows exactly where the Calculation Problem exists [no data to fill in the first column] and how it gums up the works in a socialist economy. [No data in first column means no numbers for the matrix to crunch, rendering it useless].

So for all you math whizzes and computer science guys out there, who get things better when they are laid out in neat tables and stuff, here’s the required info:

Here are the links to my humble article, which explains the Calculation Problem. It’s in three parts. Part One. Part Two. Part Three.

Here’s Mabel’s comment in full:


I am prepared to defend the premise that the calculation problem was solved by 1970.

I know that is a challenging premise, so I request that you click over to http://www.sfecon.com and ask yourself: could these arrays of numbers be regenerating themselves if the calculation problem were not solved? The software generating this demonstration is freely available for you to run on your own desktop.

I would like to address the premise that economic calculation is impossible because only free markets can generate the prices needed to guide economic order into the general optimum. All this tells me is that a true science of macroeconomics would present an understanding of how free markets generate such prices – hence macroeconomics is not yet a science. We all knew that.

All the Austrians tell me is they cannot fathom how anyone might map out the complexity behind how markets compute prices, and that this is supposed to be a sufficient proof that no else can possibly penetrate that complexity, ergo: anyone’s demonstration of the ‘swarm intelligence’ creating the ‘information-carrying particles’ of money prices is ipso factor a fraud. Invincible argument, but utterly trite.

As a partisan of the free market, I am not upset by a mathematically determined solution to the calculation problem. On the contrary, I wish to develop that solution into educational software that extolls the virtues of the freest possible markets. We would likely agree that the self-interested disposition of private property is, first and foremost, an aspect of liberty. If liberty is the objective, the we should choose markets even if they were not efficient.

I am afraid the Austrian’s insistence on merely verbal argumentation to the exclusion of objective demonstrata will ultimately be used to discredit liberty along with their harebrained economic commentaries. Anyone care to discuss a separation of these issues?

My reply:

0. Thank you for the link to that little matrix. It helps show exactly what the calculation problem is, once we grasp why that whole matrix is null and void in a socialist economy.

1. The boo-boo is in the very first column of green numbers. That whole first column, all of it, is a blunder, when applied to a socialist economy. In a socialist economy, there are no Expenditures. The State owns all factors of production. They pay no one for them. So where are all those green numbers going to come from, which represent Expenditures on means of production? On the other hand, you can’t say Expenditures are actually zero, because means of production are being used up. There are Expenditures, but no way to calculate what they are. That’s the calculation problem.

Naturally, when that whole first column is filled with question marks, the rest of that beautiful little matrix becomes useless. No data to input means no output, obviously.

2. The humble article did not say the problem was complexity of something or other. Notice that the example it used was not complex at all. There is no mention of “information carrying particles of money”, either. All it had was one factor of production, phosphorescent plastic, and two possible products, skeletons and laptops. And yet, there was an unsolvable calculation problem.

3. I don’t know whether the complexity/information carrying argument is invincible, or utterly trite. I do know that bringing it up in a comment about my humble article, and about Mises’s calculation problem, is like the bride wearing a football helmet at her wedding. Out of place.

4. Do you know why Austrians insist on verbal argumentation? What is your rebuttal of their reasoning?

5. Do you know why they claim objective demonstrata are useless in predictive economics? What is your rebuttal of their reasoning?

6. Have you read America’s Great Depression, by Rothbard?
Have you noticed how full it is of objective demonstrata?
How do you reconcile that book with your presumption that Austrians exclude objective demonstrata?

I’ll give away the secret. In fact I already have, right here: https://smilingdavesblog.wordpress.com/2014/01/31/thoughts-on-ae-and-interpreting-data/

7. Can you please give examples of what you consider harebrained economic commentaries? What is your rebuttal of their reasoning?

8. Liberty and Austrian Economics have been separated on the Internet, with many people waving the liberty flag, but lacking the intellectual capacity, or honesty, or energy, to grasp AE.



  1. Mabel says:

    Hi Dave,

    Compliment taken, and thank you for your response as well.

    My cards on the table: I think the contemporary followers of AE have solidified around positions that prevent the fullest realization of what AE has to offer – which realization would be oh so good for Western Civilization. If you are open to the possibility of coming to that conclusion yourself, then perhaps we have something to learn from each other. If not, no offense; and I will look for allies elsewhere. Your blog, your call.

    0. I think (correct me if I am wrong) that “matrix” suggests CGE modeling to you. If so, your response started off on an incorrect presumption. SFEcon has no linear programming in it. It is an engineering dynamic emulator of the distributed intelligence that generates prices, from which all else about economic adjustment follows. SFEcon’s matrix structure is detailed at their site: from the homepage, click on THEORY; then go down the outline and click on A GENERAL MATRIX STRUCTURE.

    It seems to me that Hayek (1945) subsumed I/O matrices in his specification of a solved calculation problem:

    “The conditions which the solution of this optimum problem must satisfy have been fully worked out and can be stated best in mathematical form: put at their briefest, they are that the marginal rates of substitution between any two commodities or factors must be the same in all their different uses.”

    1. Column 0 is a negative sum on physical asset acquisitions times their respective prices. Assets are acquired in the amounts that they are so as to maximize profits at current prices. There is no specification as to why maximal profits are desired. Self-interest on the part of the assets’ owners works as a motive, as does the diktat of benign economic command. All the mathematical system knows is the motive, not the motivator.

    2. I did not post in response to your “humble article”, but I now see that you use a simple problem to illustrate why the calculation problem is unsolvable. Mabel’s problem with this sort of reasoning is its presumption that your mind will only be changed by a more robust, but also verbal counter-argument. To the contrary: if you say something cannot be done, you are stating a premise in the form of a general negative. That’s fine. But it then obligates YOU to state what you find wrong in an objective demonstration that someone has done what you say cannot be done.

    There are five of these demonstrations written in ordinary MS Excel workbooks staged at the SFEcon site. Click EXEMPLARS from the homepage, and choose a workbook with whatever size I/O structure you wish. These workbooks will allow you to input I/O data of your own choosing. The program will then compute equilibrium prices for you, as well as the shapes of the technical and utility tradeoffs for which your I/O data are optimal. (Note that Hayek subsumed utility functions with his reference to “marginal rates of substitution” in 0 above.) You can then change the shape of a utility function, and watch the model go through all the chaotic states and disequilibrium prices leading up to a new general optimum.

    3. An a priori assertion that these demonstrations must be deficient because sufficient demonstrations are impossible is circular reasoning around a vanishingly small circuit. I find that to be trite. I, for one, hear these assertions a lot (but have, let it said, yet to hear one from you). Sorry about the helmet. Make specific comments about a specific demonstration and I will take it off.

    4. Asking for a “rebuttal” to someone’s “reasoning” is insisting on verbal dispute. I observe economists to me mired in Scholastic arguments that cancel one another out, while refusing to create and compare objective, dynamic, mathematically determined representations of what they hold as true. You cannot, for example, make an objective, dynamic, mathematically determined representation of a general negative.

    5. I make no claims regarding prediction. I do not say the subject irrelevant, but you will have to tell me how it relates to the calculation problem as defined by Hayek above.

    6. I have read Rothbard on the depression and regard it highly. I agree that he makes good use of quantified observations. If we have a disagreement here, it has to do with my narrow use of “objective”. The economy is a complicated, nonlinear, dynamic system. Assertions about the economy that are not objectively realized in mathematically determined, complicated, nonlinear, dynamic systems might be intelligent and useful, but they are not objective in my chosen use of the word.

    7. My favorite example of harebrained Austrianism is asserting that Hayek foreclosed the possibility of economic calculation in 1945, when we are told (e.g. by Bruce Caldwell) that Hayek spent the 47 years left to him trying to solve the calculation problem. Another gem is Lew Rockwell recounting Mises’ assertion that markets should be explicable in rational terms, rather than by “magic” or “some force that is beyond human comprehension”, and then correcting Mises with his counter-assertion that markets are “miracles”.

    The economy is out there; and we observe that, insofar as markets are free, the economy tends to efficiently search-out an optimal resting point. This is clearly systematic behavior. Upon observing such order, the civilized scientist (e.g.: Hayek) accepts the obligation to explain it. Insisting that markets are inscrutable and omnipotent in the face of these counter-indicia fits my definition of harebrained.

    8. I am glad that liberty and Austrian Economics are separated, if we can agree that liberty is the prior consideration.

    I agree that most people lack “the intellectual capacity, or honesty, or energy, to grasp AE”. That being the case, it seems to me wise for Austrians to get out from behind their hedge of esoteric verbiage and present their causality in a dynamic and visual way that people can grasp and would likely credit. Refusing to consider the possibility of economic calculation forecloses this option.


  2. Smiling Dave says:

    0. The thing is, we are talking about two different calculation problems. There’s Mises’s version, and there’s Hayek’s version. Those programs do not solve Mises’s version, which is that the first column, the green inputs, must remain question marks. Whether it solves Hayek’s version I leave to someone else to look into, since I see it as academic. If Mises’s problem remains, I don’t much care if Hayek’s problem is solved or not. But I did see somewhere that given the current state of computing power, and the mass of variables needed to input, it would take several quadrillion years [no exaggeration] to compute the answer. You’ll note that the program you linked to uses 5 variables, not five million or five hundred million.

    1. So verbal arguments are old fashioned Scholasticism, hey? That’s idle name calling, meaning carries no weight with me. I kind of see it as putting on voluntary blinders to insist on number crunching as the only possible way to get anywhere. Need we go further than Einstein, who used thought experiments [=verbal arguments] to do what he did in physics.

    You may know that Mises claims to have proven that number crunching is not the right tool for economics, because of inherent features of what is being studied, mainly people with free will who don’t obey formulas, but do what they please. So we enter deep waters here when you insist on numbers only, when I think you chose the most flawed method possible to work with, rejecting what I consider the only possible tool to work with, good old logical reasoning.

    I’m not sure if you realize it, but mathematics itself is verbal arguments, succinctly stated. There was a time [early twentieth century] when people thought there was some magic to numbers and symbolic logic, that it is a magical machinery that obviates the necessity for verbal arguments. Godel shot that one to pieces, and the picture accepted by the mathematical community world wide nowadays is that all of mathematics takes place within verbal argumentation. A math proof, it is understood today, is a mathematician convincing his peers of something, with verbal arguments. Of course, due to the intricacy of the topic discussed, a lot of shorthand has to be used [Imagine verbally stating Pythagoras’s theorem every single time, instead of A squared plus B squared equals C squared]. But there is no inherent magic in formulas and equations. They are tools used to present and clarify a verbal argument, because, humans that we are, that’s all we have. Maybe Martians have other ways of proving things. Humans don’t.

    Economics, however, is much more primitive than math or physics. The truths known to date are more readily understood verbally than as equations. As for all the equations the mainstream uses, they are fallacious, as they assume people obey some formula, which is of course nonsensical. The more insightful mainstream economists have noticed this, and reject 95% of all published economics, all the formula stuff, as nonsense. Deirdre McCloskey writes about this.

    2. The specific comment you requested is how do you know, in a socialist economy, what numbers to put into that first column, Expenditures? The State owns all means of production. Thus it doesn’t expend any money when it makes something, because it need buy nothing, because it already owns it. What price will you give the things it uses to produce something, when they are not for sale anywhere, thus have no market price?

    3. Could you kindly provide the link to Lew Rockwell’s statement?

    4. I’m very pleased that we agree on so much, even though there is a huge gap still.

    5. My humble blog tries to present AE in dynamic and visual language, understandable to all. Not everyone has the gift. Some can actually do economics, others can present it in an interesting, easy to understand way. I invite you to look around the place and see what you think.

    6. BTW, a professional mathematician might very well argue against that software program by saying something like “That first column cannot be filled in, it can only be question marks.” I’ve heard them saying similar things. You may remember how Bertrand Russell refuted decades of Frege’s work, full of formulas and symbols, with a one paragraph verbal argument. [Consider the set of all sets that are not elements of themselves. Etc.]


  3. […] her comment on my previous article, [which is comments on a previous article, if you want to be thorough], hot off the […]


  4. Mabel says:

    You are right in that we fundamentally disagree the uses of mathematics and language. Your ‘dynamic and visual language’ is a non-sequitur to me: language is neither dynamic nor visual; it is abstract and therefore does not exist in the dimensions of physical reality. It has its uses, but it is never definitive. Are not the bright people who scoff at Austrian causation equally sure of their arguments?

    I hold that AE is special insofar as it can express economic adjustment as a video game. If you are willing to consider these games as a way to move the economic discussion in AE’s direction, then perhaps we can accomplish something together. If that is the case, I am confident that some of your other points can be satisfactorily addressed. If not, this is where we part company. My purpose is to break out of the realms of dispute. If you are content in staying there, that is your choice.

    Anyway, here is your link to the Rockwell quote. LR sent me his source, but I no longer have it.


  5. Smiling Dave says:

    Thank you, Mabel.


  6. Michele says:

    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.


  7. Smiling Dave says:

    Not sure this is right. I admit I’m unclear about both your points.
    Could you kindly provide some links that talk about this, or elaborate a bit yourself?


  8. […] 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. […]


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