Mathematics and economics- The accretion argument

Economics Economics Questions
1

Again I’ve been debating and I’ve come across the accretion argument. It goes as follows.

Larger companies always have a competitive advantage over small companies due to economies of scale and a dominant market position. The inevitable result is that large companies become larger, and small ones get swallowed up or forced out of business. In the end the market becomes dominated by a handful of major players and an oligopoly is formed.

In the field of mathematical physics this process is called accretion. It explains how stars and galaxies are formed from interstellar gas (among other things). You could also apply the same mathematical principles to the growth of multinational companies. Unfortunately, unlike stars, multinationals do not generally spontaneously explode like supernovae when they exceed some economic or financial equivalent of the Chandrasekhar limit. There is no natural economic mechanism that reverses the accretion process. That is why economic systems need to be regulated. Therefore Irwin Stelzer is right to demand some government or regulatory intervention in all markets.

I told him that I couldn’t understand how he could draw parallels with the accretion of stars and of companies. I said to him that I think that mathmatics and economics simply don’t combine

He wrote back saying:

I must take issue with your statement that “… mathematics and economics just don’t combine.”

Mathematics is only a consistent (and self-consistent) and compact shorthand for our normal speech. Because it is self-consistent, it forces users to refine their thoughts. This usually also means simplifying them - sometimes drastically.

If users are not conscious of this process, their mathematical models will not be useful - but this is not the fault of the maths!

In principle, mathematics can be combined with economics - or any other discipline, but it will only give results that mean anything if the users make all of their assumptions explicit - and this is sometimes rather difficult.

To which I wrote

Mathmatics cannot simply capture the complexity and reality of human action. Mathmatics can calculate what took place in the past, but not what will take place. This is why I don’t agree with the accretion argument.

To which HE wrote:

Mathematics and physics CAN capture the “complexity” of human action. There is a whole branch of complexity theory devoted to it and it is used to predict the behaviour of communications networks, amongst other things. It has also been used to model the flow of money in the international banking system.

When one looks at entire human populations it is possible to see well defined patterns of behaviour that obey specific laws of operation. People think they have complete free will, but their actions are always influenced by those of their neighbours, their environment and basic rules of competition and cooperation. Even if people’s actions are random, one can still see patterns of behaviour based on the variation of probabilities. The truth is, mathematics is everywhere.

Well this is I have to say, my weak spot. If anyone could please elighten me that would be much appreciated.

2

BUMP - Any idea would be appreciated

3

Larger companies always have a competitive advantage over small companies due to economies of scale and a dominant market position.

This is simply not true since they face principle-agent problems and the closer a firm comes to dominating a market segment and essentially monopolizing the market the possibility of rational economic calculation is diminished (a la Mises critique of socialism)

for further reading. http://mises.org/journals/rae/pdf/R92_1.pdf

4

Thanks a lot for the reply but I was looking for answers more on the mathmatics side. I need more ideas on why Mathmatics and Economics don’t work well.

5

“Mathematics is only a consistent (and self-consistent) and compact shorthand for our normal speech.”

Believe me, if he thinks this is the max role for mathematics, then he’s not on the Keynesian side. And if he is on the Keynesian/aggregative side, then he prescribes a far larger role for mathematics than this.

There is plenty of literature here on the Austrian method:

http://mises.org/esandtam.asp

“Its statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori. They are not subject to verification and falsification on the ground of experience and facts. They are both logically and temporally antecedent to any comprehension of historical facts. They are a necessary requirement of any intellectual grasp of historical events.”

6

“In the field of mathematical physics this process is called accretion. It explains how stars and galaxies are formed from interstellar gas (among other things). You could also apply the same mathematical principles to the growth of multinational companies. Unfortunately, unlike stars, multinationals do not generally spontaneously explode like supernovae when they exceed some economic or financial equivalent of the Chandrasekhar limit. There is no natural economic mechanism that reverses the accretion process. That is why economic systems need to be regulated. Therefore Irwin Stelzer is right to demand some government or regulatory intervention in all markets.”

I have a friend who is very much into “Econophysics”(in fact I used to have an interest in it myself, and though he’s become more free market, I’m trying to get him to read AE), he even produced his project poster on Bose distributions and financial markets. In any case The above is a very colourful description and analogy, but he has not at all demonstrated any of the things he has asserted.

It is true accretion does occur due to gravitational forces and is important in the formation of stars, yet electrostatic repulsion and pauli exclusion in white dwarves also play a huge counterbalancing role in preventing everything from collapsing into unobservable black holes. My point is not to try to elaborate what I think is a flawed analogy. I merely wish to point out that the concept as used in physics is useful because we are well aware of the causal factors producing a tendency one way, and those pushing our system another, and can based on such information form a reliable impression of what the future state and behaviour of our system will be.

Similiarly his argument does make use of praxeologically based arguments, but he has settled to reach his conclusion after making an incomplete analysis. Does he really believe that there are no counterbalancing forces to continued “accretion.” Just reflecting on empirical reality I would have hoped would help him realise that. In any case, ask him if he knows anything about whether larger firms and organisations face problems based on economic calculation, knowledge, incentives management issues, transaction costs and whether he really believes that these play no role in providing limits and causal tendencies for firms to be smaller. Another larger causal factor that needs to be considered is government interventions and regulations, which it seems he has not considered. Regulations, which he seems to be in favour of, produce precisely the results this individual seems to lament, since these raise marginal entry costs for new competitors and startups, favouring larger established businesses that can handle these costs; which is precisely the reason they lobby for regulation.

Finally, ask him if he can account for these cogently using mathematics. He clearly hasn’t in the above quote, but just done shoddy praxeology without knowing it.

"I must take issue with your statement that “… mathematics and economics just don’t combine.”

Mathematics is only a consistent (and self-consistent) and compact shorthand for our normal speech. Because it is self-consistent, it forces users to refine their thoughts. This usually also means simplifying them - sometimes drastically."

I have some sympathy with what he is saying here, if only in sentiment. Mathematics is an extension of logic and reason, and reason is the only tool available to man to gain any systematic grasp of reality, that is certainly true. Yet the way in which we apply logic in analysing the phenomena we are investigating has a dependence on the phenomena themselves, producing the character of the sciences applied in each realm of investigation. It is also true that everything written in mathematics can be written in words, it would just not be pragmatic to do so.

My contention with what he seems to be saying is that I do not believe the reverse to be true. Indeed, back when I was really geeky I even tried it, inventing all these crazy symbols along the way(It’s a shame, I think i was smarter as well as crazier back then). Sorry if that’s not really a response but more of a comment…

7

My advice would be to hand this man a copy of Human Action, but don’t tell him anything about the book like that it “rejects the use of Maths”, etc just that it is one of the fundamental and rigorous treatises on economics. That’s kind of the way I started reading it… and after about 30 pages, I didn’t know what hit me!

8

The accretion argument is a false analogy. Although economies of scale “enable larger firms to produce goods and services at reduced per-unit cost,” there are also diseconomies of scale. In other words, at some point, there are diminishing returns to greater firm size. The key difference between intersteller gas and firms is that gas molecules do not have conflicting goals and incentives, nor must they communicate information to coordinate actions and ends. The problem is not a problem with mathematics per se, but with particular formulae that, while entirely appropriate for describing star and galaxy formation, do not properly describe the relations between firms.

Edit: I didn’t mean to “suggest” my own answer. Not sure how that happened.

9

Thanks for the replys guys, they helped a lot. I will be sure to keep you updated.

10

if concerned with the math side of that argument read beginning human action

11

I know complexity theory pretty well. It’s a pretty big topic for me and other colleagues in grad school. Mathematical modelling of situations that involve human actions are never able to properly predict the outcome of something in reality. The problem is, they are treating a social science (eonomics, sociology or psychology) as a natural science, and not a mathematical or logical topic.

This is very related an takes about an hour to watch. It’s about empiricism vs. rational deductionism. It’s by Hans Herman Hoppe: http://www.youtube.com/user/Nielsio#p/u/14/BojfG6fmYEU

I agree with his “endless bag of excuses” description of why these methods fail at explaining complex systems. I don’t necessarily agree with everything he says, though. Just most of it. :slight_smile:

That, and there are problems which are in NP and not in P. All of these problems require a nondeterministic turing machine equivlalent computer in order to solve any medium to large problem with guaranteed optimality in a time that may be mathematically expressed as a polynomial function of the input. In english: we have no such computer, so these problems aren’t easy to solve optimally. (Pretty much impossible)

So we can approximate near-optimal answers for complex systems, and we may model complex phenomena, but only as models. There is no way to estimate exactly what people will do and what their subjective valuations will be in the future. The problem is, your friend might think optimizing some statistical aggregates might be of utmost importance, but the true economist would know that aggregates mean very little.

There is some reading here about all this stuff: http://nobelprize.org/nobel_prizes/economics/laureates/1974/hayek-lecture.html

And one last thing by Rothbard on the use of math in economics: http://mises.org/daily/3638

If you absorb all of this, you’ll have no problem teaching the guy a thing or two. :wink:

12

I suggested abskebabs responses, I think they are the best response you could give.

13

I know complexity theory pretty well. It’s a pretty big topic for me and other colleagues in grad school. Mathematical modelling of situations that involve human actions are never able to properly predict the outcome of something in reality. The problem is, they are treating a social science (eonomics, sociology or psychology) as a natural science, and not a mathematical or logical topic.

This is very related an takes about an hour to watch. It’s about empiricism vs. rational deductionism. It’s by Hans Herman Hoppe: http://www.youtube.com/user/Nielsio#p/u/14/BojfG6fmYEU

I agree with his “endless bag of excuses” description of why these methods fail at explaining complex systems. I don’t necessarily agree with everything he says, though. Just most of it. :slight_smile:

That, and there are problems which are in NP and not in P. All of these problems require a nondeterministic turing machine equivlalent computer in order to solve any medium to large problem with guaranteed optimality in a time that may be mathematically expressed as a polynomial function of the input. In english: we have no such computer, so these problems aren’t easy to solve optimally. (Pretty much impossible)

So we can approximate near-optimal answers for complex systems, and we may model complex phenomena, but only as models. There is no way to estimate exactly what people will do and what their subjective valuations will be in the future. The problem is, your friend might think optimizing some statistical aggregates might be of utmost importance, but the true economist would know that aggregates mean very little.

There is some reading here about all this stuff: http://nobelprize.org/nobel_prizes/economics/laureates/1974/hayek-lecture.html

And one last thing by Rothbard on the use of math in economics: http://mises.org/daily/3638

If you absorb all of this, you’ll have no problem teaching the guy a thing or two. :wink:

Such a very amazing link!
Thanks you for the post.

Watch The Karate Kid Online Free

14

Even Econ 101 (neoclassical) classes deal with diseconomies of scale. Has he never heard of diseconomies of scale? The second part of this sentence is refuted by history. How many times has a smaller company outcompeted a larger company with more market share. It is hard to believe he has internet access and has never heard of Google.

15

I challenge the idea that economies of scale is a hard fast rule. See barbershops and computer stores, etc.

For those industries where economy of scale is an advantage, the scale does not increase indefinitely. For example, there is an optimal size for any factory, and doubling/tripling output simply means doubling/tripling the number of factories you have. In this way, n competitors with 1 factory is as economically efficient as 1 competitor with n factories.

For those industries where economy of scale is a continuous advantage, competition still exists even if there can be only one provider at any given time. Consider that if MoneyBagz Water Company were charging everyone a 200% markup, I could offer everyone only a 5% markup through a dominant assurance contract or contingency fee scheme. If there’s money to be made, someone will work something out :slight_smile:

In short, to believe in the free market is to believe in the creativity and perseverance of the human mind. Thus far, we have gone from sticks and stones to instant global communication in a few thousand years. Want to give it a couple more? :slight_smile:

16

  1. I’m glad somebody mentioned diseconomies of scale. I’ve worked for big companies before, and it is very true. For a real world example, think of Southwest and JetBlue eating everybody else’s lunch until they finally accrued some legacy costs and inefficiencies of their own.

  2. Mathematics and economics - I’m an engineer who has taken one too many advanced math courses. As ridiculously complex as the math became, we were still modelling only simple shapes (cylindrical rods, square tubes, I-beams), making many simplifying assumptions (neglect thermal expansion, neglect friction) and adding huge safety factors (3 or more). In the real world we either over-design, or make as many prototypes as possible to test by trial and error. Now, subsitute human behaviour for a physical system, and your mathematical models get even more inadequate.

17

You can fit a curve to anything. Any set of data, no matter how random. The coefficients on the curve may or may not have any corresponding real variables. The model has no predictive power if it does not correspond to reality.

In engineering, we do not blindly fit curves to data. Instead, we start from basic physical and termodynamic equations and try to work our way to coming up with a model that will fit the curve when real world variables are selected as inputs.

Physical variables are numeric. Human variables are not…

18

In engineering, we do not blindly fit curves to data. Instead, we start from basic physical and termodynamic equations and try to work our way to coming up with a model that will fit the curve when real world variables are selected as inputs.

And when that does not work out, we just pick two data points to obtain a perfect linear relationship!

19

I love this quote from Mises (Prices chapter in HA):

If one says that prices tend toward a point at which total demand is equal to total supply, one resorts to another mode of expressing the same concatenation of phenomena. Demand and supply are the outcome of the conduct of those buying and selling. If, other things being equal, supply increases, prices must drop. At the previous price all those ready to pay this price could buy the quantity they wanted to buy. If the supply increases, they must buy larger quantities or other people who did not buy before must become interested in buying. This can only be attained at a lower price.

It is possible to visualize this interaction by drawing two curves, the demand curve and the supply curve, whose intersection shows the price. It
is no less possible to express it in mathematical symbols. But it is necessary to comprehend that such pictorial or mathematical modes of representation do not affect the essence of our interpretation and that they do not add a whit to our insight. Furthermore it is important to realize that we do not have any knowledge or experience concerning the shape of such curves. Always, what we know is only market prices—that is, not the curves but only a point which we interpret as the intersection of two hypothetical curves. The drawing of such curves may prove expedient in visualizing the problems for undergraduates. For the real tasks of catallactics they are mere byplay.

20

Also, you can’t make grand economic predictions without changing the outcome. If I predict a market crash will come 6 months from now, I will sell all my shares right before then. If I tell anyone else, they will do the same. This will bring about the market crash prematurely…