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Economic Models

Discussions about the economic and financial ramifications of PEAK OIL

Economic Models

Unread postby MikeT » Wed 25 Aug 2004, 06:52:33

I have viewed the debate on oil peak over some time and the impression I get now is that there is a shift from 'whether' production will peak to 'when'. There seems also to be an increasing agreement that this will be sooner rather than later.

Richard Heinberg's book (amongst others) paints a pretty gloomy picture of the consequences. I have no reason to doubt this overall assessment.

However I would appreciate some guidance on whether there are any other analyses or models on the economic impact of oil peak - and the characteristics of businesses and country economies that would make them more or less susceptible to these changes.

Regards

Mike
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Re: Economic Models

Unread postby trespam » Wed 25 Aug 2004, 07:20:27

MikeT wrote:Richard Heinberg's book (amongst others) paints a pretty gloomy picture of the consequences. I have no reason to doubt this overall assessment.

However I would appreciate some guidance on whether there are any other analyses or models on the economic impact of oil peak - and the characteristics of businesses and country economies that would make them more or less susceptible to these changes.


A good starting point is the book "Beyond Oil: The Threat to Food and Fuel in the Coming Decades"by John Gever et. al. This was written in 1986. Interestingly enough, at the time they wrote, Asia, including India, were in the dumps and the authors were not sure whether they would become a major energy consumer or not. Of course, we now know the answer. The authors also strongly argue that the US not take the "let's waste cheap energy" route and instead start focusing on the problem. Well, we know what happened there as well.

There is another book I've got called "Global Energy: Assessing the future" which does not model the economics but looks at the big picture of future energy sources.

This paper is sort of good:
http://www.rpi.edu/dept/economics/www/w ... pi0410.pdf

A little on the technical side. Just discusses the models if I remember correctly.

Also Australian look at economics of energy transition:
http://www.cse.csiro.au/research/Progra ... emmas5.pdf

Another example of a model:
http://www.konj.se/download/18.2f48d2f1 ... 7/WP69.pdf

I've been focusing on this particular and have a fairly large listing of resources I've found on the internet regarding this topic. My feeling is that, if it doesn't already exist, a modeling group should be formed ASAP to focus on this particular topic. Up to this point, economic models have considered energy to be just another resource that can be replaced or increased when pricing signals indicitate as such. Those days will soon be over.

Up to now, most of the economic/modeling work seems to have focused on the outputs, e.g. CO2 and global warming, how to minimize etc. These same models, or the work that has gone into them, will prove useful as we focus on the inputs as well, namely energy.
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Re: Math Models of Depletion

Unread postby WebHubbleTelescope » Tue 23 Aug 2005, 00:17:59

Can't read your mind. Offer up a curve and see how it fits historical price changes. You probably won't get anywhere because humans use reverse psychology to defeat the effects of the best predictions.

On the other hand, the title of your post refers to "models of depletion". Price plays a second-order role in how that evolves. More precisely, price is a side effect of depletion.

For example, many people say that tar sands may become economical now because it costs $30 per barrel to extract. (Which is much below the current oil costs) But they forget that the $30 was the estimated costs before the current oil price hikes. And since the $30 included the energy used for extraction, that has to go up as well. And likely a lot. Basically, its hard to predict feed-forward (inflationary) systems.
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Re: Math Models of Depletion

Unread postby pup55 » Tue 23 Aug 2005, 08:02:34

P'=k(D-S) => P=k*int( t[0]->t , D-S) + C


Is K just some constant?

How do you compute or derive it?
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Re: Math Models of Economic Concepts

Unread postby WebHubbleTelescope » Tue 23 Aug 2005, 23:16:20

Elijah, keep talking and I will keep reading. I appreciate your approach of starting simple and working your way forward. If it doesn't match reality precisely, maybe it doesn't matter as long as people can understand mathematically how the market may respond or evolve.

By second order I mean as in a Taylor's series. You can get by most of the way in modeling depletion without introducing price. However, if oil prices were perfectly inelastic and we hit the inflection of a vertical supply curve, perhaps no one would ever buy oil again and we would stay in a perfectly stable nirvana. Nothing would deplete because it would cost too much to extract.

The two attempts I have made in modeling depletion happen to use a statistical, first-order Markovian models. These are the simplest models I can come up with:

Macro Depletion
http://mobjectivist.blogspot.com/2005/0 ... model.html

Micro Depletion
http://mobjectivist.blogspot.com/2005/0 ... model.html
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Re: Math Models of Economic Concepts

Unread postby EnergySpin » Tue 23 Aug 2005, 23:30:18

I think that Hotteling (the same guy who invented the T-square test for multivariate Student T data) worked out the economics of depletion of a finite resource in the 30s. If my memory is playing games with me he said that the price should go up by the same percentage as the rate of depletion (expressed at the same unit of time).
My introduction to economics has always been through math (this way one can nail the bastards when they are lying for political reasons). The tool that is most likely to be useful in modelling is not an ODE but a Stochastic Differential / Difference Equation , making the approach of WebHubbleTelescope especially appealing
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Re: Math Models of Economic Concepts

Unread postby jaws » Wed 24 Aug 2005, 00:06:34

EnergySpin wrote:I think that Hotteling (the same guy who invented the T-square test for multivariate Student T data) worked out the economics of depletion of a finite resource in the 30s. If my memory is playing games with me he said that the price should go up by the same percentage as the rate of depletion (expressed at the same unit of time).
That's ridiculous. Prices are a result of completely subjective valuations on the part of consumers. It's impossible to determine how people will value any resource in the future. Maybe in the future everything is made of synthetic diamond and diamond has become worthless, regardless of the level of depletion of diamond deposits.
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Re: Math Models of Economic Concepts

Unread postby jaws » Wed 24 Aug 2005, 00:29:29

ElijahJones wrote:However I have to tell you that I know the price of oil tomorrow will not be under $30 per barrel and not over $100. Now if you ask me how much I will bet on that that is the measure of my certainty. Yes, as we move forward in time the typical person is willing to bet less and less on a prediction about the price of oil. And yet since the resource is depleting and there is a current built in demand we feel good about saying that prices will continue to rise as long as these factors persist. You see people are both free and not free, this is true economically, sociologically and psychologically. EnergySpins idea of a stochastic dynamical system is right on the money.
You can say all of these things but the fact remains that you are only engaging in speculation. Your predictions are not grounded in any science. An statistical measure of change in prices is only speculation, and so is a differential equation. They are not economic science. All economic science can say is that value is subjective, and tastes and preferences change. It's possible, although improbable, that a new energy source will be discovered and the value of oil will vanish entirely as an economic good, making Hubbert's depletion model irrelevant. The subjective valuations made by consumers will price oil at 0. You can't predict future valuations like you can predict the movement of a physical body subject to a force. To make a prediction would require knowledge of the preferences of every consumer now and into the future, something they probably don't even know about themselves. You would need to be omniscient.

Economics is not math-phobic, it's just that math is not useful to the field other than to construct illustrations of phenomenons discovered through the logical method. You can't say that psychology or philosophy is math-phobic.
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Re: Math Models of Economic Concepts

Unread postby EnergySpin » Wed 24 Aug 2005, 01:07:05

jaws wrote:
EnergySpin wrote:I think that Hotteling (the same guy who invented the T-square test for multivariate Student T data) worked out the economics of depletion of a finite resource in the 30s. If my memory is playing games with me he said that the price should go up by the same percentage as the rate of depletion (expressed at the same unit of time).
That's ridiculous. Prices are a result of completely subjective valuations on the part of consumers. It's impossible to determine how people will value any resource in the future. Maybe in the future everything is made of synthetic diamond and diamond has become worthless, regardless of the level of depletion of diamond deposits.

Jaws I suggest you obtain Hotteling's paper. Primary reference is
Hotelling, H. (1931). “The Economics of Exhaustible Resources”.
Journal of Political Economy, 39, 137-175.

The paper deals with resources that are finite and cannot be substituted for something else. So your diamong example is irrelevant. Oil clean water, minerals and forests (these are the examples that Hotteling uses in the intro of the paper) are more relevant examples. Oil and natural gas are addressed as examples of "resource-waste" in page 144 of the paper.
Anyway: Hotteling's paper in summary :
1) the ownership status of such resources which maximizes the society's utility is public ownership and control
2) Value and market equilibrium requires that the in situ value increase at the rate of interest (this means that if the non-renewable source "backs" the currency then the rate of depletion should determine the rate of interest and not the otherway around)
3) Assumptions" known finite resource (petroleum seems to be such a case in our days), non-substitution possible, extraction cost is independent of the remaining stock (if it is dependent ... then the math get really complicated, and good old variational calculus should be applied), efficiency, recyclability etc are not possible
For such resources the "consumer - value" is constant i.e. my assessment of the value of gasoline/water etc under those assumptions will not change in the future.
Hotteling's (and other methods) have been specifically applied to oil data in this
publication
where it is argued that Hotteling's predictions have not been observed in real life due to technological change and the assumption of increasing scarcity. When it comes to oil we have been more efficient in using it in the last years and the "perceived level of scarcity" had been declining due to the recent reserve growth. However if the reserves DO not grow (which seems to be the most probable scenario i.e. due to the fact that the earth has been mapped completely), then one may argue that the markets might apply "backdate" a correction and rapidly bring the price of the resource to the point where it would have been if the reserves were known when the oil exploitation started 150 years ago. How much has the world economy grown since 1850? Multiply this number by the current oil price to get an idea of what the markets may do to the price of petroleum in the equilibrium situation. Simmons is implicitly using Hotteling's valuation principle when he argues that the price of the "stuff" should be $400 per barrel.
Of course those thingies do not tell us anything about the road towards the equilibirum ... nothining like a few carefully planted nuclear warheads in Beijing, Washington DC, London, Paris, Tokyo to mess all these calculations and even make markets disappear 8O 8O :twisted: :twisted:
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Re: Math Models of Economic Concepts

Unread postby EnergySpin » Wed 24 Aug 2005, 01:25:33

jaws wrote:
ElijahJones wrote:However I have to tell you that I know the price of oil tomorrow will not be under $30 per barrel and not over $100. Now if you ask me how much I will bet on that that is the measure of my certainty. Yes, as we move forward in time the typical person is willing to bet less and less on a prediction about the price of oil. And yet since the resource is depleting and there is a current built in demand we feel good about saying that prices will continue to rise as long as these factors persist. You see people are both free and not free, this is true economically, sociologically and psychologically. EnergySpins idea of a stochastic dynamical system is right on the money.
You can say all of these things but the fact remains that you are only engaging in speculation. Your predictions are not grounded in any science. An statistical measure of change in prices is only speculation, and so is a differential equation. They are not economic science. All economic science can say is that value is subjective, and tastes and preferences change. It's possible, although improbable, that a new energy source will be discovered and the value of oil will vanish entirely as an economic good, making Hubbert's depletion model irrelevant. The subjective valuations made by consumers will price oil at 0. You can't predict future valuations like you can predict the movement of a physical body subject to a force. To make a prediction would require knowledge of the preferences of every consumer now and into the future, something they probably don't even know about themselves. You would need to be omniscient.

Economics is not math-phobic, it's just that math is not useful to the field other than to construct illustrations of phenomenons discovered through the logical method. You can't say that psychology or philosophy is math-phobic.

But jaws ... most of the recent Nobel prizes in Economics have been given for mathematical breakthroughs (Black Scholes formula for example is an SDE solution). And the logical method as you call it was the foundation of Jaynes approach to Bayesian probabilistc reasoning. The subjective valuations as you call them can be codified in utility functions (zero-one if you are a Bayesian) and then examine expectations combining both uncertain events and personal utilities (de Finneti's approach).
As I said in my first post, my BS detector starts ringing when (Economists) or other scientiest CANNOT or WILL NOT use quantitatve reasoning. That puts them at the same level of credibility as astrologists, tarrot card readers, alchemists and other nutcases.
In my field (i'm a physician) the mathematical/statistical approach is the standard way of formulating hypotheses and testing research questions. It is only when medicine accepted this "statistical" and "scientific" method that we were able to do awat with quackeries. Hearing that mathematics are not applicable to economics reminds me of the objections that supporters of medicinal leaches and blood letting used to discredit Louis studies against those methods in the early 19th century. :twisted: :twisted:
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Re: Math Models of Economic Concepts

Unread postby WebHubbleTelescope » Wed 24 Aug 2005, 01:33:55

Elijah,

Using the Latex markup, are you going to convert the stuff to PDF's or is there a good XML type plugin for rendering the equations?
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Re: Math Models of Economic Concepts

Unread postby CrudeAwakening » Wed 24 Aug 2005, 06:03:39

ElijahJones wrote:Honestly, I really don't like your attitude, whatever your personal beliefs are and I think that to keep this thread from flamesville I will just ignore you until you start making some sense. Do you have a degree in something? Maybe we should comfort one another with an exposition of formal logic. Did your econ 101 class teach you axiomatics or prepositional calculus or how about graph theory? Do any of these have things to teach us about economic systems?

Peak Oil is a serious issue that is likely to cost the lives of millions of people and I am not interested in entertaining children or bullshit! So please, if you cannot respond here with logical argument kindly start your own thread. And do not flame the participants or I will report you to the moderators.


Elijah

I think your posts have been interesting, but I have to chip in in support of Jaws here. I don't think he was flaming, he just seemed to be expressing another viewpoint. You seem to be patronising him when all he seems to have done is disagree with you. I sense some inter-specialty antagonism..
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Re: Math Models of Economic Concepts

Unread postby kmann » Wed 24 Aug 2005, 10:42:41

EJ,
I'd like to give you a word of encouragement. This is good stuff, it will be interesting to see where it goes. I wish I could contribute, but my math at this level has accumulated several layers of rust. I plan on following this thread, and if I'm not careful I might learn something.
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Re: Math Models of Economic Concepts

Unread postby jaws » Wed 24 Aug 2005, 13:24:39

EnergySpin wrote:But jaws ... most of the recent Nobel prizes in Economics have been given for mathematical breakthroughs (Black Scholes formula for example is an SDE solution). And the logical method as you call it was the foundation of Jaynes approach to Bayesian probabilistc reasoning. The subjective valuations as you call them can be codified in utility functions (zero-one if you are a Bayesian) and then examine expectations combining both uncertain events and personal utilities (de Finneti's approach).
No, the valuations cannot be codified because they are unknown until individuals act on them. That creates a historical fact, an exchange of such goods took place for such goods on such date between two such people. This is why econometrics is useless. Aggregating historical facts and running mathematical analysis on them yields no valuable insight. Garbage in, garbage out as they say. What do you think would be the point of doing an econometric analysis of major battles fought in Western Europe?
As I said in my first post, my BS detector starts ringing when (Economists) or other scientiest CANNOT or WILL NOT use quantitatve reasoning. That puts them at the same level of credibility as astrologists, tarrot card readers, alchemists and other nutcases.
In my field (i'm a physician) the mathematical/statistical approach is the standard way of formulating hypotheses and testing research questions. It is only when medicine accepted this "statistical" and "scientific" method that we were able to do awat with quackeries. Hearing that mathematics are not applicable to economics reminds me of the objections that supporters of medicinal leaches and blood letting used to discredit Louis studies against those methods in the early 19th century. :twisted: :twisted:
My physicist detector lights up whenever one thinks the methods of physics are appropriate for every field. What good are hypothesis and experiments to geology and meteorology? They have no laboratory to test. They are studying an immensely complex system in motion. All of their insights are based on observations and predictions. Economics is the same kind of field, except for two important differences. First, there is no constant metric in economics, therefore "measures of prices" are useless. The value of both money and goods is fluctuating. And the indexes constructed to adjust money to "real values" also fluctuate. Constructing a CPI based on eggs and a suit and a Ford Model T stops being useful when people's tastes naturally change and they buy different things. Since you have nothing constant to measure against, taking measures is not scientific, no matter how much you want it to be. By using prices as measures, you are making the same mistakes you accuse those quack doctors of making before using your methods.

Second, the knowledge of economics is embedded in us. It is not a natural phenomenon, it is a human phenomenon arising out of deliberate, willful human action. The goal of the science is then to identify the motives of this action in the most general possible way, and extrapolate the behavior it generates to its final logical consequence. Truth or falseness is easy to identify because we know ourselves. That is how economics must operate because there is no other way to operate. The application of other methods is left to other scientific fields.
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Re: Math Models of Economic Concepts

Unread postby nero » Wed 24 Aug 2005, 14:13:58

Elijah,

I see a problem with your initial model for P'= f(D,S) It perhaps is what jaws is also talking about. Your model is trying to model the inefficiency of the market. If the market was efficient then there would never be any lag between demand and supply. Prices would move smoothly to correct for any changes in the curves. While this doesn't happen in the real world the problem is we don't know what D (Demand at any instant in time) really is. It is extremely hard to quantify. Perhaps you could set up an experiment where D and S and quantifiable and sufficiently different so that the driving force you are after is significant. However in the real world, markets are much more efficient and the driving force is relatively small and hard to measure. Therefore economists are left talking theoretically about the ideal situation where D and S are always equal by definition.
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Re: Math Models of Economic Concepts

Unread postby nero » Wed 24 Aug 2005, 14:31:30

jaws,

Economists can perform experiments. As opposed to say astronomers or geologists or anthropologists. Economists have the same ethical and financial problems performing experiments that doctors or ecologists have. They also do not want to harm the patient or experimental subjects. They also are dealing with enormously complex situations where to perform useful experiments it takes alot of money, time and resources to isolate for the parameter of interest.

It's not impossible and some economists are doing it. On the other hand making a facile mathematical model from historic economic data isn't likely to be very useful. Before the math has to come the hypothesis or else it is probably only curve fitting. The data is just too dirty to hope to glean data from it otherwise.
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Re: Math Models of Economic Concepts

Unread postby MacG » Wed 24 Aug 2005, 15:45:57

Not "jaws", but anyhow...

EnergySpin wrote: But jaws ... most of the recent Nobel prizes in Economics have been given for mathematical breakthroughs (Black Scholes formula for example is an SDE solution).


One of them blokes showed up in LTCM. Some piece of bancruptcy that one. Heh! And that bloody Nobel Price in economics is a joke altogether. It was bribed into existence in the 70's. Alfred Nobel did not indicate any interest in such a prize in his will.

Not that I think "jaws" have anything to say on this issue either. (I seem to be slightly irritable tonight. Sorry all.)
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Re: Math Models of Economic Concepts

Unread postby nero » Wed 24 Aug 2005, 17:23:57

EJ wrote:Efficiency by definition is "achieveing a goal as cheaply as possible" (Colander, G4) There is no reason to suppose that perfect efficiency is even possible or that the model makes this assumption. I agree the actual working models will be difference equations but ODE's are the continuous analogs of difference equations, I am making no logical err by starting here.


That was not a critisism of your post, it was explaining my understanding of it. I did not say or think that model assumes perfect efficiency, in fact quite the opposite. If that is not your meaning then we aren't going to get very far. So I'll be a bit more explicit. Try not to be too critical of the math from a non mathy:

D(t) = the "demand" at time t given current prices P(t).
S(t) = the supply at time t given current prices.

D(t) does not equal S(t) at any given t.

However P(t+dt) = P(t) + k(D(t)-S(t))

I was saying that in an ideal "efficient" market where information was processed instantaneously and where there is no lag in response then k approaches infinity and (D(t)-S(t)) approaches 0.

So you are assuming that k does not approach infinity which is a GOOD thing. But it does make life complicated because unless you're not interested in testing your hypothesis now you are going to have to find a way to measure (D(t)-S(t)).



Yes we have to get an estimate of D[0] and S[0], since we are interested in the long term behavior of the systems and most trajectories will be captured by the trend we can feel ok with being off by possibly as much as 15%. This is a calibration issue separate from the notion of process realism.


By D[0] and S[0] you mean you nead the initial values at time t =0? What I was meaning is that you need D(t) and S(t) for any point in time. These are MEASURED values aren't they? Or do you propose to model D and S as well. I don't know how model D and S might be modelled, but then I don't really know how you can measure D and S either so I'll let that go. We really do seem to be on different wave lengths.

How small do you think is to samll to account for with mathematics? This point does not make sense nero. I can keep a math model that tracks to 30 digits of precision in both Mathematica and Maple certainly that is good enough to stay wihtin a percentage error of any real trend. Unless of course the trend we are looking at is chaos.


No too small to be measured by experiment, due to limitations in the experiment.

I think your conclusion is totally invalid the study of far from equlibbrium systems is gainaing ground in mathematical ecology as we speak. You've done nothing to show that the model is invalid. The argument you are using is often called "The Strawman Fallacy." It means you constructed an argument different than my position without really understanding my position. Then you defeated your own imagined foe and declared victory. You'll have to do better than that my friend. Try this link for starters http://www.datanation.com/fallacies/ . He does a pretty good job with it. Of course any good math program is going to teach formal logic and set theory (which is the foundation of everything logical).


I didn't set out to show that the model was invalid I was attempting to explain why I thought that the model wasn't useful.

Don't go throwing around "strawman fallacy" unless you're pretty darned sure it isn't simply a matter of misinterpretation. Them's fighting words.
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Re: Math Models of Economic Concepts

Unread postby EnergySpin » Wed 24 Aug 2005, 17:39:19

The scientific method IS valid even in fields that cannot perform experiments (like geology or astronomy). The kind of Statistics that is applicable there is Bayesian statistics and models are used as proxies for a complex reality which cannot be known fully (hence models are uncertain variables themselves). Using traditional i.e. frequentist statistics in those fields is at best a grave mistake. One does not have repetitive experiemnts and in many cases symmetry assumptions cannot even be madel.

Many of the objections that Jaws raised about the application of mathematical models in economics are identical to objections raised against the mathematization of medicine and biology. Objections that were raised then had to do with the complexity of biological organisms/humans, the fact that no two humans are identical etc. The debate about quantitative reasoning in medicine actually dates back 2500 years ago with people debating whether a logic-based or data-based approach is suitable for the field. The fact that the argument seems to have been settled in favour of an approach combining theoretical mechanisms of disease AND empirical measurements in an increasingly Bayesian framework does show that there are NO limits to quantitative reasoning. Maintaining that a logic/language based approach is not amenable to mathematization is incorrect. First of all traditional (i.e. Aristotelian logic) can be represented by a Boolean Algebra notation; the extention to situations of uncertainty IS the Bayesian paradigm and that has been rigorously proved by both Jaynes and De Finetti. If one argues that it is not possible to reduce a linguistic/logic based approach to mathematics then one is not using logic in the first place , thus making his or her statement either vacuous or extremely suspect.

John Kenneth Galbraith has actually explored the question whether economics is science or not in his book "History of Economics"; he openly admitted that in the majority of historical cases economics was the "scientific" cloak that was used by the power structures to maintain control. Both the "invisible hand" and the "socialist state" are examples of such constructs IMHO.

Regarding the use of equilibrium models. It is fascinating to me to watch economics go through the same transformation that quantitiatve physiology or quantitative medicine went through. First there were qualitative observations (i.e. Louis Paster's germ theory), then quantitative data (i.e. the German physiologist of the late 19th early 20th century working on the cardiovascular system) and equilibrium as well as steady state models followed by differential equation modelling (i.e. Hodkin and Huxley models of nerve cells) and stochastic approaches in the last 20 years (i.e. ion channel kinetics).
Sorry to say that the future of all sciences is mathematics. Unless one adopts a dualistic philosophy towards the nature of man, all reality is based on matter and its properties. Laws on higher levels of organisation are grounded AND restricted by physical laws operating in the lower level . Even though I do not expect to see a quantum dynamical description of the economy or one of my patients, it is useful to remember this simple truth. Of course If one accepts the existence of a soul that is not subject to material laws then there is no point in debating the whole issue at all. For whenever a dualist is cornered he or she will always evoke a law based on the "properties of soul or human nature" thus destroying any opportunity of a real scientific debate.
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Re: Math Models of Economic Concepts

Unread postby nero » Wed 24 Aug 2005, 23:35:19

EJ wrote:The equation P'=k(D-S) lacks many real world properties but as a starting point is has the following. Price goes up when D-S>0 and it goes down when D-S<0. Howmuch price changes under these conditions has to do with elasticity so k is not really constant, but that would be the next step in building the model. No k does not have to go to infinity for D-S to be zero. In the real world D-S=0 is the equilibrium the market is seeking but never finds.


k doesn't have to approach infinity for D-S to be zero but given (D-S)-> 0 in an ideal (equilibrium) market, for P' to be any real non zero value k must approach infinity.

I think you said that part of the reason it never finds the equilibrium is because it is actually discrete and not continuous.


That wasn't me. I haven't said anything like that.
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