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[UPDATED] Division of labour and comparative advantage: what linearity hides in economics

by Migeru Sun Nov 13th, 2005 at 12:12:30 PM EST

As a mathematical physicist I am bound to take a peculiar approach to economic issues, so I hope you will forgive me if this diary strikes you as, well, peculiar.

On the other hand, we have had a number of interesting comment threads about free trade and comparative advantage, the nontrivial true result of economic theory. A number of mathematically inclined types around here, including me, can't seem to let an economics discussion go by without taking a swipe at economists for mathematical naïveté or physics envy, and we keep hinting at parallels between economics and our own pet theories. It's about time we stuck our neck out. Maybe we'll get those promised diaries about economics and thermodynamics, economics and dynamical systems, or economics and Darwinian evolution.

So let me sum up the gist of my argument so you can jump directly to the comments after this if you wish. To make things easy to calculate, easy to visualize and easy to reason with, economic models are often formulated in terms of linear equations (if this is twice as big then that will be twice as big, too!). The problem is, to justify linearity one would have to impose a long list of implausible conditions on the economic system at hand. Ceteris paribus does look like a weak excuse. Comparative advantage is indeed a robust result which does not depend on all these extraneous hypotheses, but it is often presented (as it was originally by Ricardo) with the help of a linear model.

Thinking about this linear model I realized that division of labour can be described by a linear model without stretching reality too much, so I start from there. I imagine an economy consisting of just two people producing two goods. A simple linear diagram illustrates why specialization helps, and why it is possible that some tasks won't be carried out by those most capable of carrying them out. The result, though, is that the production line of more than one person is not linear but convex, and this is what makes division of labour possible.

I then look at comparative advantage, which is the generalization of division of labour from two people to two countries. Now, the discussion of division of labour makes it clear that a linear model is no longer adequate to describe the production of either economy, so I give a diagram full of nonlinear production curves.

A feature of both analyses is that, starting from a situation where both people (countries) share work (production) equally across all tasks (goods), a fairly large reassignment of tasks is needed to achieve a modest improvement in efficiency. If we take into account how reluctant people are to change careers, or how long it takes to convert an entire industry to another purpose, it is easy to see that the optimal solutions on paper will usually be implemented at a large human cost, if at all. This gives an explanation, on paper for the widespread resistance to liberalization.


Division of Labour

Alice (A) and Bob (B) work together. They need to perform two tasks, X and Y. They have an egalitarian agreement whereby each tries to spend the same amount of time on each of the two tasks. In the diagram below, the line C represents the possible amounts of X and Y that they can obtain in this way. The dashed line to the point C represents one possible choice.

An alternative arrangement will be a Pareto improvement if it increases the amount of both X and Y that is accomplished. This is impossible staying on the line C. All the points on C are indifferent. The dotted lines from C delimit the directions of Pareto improvements.

A Pareto improvement can be achieved (along the bold line) by having Bob specialize completely in Y and Alice partially in X. The bold arrows represent the necessary adjustments. They are quite drastic even for a modest improvement in overall performance. The direction of the adjustments leading to a Pareto improvement is determined by the slopes of the lines A and B.

The convex broken line D is the "production possibility frontier" of Alice and Bob together. It would only be a straight line if the lines A and B were perfectly parallel.

Comparative Advantage

Here is an analogous diagram illustrating comparative advantage. We now have, say, Australia and Belgium, producing two commodities X and Y. Each country has a convex, nonlinear production curve due to division of labour within it.

The curve C can be obtained by assuming that Australia and Belgium produce the goods X and Y in the same ratio. The curve D, which is Pareto-optimal, has the property that the vertices of the parallelogram on the curves A, B, and D correspond to where all three curves have the same slope. This common slope is the relative price of the goods X and Y assuming a given ratio of production of X to Y, and that the productive resources of Australia and Belgium are fully employed. Comparative advantage is advantage in terms of this relative price. In the linear model the slopes are all independent of what the two economies are doing, and so a lot of the richness of possible behaviours is lost. Does linearity throw the baby out with the bathwater?

Once again the gain in productivity from C to D is much smaller than the necessary adjustments in the employment of resources within Australia and Belgium.

These are the generic features of the diagram. There are a lot of features that are not generic. The way I've drawn the curves, neither country is more efficient than the other across the board, but Australia has a larger aggregate production on account of its larger size. The most efficient producers of X are in Australia, and the most efficient producers of Y are in Belgium. Basically, the linear model I drew above can be fully specified by three numbers, but the convex model for the second diagram has a whole lot more features that affect the answers to questions such as: can free trade between A and B wipe out the entire production of X or Y in one of the two countries? This is determined by the slopes of the curves A and B at the endpoints. The diagram will be qualitatively different if the curves A and B intersect. In that case, if we imagine that the economies of A and B "evolve in time" by sliding continuously on the production curves, there may be a suboptimal equilibrium where A and B are both poised at the crossing point. And many more nongeneric features.

Conclusion

This should come as no surprise, but as soon as the model got a little more realistic it also got a little unwieldly. The linear model can be dissected ad nauseam in all generality, but the convex one cannot, or not so easily. The fact of comparative advantage reduces (mathematically) to the fact that free trade partly combines the smaller economies into a single one. This means that the possible arrangements of the whole economy are more numerous than the arrangements where each subeconomy must satisfy all its own needs. The underlying mathematical fact is that optimizing over a larger set of possibilities improves the optimum.

But this whole analysis is static. We can introduce bastard dynamics by imagining that the economies of A and B are like beads sliding on wires (the production curves) but we are basically unable to study questions of time scales. We also forget that in order for the beads to slide on the wires a large number of resources need to be transferred from one industry to another. In a real economy all these things take time, and we are talking about real people. Also, all the responses are delayed with respect to the signals that cause them, and the responses tend to overshoot. When an economist draws a diagram like this, he is behaving like a Platonic Socialist master planner even if he's modelling a free market: he has access to perfect information about the system and can assume that resources are allocated to their optimal uses as needed. But even this Platonic allusion is misleading: it is the ideal economic model that is a shadow of the real world.

Update [2005-11-15 19:41:3 by Migeru]: By popular demand... here are some equations. And then after that I really stick my neck out and make some outlandish claims about economics based on a drawing on a piece of paper. So don't hit me too hard.

Gold for Soybeans

I wanted to call this "oil for food", but it would have made the argument a little convoluted, as well as requiring me to put money on an oil standard.

There is a lot of information that can be obtained from the production curve of an economy. As I have mentioned above, its slope at any given point is the relative price of the commodities X and Y. Suppose that Y is a foodstuff (say, soybeans), and that X is something the people use as money (say, gold). At any given point of the production the slope of the normal (M) is the (marginal) number of units of gold per unit of soybeans, i.e., the price of food. If we plot the rate of production of Y against the slope M we obtain the supply curve of soybeans:

If you want some equations, suppose the production curve is defined by some equation of the form

U(x,y) = 0

then, the ratio of partial derivatives

M = Uy/Ux

is the ratio of the price of Y to the price of X, that is, the price of Y if X is used as money. Then, the quantity

G = X + (Uy/Ux)Y

is the value of X + Y measured in units of X, that is, the GDP. The value G' is the GDP if you used Y as currency. For those of you Thermodynamics buffs, G as a function G(M) is the Legendre transform of Y(X).

Now I am ready to justify why the production curve of an economy cannot be linear. First of all, the GDP and the price of food in that economy would be fixed and immutable (assuming the economy is fuctioning efficiently). But, worst of all, the supply of food could take any value but its price would be fixed.

Nonconvexity and catastrophes

I really don't want to write any more equations: they're ugly. Besides, if you're a thermodynamics buff you can take what I said earlier about U(x,y) and run with it, and if not it's just Greek to you. Instead I'll draw another couple of pretty pictures.

So, why should the actual production curve of an economy (as opposed to the ideal production possibility frontier) be convex anyway? All it needs to be is Pareto-indifferent, but that only means that as you increase the production of X you must decrease the production of Y. The bold curve below on the left is Pareto-indifferent but not convex. What's wrong with that?

Well, what's wrong is that the portion of the curve below the thin straight line is not convex, and it corresponds to a bizarre situation in which decreasing the price of Y increases the supply (see on the right). This is an unstable situation. The market will never do that. In fact, what will happen is that, as the price M increases, the supply of Y increases slowly and then, at some point, as increasing demand tries to push the price of Y a little higher a huge irreversible rearrangement of productive resources (from X to Y) is triggered, causing a supply glut together with a collapse of the price (along the dashed arrow in the diagram on the right). If the system starts out in the high-supply (of Y), high-price regime and the demand starts to sag, driving the price and supply down, again a point will be reached where a large shock in the economy shifts production from Y to X, with a drop in Y production and a price increase (along the other dashed arrow).

Now, the whole economy is likely to rearrange itself in such a way that the production curve changes. Such a large amount of resources change use so quickly that all bets are off. The system will likely settle somewhere between the thin solid line (the convex envelope of the production curve) and the curved dashed line (the production possibility frontier). This is, I suppose, the creative destruction of Schumpeter.

How can something like this come to pass? Starting from a stable, convex production curve, as time goes by innovation at different rates in different sectors of the economy (and even in different parts of the same sector) causes the production curve to push outwards unevenly, and it may cease to be convex. Now, if the demand does not change much the new instability in the system may not be triggered for a long time. So, the production curve of the economy will naturally develop "kinks" which will be relaxed in more or less catastrophic events. The demand changes triggering these events need not be very large, and the root causes of the catastrophe will not be apparent.

By the way, in the 1970's Catastrophe Theory was popularized by René Thom. The S-shaped curved on the right is called a "Fold Catastrophe". The Thermodynamics buffs will realize this is pretty much analogous to the Van der Waals model of the gas/liquid phase transition in imperfect gases.

To link back to the discussion of free trade, opening an economy to free trade will expose its economic sectors to large changes in price and demand (how large? look at the first two diagrams I drew for this diary above). If the economy is efficient and in a stable "convex" state, nothing much will happen, but if the economy has been closed on itself for a long time, and has had little mobility of labour and capital among its different sectors, its production curve will likely be far from the PPF as well as rather bumpy, and a few of these "catastrophes" will be triggered. The economy will settle down to a more productive and stable state (hopefully), but not without a lot more pain than the first part of this diary hinted at.

Poll
How did it come out?
. Boring 0%
. Much ado about nothing 0%
. I learnt as much by reading this as you learnt by writing it 80%
. Huh? 20%

Votes: 5
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They say the best way to learn something is to teach it. No allowance is made for the damage done to the students.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sun Nov 13th, 2005 at 04:36:38 PM EST
not to worry, what I gave you is not a tip!
You make a lot of very good points. Thanks.


In the long run, we're all dead. John Maynard Keynes
by Jerome a Paris (etg@eurotrib.com) on Mon Nov 14th, 2005 at 06:04:38 AM EST
[ Parent ]
Now I also make a lot of very bold points.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Tue Nov 15th, 2005 at 07:46:44 PM EST
[ Parent ]
 that I am speechless.

And this is not a tip jar indeed.

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sun Nov 13th, 2005 at 04:48:37 PM EST
There is something very familiar - even canonical? - about the second graph.  I'm pretty sure I've seen it before but where? I can't place it.  

Something about loosely coupled systems with intermittent information exchange?  Or inductive resonance?  

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sun Nov 13th, 2005 at 06:55:30 PM EST
Your analysis makes an excellent and (to me, at least) fresh point. Although the (equilibrium) gains from trade in some circumstances will be large compared to the (dynamical) costs of economic restructuring, your analysis clearly shows that in other circumstances small gains can, through changed relative prices, drive enormous dislocations.

The latter circumstance may be very common. Two economies with similar relative prices will gain little from trade (in the limit, a gain of zero), yet as your diagram shows, movement toward equilibrium may nonetheless produce huge dislocations even near the zero-gain limit, albeit with lesser driving forces, hence slower change.

Thank you for deepening my understanding of this issue.

Regarding current dislocations, the Economist recently observed that the entry of China into the world economy is creating large dislocations (with large driving forces) precisely because its entry is changing the relative prices of labor, capital, and energy. Because China has very different relative costs, its entry pushes toward large changes at equilibrium, large gains from trade, and large, hard-driven dislocations.

Considering dislocations more broadly, I see a substantial nonlinearity between the aggregate magnitude of the dislocation and the magnitude of its effects. At least two mechanisms seem clear: First, individuals encounter new modes of suffering as the inputs to suffering increase -- eg, passing the threshold of losing a house. Second, social effects are nonlinear in the number of individuals affected -- eg, if one person in a hundred encounters a disaster, each has 99 others to help, but if all encounter a disaster, each has no one to help, hence the effect is more than 100 times greater.

I expect dislocations resulting from technological change to increase sharply over the next few decades (I base this judgment on my own assessment of specific emerging developments). These technology-driven dislocations will likely be difficult to avoid, for various reasons. From the nonlinearity of effects, one may argue that dislocations from trade will therefore be more costly than they seem.

For the record, I say this as a habitual, reflexive free-trader, and I think that greater support for freer trade is probably, at the margin, a good thing, in part because so much of the opposition to trade is based on false beliefs.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Sun Nov 13th, 2005 at 07:08:30 PM EST
The Economist point is a very interesting one. I'd love to see a diary on that. It seems key to understanding the changes of the next decade.
by Metatone (metatone [a|t] gmail (dot) com) on Wed Nov 16th, 2005 at 05:47:24 AM EST
[ Parent ]
I've kept the article on my to-do list for a while now, as it was really interesting.

Maybe I should focus on this now.

In the long run, we're all dead. John Maynard Keynes

by Jerome a Paris (etg@eurotrib.com) on Thu Nov 17th, 2005 at 04:18:45 AM EST
[ Parent ]
IMNHO, yes, you should...  ;)
by Metatone (metatone [a|t] gmail (dot) com) on Thu Nov 17th, 2005 at 06:23:08 AM EST
[ Parent ]
i'm always impressed by these kind of demonstration, i got HD at my ECON71-500 without understanding how to link Ricardo's theory with our reality ( less and less frontiers) ;-)

i refuse the international competition, i'm doing real estate : i do not want to be screwed.

by fredouil (fredouil@gmailgmailgmail.com) on Mon Nov 14th, 2005 at 02:31:01 AM EST
You should write a mathematical model to this.  I enjoyed it.

Be nice to America. Or we'll bring democracy to your country.
by Drew J Jones (pedobear@pennstatefootball.com) on Mon Nov 14th, 2005 at 12:00:12 PM EST
But this was a mathematical model already. Can you be a little more specific?

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 01:43:07 PM EST
[ Parent ]
Where are the equations, eh? Can't be mathematical unless it has funny symbols everywhere.

Only physicists think they can draw some lines and call it a mathematical model.

by Colman (colman at eurotrib.com) on Mon Nov 14th, 2005 at 02:58:10 PM EST
[ Parent ]
Yes, Colman knows what I mean -- funny symbols and all.

As in
U = U(x,y),

and all the functions that follow.

Be nice to America. Or we'll bring democracy to your country.

by Drew J Jones (pedobear@pennstatefootball.com) on Mon Nov 14th, 2005 at 03:03:22 PM EST
[ Parent ]
You actually want me to write a publishable paper about this stuff?

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 03:51:52 PM EST
[ Parent ]
Hey, Drew, is it good enough for you now?

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Thu Nov 17th, 2005 at 02:25:52 AM EST
[ Parent ]
Grief, I (at least) was joking, but the new stuff is great. I'll have to go think about it quite hard though.
by Colman (colman at eurotrib.com) on Thu Nov 17th, 2005 at 09:10:57 AM EST
[ Parent ]
To borrow from another diary, you guys think Jerome and I are joking, but we're dead serious :-)

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Thu Nov 17th, 2005 at 09:13:58 AM EST
[ Parent ]
Be nice to the physicists, though.  Physics majors usually perform very well in graduate-level economics.

Be nice to America. Or we'll bring democracy to your country.
by Drew J Jones (pedobear@pennstatefootball.com) on Mon Nov 14th, 2005 at 03:04:23 PM EST
[ Parent ]
Yep, that's what's wrong with graduate economics courses.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 03:52:20 PM EST
[ Parent ]
I guess I am a synthetic geometer at heart.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 03:50:37 PM EST
[ Parent ]
The problem with macro-economics is that it fails the most basic criteria as a science - testability.

So, one makes a model and predicts the future based upon it. Whatever the results someone will say the model failed to take X into account if the results are not as predicted.

Another way to test a model is to make a prediction using past data and see if things developed as the model indicated. The problem with this is that with so many variables in both the data and the model it is possible to fit almost any graph. Just use a polynomial of the right order and you can fit any curve over a limited range.

Perhaps we should compare economic models to the epicycle model of the solar system. Every time a discrepancy was found they just added another cycle. They were just doing a type of Fourier analysis where the functions were circles. Any orthogonal set would have worked as well.

If the point was that economic models are too simple, this is of course true. The problem is that even if they were accurate the policy makers would still ignore the results. Much policy is driven by ideology not data.

Is there anything that can be done to make economic policy socially responsive and sustainable? I don't know, but so far the critics are not having much impact.


Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Mon Nov 14th, 2005 at 03:54:11 PM EST
I don't know what the point of the diary should be. You see a tremendous but trite point in it. Technopolitical earlier thought the point was something excellent and fresh which I am not sure is what I intended. I suppose I just wanted to wrap up all my earlier comments on free trade into one diary.

To address the points you make in your comment, I have to start by disagreeing that macroeconomics cannot is not a science. I think it is the only part of social sciences which has any hope of calling itself a science. The fact that it has been hijacked by ideologues is unfortunate, but tangential.

Microeconomics is almost a branch of psychology, because it is fundamentally about behaviour. Consumer choice, (un)bounded rationality, (im)perfect information, game theory... A friend of mine was  writing her Economics dissertation on keeping up with the Joneses!

Macroeconomics, on the other hand, is like thermodynamics. It deals with economic systems so large that the specific details of the economic behaviour of individuals are irrelevant. Macroeconomics shares a lot with non-equilibrium thermodynamics and population ecology. So, it really should be possible to elucidate a few simple but general laws of macroeconomics.  

I have many problems with mathematical economics, but the main one is the concept of the utility function. Pareto demolished utility, but people keep reviving it because they can't get their head around multiple, competing criteria of goodness. The only people who seem to be able to live with Pareto are decision-theoretic statisticians.

Regarding your comparison of economic models to Ptolemaic astronomy, the great Richard Feynman (again) wrote that the difference between fundamental laws and effective laws is that the more you study fundamental laws the simpler they get (simplicity does not exclude mathematical sophistication), but the more you study effective laws the more complex they get. Economic laws are not fundamental laws, so the more you study them the more complex they should get. There's nothing wrong with that.

But I am beginning to ramble, so I'd better stop.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 05:03:42 PM EST
[ Parent ]
I think your two observations:

Microeconomics is almost a branch of psychology, because it is fundamentally about behaviour

and:

Macroeconomics, on the other hand, is like thermodynamics. It deals with economic systems so large that the specific details of the economic behaviour of individuals are irrelevant

Are pertinent.  I think your observation that microeconomics is almost a psychology is exactly right.  However, I strongly disagree with your conclusion about macroeconomics, even though I believe your supporting statements about individual behavior being irrelevant, etc., to be correct.

I think with macroeconomics, what we're witnessing is group psychology and behavior.  In these fields, individual behavior and predictions are next to impossible while large groups tend to act predictably.  Thus, it is tempting to think of it as a science which can be mathematically explained.

But that's very wrong.  The seeming stability of macroeconomics is explained by group behavior and things like disbursal of responsibility which make larger groups more stable than smaller ones.

The key difference is that the laws of thermodynamics will still exist even if everyone in the world stops believing in them.  The same cannot be said of the economy.  You're correct that individual behavior has little effect, but group behavior does.

Maybe we can eventually make language a complete impediment to understanding. -Hobbes

by Izzy (izzy at eurotrib dot com) on Mon Nov 14th, 2005 at 06:38:02 PM EST
[ Parent ]
Hmmm, psychohistory all over again.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 06:43:34 PM EST
[ Parent ]
Exactly!  ;-)

Maybe we can eventually make language a complete impediment to understanding. -Hobbes
by Izzy (izzy at eurotrib dot com) on Mon Nov 14th, 2005 at 06:50:28 PM EST
[ Parent ]
Intelligible does not mean predictable. I think I may eventually have to write a diary about this, but in the meantime I'll just drop a name, Stuart Kauffman, and suggest the last few chapters of his book At Home In the Universe.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 07:09:51 PM EST
[ Parent ]
Regarding utility, psychology and experimental economics do indeed show that human behavior is incompatible with models that assume utility maximization. If an individual's preferences were fully ordered, however, then there would exist one or more utility functions that yield that same order, hence those preferences could be described by a utility function. (And full ordering is compatible with multiple, competing criteria of goodness.)

There is an evolutionary reason to expect that behavior will, at least, not reflect cyclic preferences. If preferences run A > B > C > A, then no utility function can be found -- but a game player with these cyclic preferences can be exploited: trade B for C plus a side-payment, then A for B, then C for A. Repeat, and extract value from the cyclic player for free. The exploitability of cyclic preferences drives evolution (genetic and cultural) toward eliminating them.

(On the other hand, transaction costs and refusal to play certain games should be enough to protect some cyclic preferences from exploitation, which reduces the consequence of this result.)

The above description of classes of preference structures will, however, seem to be more-or-less complete only if one falls into the fallacy of treating "fully ordered" and "unordered" as the only sorts of order. This of course neglects partial orders: for example, models based on Pareto optimality. The preference aspect of partially ordered preferences can be described by many utility functions, but their indifferences (or non-preferences) cannot be so described. Because partial orders lack cycles, they are immune to exploitation of the sort described above, yet they are not strong enough to support some arguments that go through in the case of full orders. Utility functions are just too strong.

Utility functions for groups are of course quite problematic and strongly motivate the use of Pareto orderings. Schelling argues that an "individual" mind is in fact divided in ways that make it more like a group, which motivates his application of game theory to purely personal choices and may explain some of the deviation of human behavior from utility-based models.

Saunders Mac Lane observes (and I agree) that neglect of the concept of partial orders is a major source of erroreous thinking in the social sciences, even beyond mathematical economics.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Mon Nov 14th, 2005 at 06:50:11 PM EST
[ Parent ]
The Saunders Mac Lane?

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 07:01:13 PM EST
[ Parent ]
Is there another? I count him as my favorite mathematician (and his writings gave me a much better appreciation of synthetic geometry).

I never met him, though I did have an opportunity to converse with Feynman about some matters regarding physics, future technology, and policy.

Words and ideas I offer here may be used freely and without attribution.

by technopolitical on Tue Nov 15th, 2005 at 02:06:20 AM EST
[ Parent ]
You could tell us what Feynman said, you lucky dog.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Thu Nov 17th, 2005 at 02:40:02 PM EST
[ Parent ]
I am proud to say that I wrote a PhD in economics without a single equation in it (there are some game theory 2x2 result boxes). I also attribute this to my earlier background in math and physics.

In the long run, we're all dead. John Maynard Keynes
by Jerome a Paris (etg@eurotrib.com) on Mon Nov 14th, 2005 at 04:09:19 PM EST
Proud you should be.

The great Richard Feynman thought that the basic conceptual issues of quantum mechanics could be illustrated on a system with two degrees of freedom. But most others confuse quantum mechanics with partial differential equations.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 04:37:47 PM EST
[ Parent ]
...path integrals, path integrals. I want path integrals in your model!!! Now!

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Mon Nov 14th, 2005 at 04:51:43 PM EST
[ Parent ]
Writing a path integral is easy, the hard part is getting anything meaningful out of it.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 05:07:57 PM EST
[ Parent ]
you can always make a t-shirt and look smart :)

Excellent points on the diary, even without them.

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Tue Nov 15th, 2005 at 03:53:43 AM EST
[ Parent ]
How about taking my second diagram above with the slogan "Liberalize this!".

Well, not such a good idea, is it? I should keep my day job.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Tue Nov 15th, 2005 at 05:19:44 AM EST
[ Parent ]
Path integrals are so "last century."

And nothing but nothing is going to make me learn topology!  I am all grown up and you can't make me!  ;-)

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Tue Nov 15th, 2005 at 11:41:22 AM EST
[ Parent ]
But topology is sooo pretty.
by Colman (colman at eurotrib.com) on Tue Nov 15th, 2005 at 01:16:53 PM EST
[ Parent ]
Fear not, I am preparing an [UPDATE] including catastrophes à la Thom.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Tue Nov 15th, 2005 at 01:44:34 PM EST
[ Parent ]
Feynman's autobiography is one of the first I ever read, and I found his life fascinating. I remember learning of his death in high school (it was in 1986 or 87) and being really sad for the first time upon learning of the death of a total stranger - if a somewhat famous one.

In the long run, we're all dead. John Maynard Keynes
by Jerome a Paris (etg@eurotrib.com) on Mon Nov 14th, 2005 at 05:09:51 PM EST
[ Parent ]
1988, actually. I was only introduced to Feynman after his death. Oh, the frustration of knowing that even if I managed to make it to CalTech it would have been too late!

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Mon Nov 14th, 2005 at 05:49:48 PM EST
[ Parent ]
Well I wrote a Ph.D. thesis in physics without any economics in it (wink).

I did attend a Feynman (no relation) lecture once and he was just as captivating in person as he sounds in print. The ability to see the forest for the trees was his strong point. Hence the invention of Feynman diagrams. A way to see the big picture without any equations.

As to economics and psychology, I would think that micro-economics and human behavior go together. Lots of real experiments are done on human behavior to help explain economic choices. These can then be applied to new situations with reasonable success. But trying to direct an economy by means of theories doesn't seem to work as well.

Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Mon Nov 14th, 2005 at 07:21:44 PM EST
[ Parent ]
Is it possible for this diary to get moved back to the head of the 'Diaries' section or even to the Recommended Diaries' section?

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre
by ATinNM on Tue Nov 15th, 2005 at 08:49:26 PM EST
(De)-front-paging a diary changes the datestamp, I think.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Wed Nov 16th, 2005 at 02:20:29 AM EST
[ Parent ]
speechless.

 I am sorry  I am not going to write any diary about the first or second law of thermodynamcis after that.
I will be humiliated. No way.

Wonderful diary and  update...

The first serious note of the day: I really wanted to say that to you. Have you thought to write this down in a paper format and sent it to a economical journal. Seriously, seriously. Today I read in The Economists that free trade is something all the economists in the world think is just wonderful. Trying to publish this stuff will give us a lot of information about the peer review process.
Even there is a slight chance you will find someone who understands it. And it is certainly worth publishing there.

I am not joking. Just an idea OK. Do not jump on me if you do not like it.

A pleasure


I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Wed Nov 16th, 2005 at 01:35:29 PM EST
I can try, but I think there must be a textbook somewhere that discusses this kind of stuff. I mean, the least you expect people would to with a PPF is take its derivative.

This is not publishable because

  1. it can't be new, and if it is it challenges the conventional wisdom
  2. I don't have any references to the literature
  3. I am not in academia
  4. I come from outside the field


A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Wed Nov 16th, 2005 at 05:52:48 PM EST
[ Parent ]
There is this, for instance.

Maybe what I am doing that is new is to consider the difference between the actual production curve and the optimal production possibility frontier.

The PPF is platonic and exists only in the mind of each economist's inner Socialist Master Planner.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Thu Nov 17th, 2005 at 05:15:46 AM EST
[ Parent ]
I think there must be a textbook somewhere that discusses this kind of stuff.

Not that I am aware of.  Papers and books are being written using Catastrophe and Chaos mathematics but the insights haven't made it to the textbook level.  Catastrophe has the problem of quantification: it is next to impossible to apply data to the variables in the formulae.  Chaos math slams directly into bifurcation if the formulae are kept tractable and if more accurately formalized into unsolvable differential equations, e.g., Weierstrass groups.

See here for a discussion and exposition.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Thu Nov 17th, 2005 at 10:53:32 AM EST
[ Parent ]
I have cheked and look around.

My conclusion is that if you find a godfather there is no doubt you can publish this (Godfather will give you status, reference and fit the paper to the general framing in the field).

Of course, the most difficult thing would be to publish it without godfather. This seems difficult: when all the papers and research are fuzzy in a lot of aspects, how is going someone to decide if your results is pure speculation or well-grounded logic? When there is hardly a strong standard for publishing it seems very difficult to know the answer in advance.

I would say that your present status in the university would allow the paper to peer-review it. You would need to choose the journal with the help of someone around and then look for the references. Success will not be guaranteed...

So I will say the best way is to find a godfather to write the article with. It would be the easiest path. Find someone who is known as trustworthy and good person, he does not need to be a crack. Better if he is not....

Of curse, this is you have time and desire... but it was fun to look for it.. I doubt someone used before the thermodynamic instabilities to analize the dislocation int he economy wiht a model as simple as the one you are considered.

By the way I am still surprised that the idea that consumers make rational choices is accepted. Research has shown with literally thousand of studies that there is no such a thing as rational choice... but this is another topic...

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Fri Nov 18th, 2005 at 06:35:01 AM EST
[ Parent ]
I appreciate your enthusiasm, but you are as much an amateur as I am: we're both physicists. I'd appreciate to have an actual economist provide some context and a critique of what I have written.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sat Nov 19th, 2005 at 07:15:49 PM EST
[ Parent ]
The axiom that "The Economy is Efficient" is a philosophical position rather than a Economics position.

The asymmetry of information flow is easy to demonstrate and persuasive, IMO.  It is a fact the CFO of IBM knows more about the financial position of IBM than I do and the CFO can act upon that information before I do.  Once it is cognized information transmission takes time then some actors have, and seize, the opportunity to profit by their superior knowledge.  

Once "knowledge" as a factor in Economic activity is posited then it can be shown specific macroeconomic activity ('a market') is the epistemic consenus of the various microeconomic agents comprising that market.  And the schema (roughly: 'what is used to decide and how to weight the input data flow') within the agent's epistemic system can only process some of the totality of information presented to an agent as qualified by the cognitive heirarchy their schema uses to process the information.  

Eliding some argument, what we see is the "efficient market" (sic) is the result of the inefficient epistemic consensus of the agents not a fundamental Property of "The Economy."

 

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Thu Nov 17th, 2005 at 11:23:05 AM EST
What Migeru has demonstrated is continuous net postive feedback drives the system into instability and then into a new equilibrium, true of any system: the economy, a transistor, telephone lines ... whatever.

This conclusion has been vigouriously resisted by people intellectually wedded to statistical analytical methodologies and techniques.  Several reasons for this but, in my view, the most important being it eliminates the ability to pontificate all over the place.


She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Thu Nov 17th, 2005 at 11:43:06 AM EST
I think the point is that the way the economy progresses (the way the PPF expands) is through catastrophes of this sort. A well-greased economy has lots of little catastrophes. A rigid one has a few huge ones.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Thu Nov 17th, 2005 at 12:05:47 PM EST
[ Parent ]
Yup.  You can either have little Catastrophes or a great big whumping Catastrophe that is a "Catastrophe."  

I think, but cannot prove, one could use Catastrophe Theory as a qualitative tool for to describe Chaotic bifurcation to a different wing of a Lorenz Butterfly, say.  To actually show this would reguire more math than I care to handle.  :-)

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Thu Nov 17th, 2005 at 01:05:40 PM EST
[ Parent ]


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