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Fundamental Equation of Economics

James J. Wayne

posted on 15 November 2014

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Recent experience of the great recession of 2008 has renewed one of the oldest debates in economics: whether economics could ever become a scientific discipline like physics. This paper proves that economics is truly a branch of physics by establishing for the first time a fundamental equation of economics (FEOE), which is similar to many fundamental equations governing other subfields of physics, for example, Maxwell’s Equations for electromagnetism. From recently established physics laws of social science (PLSS), this paper derives a fundamental equation of economics, which is the one mathematic equation that governs all observed economic phenomena. FEOE establishes a common entry point to solve all economic problems without any exception. We show that establishing FEOE clarifies many open questions regarding the foundation of economics. For example, the number one question for all economists ought to be what can be forecasted and what cannot be forecasted in economics. Without FEOE and PLSS, this number one question cannot be answered scientifically within the existing framework of economics. While FEOE re-affirms many existing economic theories, we also have found that many other popular economic theories are not compatible with FEOE, and we conclude that FEOE comes with its own version of microeconomics and macroeconomics. In microeconomics, the framework of laws of supply and demand and market equilibrium, which is traditionally assumed by most economists as the foundation of economics, is replaced by a new model called indeterministic supply demand pricing (ISDP) model. ISDP model is far more precise and universal mathematical abstraction of market reality than the framework of Marshall’s market equilibrium and laws of supply and demand. In macroeconomics, a new macroeconomic model called indeterministic balance sheet plus (IBS+) model can be derived from FEOE. Unlike the popular DSGE and Agent-based Computational Economic (ACE) models, the IBS+ model is universally applicable in any kind of economy, empirically falsifiable, making forecasts with reasonable accuracy, truthful abstraction of reality, capturing macroeconomic dynamics accurately, and most importantly based on a sound theoretical foundation. In conclusion, this paper shows that FEOE provides a solid physics foundation for both theoretical and practical economics. Therefore, after establishing the fundamental equation of economics in this paper, there should be no doubt that economics is simply a branch of quantum physics in parallel with chemistry and optics.  Over last four hundred years, there are many schools of thoughts emerged in economics while there is only one school of thought by Newton-Einstein-Bohr survived the experimental and theoretical scrutiny in physics over the same period. The logic conclusion is that there must be only one school of thought allowed in economics as a subfield of physics.

 

Discussion

Many econophysicists are right: laws of supply and demand are no laws of physics. They are just statistical relationships, which works ONLY something. There is no market equilibrium. Most makets are dynamics and cannot be described by static Marshallian cross. Even worse, there are inventories for most products in a free market-based economy. By defination, the existing of inventory means supply is always greater than demand and the supply curve would never intercept with the deman curve!

Just walk into any auto dealers in the US. The supply is usually 60x more than the daily demand. Yet the auto market works just fine! 

The right physics model for the markey dynamics is the ISDP model. This model always work.

    

The Path Core as economic Schrödinger equation

Comment on James J. Wayne's 'Fundamental Equation of Economics'

 

Your basic idea is, of course, right. However, the true equation is given by:

https://commons.wikimedia.org/wiki/File:AXEC25.png

For details see the working paper: The Synthesis of Economic Law, Evolution, and History

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2500696

Eq. (15) is the Fundamental Equation.

For the Law of Supply and Demand see the working paper: Economics for Economists, eq. (12)

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2517242

Egmont Kakarot-Handtke

Advertising talk, no math.

 

The starting point of an ISDP [Indeterministic Supply Demand Pricing] model is the construction of the future probability distribution functions of supply, demand, and pricing. These are basic and most important aspects of any market analysis.” (p. 21)

 

Okay… but that is the one thing you haven’t done!  After copying and pasting Schrodinger’s Equation on p. 3 and claiming that – with the symbols redefined – it applies to everything (including economics), the next 28 pages include no more mathematics.  The rest of your paper is just advertising talk about how wonderful and amazing this procedure is. 

 

What FEOE [Fundamental Equation of Economics] teaches is that the probabilities can be estimated scientifically and that future probabilities can be manipulated by ones’ actions. Therefore, with FEOE, you actually can have a realistic and scientific sound way to become a millionaire or billionaire. It is all in probabilities. Even better this is all physics!”  (p. 26)

 

It sounds like Mr. Wayne has been reading Douglas Adams.  Recall the improbability drive on the spaceship in The Hitchhiker’s Guide to the Galaxy?

 

Of course, it is easy to say that probabilities can be estimated scientifically.  Let me know when you have actually defined the pdf that you speak so frequently and so fondly of, Mr. Wayne; then I’ll look at your work.

 

On the bright side, your criticism of supply and demand cuts to the quick, though oddly your theory is still about supply and demand, only now with the adjective “indeterministic” to remind us that it does not actually work.

 

Strangely, most standard economy textbooks rarely talk about inventories. Why? It is simply because the existence of inventory almost invalidates the entire framework of laws of supply and demand and market equilibrium.” (p. 19)

 

True that!  The existence of inventories is also why I do not believe in supply and demand.  My theory is about price and stock:

 

Simplified Exposition of Axiomatic Economics

 

And, as you can see, even in the simplified exposition, I have actual equations; not just advertising talk about equations that go unwritten.

 

An ISDP model would simply treat the inventory as a state variable of supply.” (p. 20)

 

This is not the right way to do it.  You’re just putting a band-aid on supply and demand theory, which I reject entirely.  My theory is about the total stock in existence at any given time; the supply (inflow) plays no part whatsoever.

 

(1)I like your comments on inventory. For many business managers,managing inventory is everything.

Yet I checked a few econ textbooks,no discussion on inventory.

(2)Regarding pdf,the 600 trillion dollar derivative markets use them all the time.  In the paper,I mentioned to use pdf and copula to price CDOs. The derivative pricing theory is a few areas in economics that FEOE agrees almost totally.

(3)Regarding math, the paper is the conceptional framework. It is a good thing with few math. 

(4) Regarding supply and demand, the available supply is usually well-defined in a market economy.  For example, in the US auto market, the dealer inventory usually is the available supply. That is just economic reality.  It has nothing to do with any economic theory. I do not understand how could you ignore the reality in your model. 

 

 

 

 

You're conflating supply and stock.  

 

Supply is the number of new cars rolling off the assembly line in some established time unit; say, every week.  Stock does not have a time unit because it is the total number of new cars in existence at a given moment.  This includes both those on the dealer's lot (inventory) and those owned by people who have purchased them recently enough that they are still considered new.

 

In the Simplified Exposition I write:

 

"Both the people traditionally labeled 'consumers' and those labeled 'producers' appear in the demand distribution. The conceptual separation of consumers and producers is a great mistake of mainstream economics. They are all just people, each with a bit of the stock, and they are all prepared to sell if the price is above a certain point and buy if the price is below that point. The only thing that distinguishes people from one another is their point of indifference."

 

http://axiomaticeconomics.com/axioms.php is a less mathematical explanation that may appeal to you more than the Simplified Exposition.  In particular, the "example" section discusses the market for eggs, which is similar to the market for cars that you mention.

Toolism -- a strange déjá vu of the third kind

Comment on James J. Wayne's Fundamental Equation

 

The outstanding characteristic of physicists/engineers is that they clearly see the green cheese assumptionism of economics. Here is the key scene:

“The physicists were shocked at the assumptions the economists were making -- that the test was not a match against reality, but whether the assumptions were the common currency of the field. I can just see Phil Anderson, laid back with a smile on his face, saying, ‘You guys really believe that?’“The economists, backed into a corner, would reply, “Yeah, but this allows us to solve these problems. If you don't make these assumptions, then you can't do anything.”And the physicists would come right back, “Yeah, but where does that get you -- you are solving the wrong problem, if that's not reality.” (Waldrop, 1993, p. 142)

 

And physicists/engineers draw the correct conclusions: 

“When Phil Anderson first heard about the theory of Rational Expectations in the famous 1987 Santa Fe meeting, his befuddled reaction was: You guys really believe that? He would probably have fallen from his chair had he heard Milton Friedman’s complacent viewpoint on theoretical economics: In general, the more significant the theory, the more unrealistic the assumptions. Physicists definitely want to know what an equation means in intuitive terms, and believe that assumptions ought to be both plausible and compatible with observations. This is probably the most urgently needed paradigm shift in economics.” (Bouchaud, 2009, pp. 7-8)

 

But then physicists/engineers walk straight into the wood, that is, they apply whatever tool they have become acquainted with in their respective courses to economic phenomena (2013). This is how marginalism, chaos theory, complexity theory, and recently the Schrödinger equation (Wayne, 2014) came to economics. Thus, physicists/engineers themselves helped that economics resembles what Feynman famously called a cargo cult science (see Wikipedia http://en.wikipedia.org/wiki/Cargo_cult_science).

 

It is the same mistake again and again:

“... it should be recognized that most of mathematics used in physics was developed to meet the theoretical needs of physics. ... The moral is that the symbolic calculus employed by a scientific theory should be tailored to the theory, not the other way round.” (Wittgenstein, quoted in Schmiechen, 2009, p. 368).

 

A methodological headstand is not a paradigm shift.

 

Egmont Kakarot-Handtke

 

References
Bouchaud, J. P. (2009). The (Unfortunate) Complexity of the Economy. Econo-
Physics Forum, 0904.0805: 1–9. URL http://www.unifr.ch/econophysics/paper/
show/id/0904.0805.

Kakarot-Handtke, E. (2013). Toolism! A Critique of Econophysics. SSRN Working
Paper Series, 2257841: 1–13. URL http://papers.ssrn.com/sol3/papers.cfm?
abstract_id=2257841.

Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited,
volume 1. Norderstedt: Books on Demand, 2nd edition. URL
http://books.google.de/books?id=3bIkAQAAQBAJ&printsec=frontcover&hl=
de&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false.

Waldrop, M. M. (1993). Complexity. London: Viking.

Wayne, J. J. (2014). Fundamental Equation of Economics. SSRN Working Paper
Series, 2522492: 1–31. URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=
2522492.

Foundation, Not Tool

The most important point of this paper is that the quantum physics is the true foundation of economics because  human free wills and choices are quantum phenomena, and quantum economics works better or the same than traditional economics in macroeconomics and many fields of microeconomics.

 

Nothing wrong with supply and demand concept

There is nothing wrong with the supply and demand concepts in the traditional economics, as long as they are clearly defined and empirically observable. 

The words of supply, demand, and inventory are in general vocabulary. Everyone adult on the planet can understand these words. There is no reason to reinvent a new set terminology. What is wrong with the traditional economics is the mechanic laws of supply and demand, the non-existence of market equilibrium, the fairy tale of the perfectly competitive markets, the static view of dynamic markets, the deterministic view of the human behavior, and ignoring inventory analysis. The Indeterministic Supply Demand Pricing Model can easily overcome these weakness.

Directed randomness instead of indeterminism

Comment on James J. Wayne's Fundamental Equation

 

The correct characterization of intentional target-oriented human behavior is directed randomness which is fundamentally different from the concept of indeterminism as applied in the Schrödinger equation.

 

For the fundamental behavioral equation see (21) in Economics for Economists

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2517242

or directly on Wikicommons

https://commons.wikimedia.org/wiki/File:AXEC15.png.

 

For the non-quantum-mechanical relationsships between supply-demand-inventory-price see also on Wikicommons: https://commons.wikimedia.org/wiki/File:AXEC_001.png.

 

The Schrödiger equation is inapplicable in economics. As Joan Robinson said: "Scrap the lot and start again."

 

Egmont Kakarot-Handtke

No need to reinvent the QM

I like the directed randomness. But that is just one type of quantum indeterminacy. Do you think QM is wrong? Then fix QM. I fixed the Copenhagen interpretation, and solved the measurement problem.

Good for QM

However, you seem to have troubles with logic. I did not say that QM is wrong, I said that it is inapplicable in economics.

What's directed randomness?

If the directed randomness is not from QM,what is it?Human choice  is well beyond the scope of Newtonian physics, the second laws of thermodynamics, and Einstein's spacetime. It must be from QM. Bacteria have free wills and make smart choices too. At the E Coli bacteria level, there is nothing other than atoms and molecules obeying QM.

 

E coli is enthusiastic

about the Fundamental Equation.