Economic Uncert Principle 060903

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Economic uncertainty principle? Alexander Harin This preliminary paper presents a qualitative description of the economic principle of (hidden, latent) uncertainty. Mathematical expressions of principle, consequence, hypothesis and results are offered. Examples of solutions of the first three types of fundamental problems are reviewed. Contents Introduction. …………………………………………………………….. 1. Economic uncertainty principle ……………………………………. 1.1. General economic uncertainty principle 1.1.1. Preliminary
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    Economic uncertainty principle? Alexander HarinThis preliminary paper presents a qualitative description of theeconomic principle of (hidden, latent) uncertainty. Mathematicalexpressions of principle, consequence, hypothesis and results areoffered. Examples of solutions of the first three types of fundamental problems are   reviewed. ContentsIntroduction. …………………………………………………………….. 21. Economic uncertainty principle ……………………………………. 2 1.1. General economic uncertainty    principle1.1.1. Preliminary definition1.1.2. Evident and hidden (latent) uncertainties1.1.3. Influence of the principle1.1.4. Example1.1.5. Miscellaneous1.2. Specific economic uncertainty principle1.2.1. Preliminary definition1.2.2. Mathematical expression of the definition1.2.3. First consequence1.2.4. First hypothesis1.2.5. Example 2. Problems solving ……………………………………………………. 8 2.1. General2.2. Allais paradox, risk aversion, overweighting of low probabilities …2.2.1. First type of results. High probabilities2.2.2. Second type of results. Gains and losses2.2.3. Third type of results. Low probabilities2.3. Universality and uniformity of the approach of the principle 3. Arrangements’ infringements ……………………………………… 11 3.1. Plans and the need for this paper 3.2. Arrangements’ infringements3.2.1. Definitions3.2.2. Hypotheses. First results. Applications3.2.3. Analogies Conclusions ……………………………..…………………………... 13Acknowledgement ………………………………………………….. 13References ……………………………..………………………….... 14 1    Introduction There are a considerable number of discussed aspects of uncertainty. There is a wealth of aspects of uncertainty to be discussed. This preliminary paper qualitatively examines one of them. 1. Economic uncertainty principle  1.1. General economic uncertainty    principle1.1.1. Preliminary definitionFuture events may be considered as, at least partially, uncertain.This uncertainty or partial uncertainty may be invisible, imperceptible. It may be crucial. Inany case, the overwhelming majority of future events contain, at least a part of uncertainty. In asimple form this principle may sound like:Future events contain (at least) a degree of uncertainty.1.1.2. Evident and hidden (latent) uncertaintiesThere are evident and hidden, latent uncertainties. To consider evident uncertainties is, in asense, obvious and trivial and often not helpful. The primary (but not the only) goal of theeconomic uncertainty principle is to consider hidden, latent uncertainties. So the new principlemay sound like:Future events contain (at least) a degree of (hidden) uncertainty.It may also be (but not always) referred to as the principle of hidden (latent) uncertainties.1.1.3. Influence of the principleIn some cases, an influence of this principle will be negligible. In some cases, this influencewill improve a precision of calculations. In some cases, it will be essential, even crucial.In any case, collective elaborate definition, development and application of economicuncertainty principle will improve the scientific accuracy of economic theory.1.1.4. ExampleSuppose Mr. Somebody offers you a prize. The choice is between a guaranteed prize or oneof a lottery. The lottery prize has value, which is greater and the probability, which is less, thanthose of the guaranteed one. The mathematical expectations to win the lottery and guaranteed prizes are exactly equal to each other. The probability to win in the lottery is (certainly!) equalto  P  (  P < 100% ).This scenario gives rise to a number of unsolved fundamental problems (e.g., the Allais paradox, risk aversion, loss aversion, overweighting of low probabilities, the Kahneman-Tversky paradox, the equity premium puzzle).So, instead of 50 years of numerous attempts at solving the famous paradox of Nobellaureate Allais, another Nobel laureate Kahneman, along with Thaler, (2005) noted “… the paradoxes of Allais (1953) … have demonstrated inconsistency in preferences.”The situation contains the evident uncertainty in the lottery (You may whether win or not).But there is a hidden uncertainty. It is, e.g., the probability to win in the lottery (and in realityreceive your prize) may not be certainly equal to P (The lottery may have a defect or suffer afailure; suddenly, you or Mr. Somebody may become ill; Mr. Somebody’s offer may be a joke or trick; anybody (curious person, terrorist, policeman, etc.) may interfere in the process, etc.).2   Suppose three variants of the preliminarily determined probability  P   preliminary . They areregarded as high, medium and low:  P  high preliminary = 99%. P  medium preliminary = 50%, P  low preliminary = 1%, Suppose the probability’s uncertainty is ±  ∆  P  . Then all variants of the real probability  P  will be uncertain  P ~ P  preliminary ±  ∆  P  .Suppose the probability’s uncertainty is essentially more than 1% (e.g.  ∆  P = 10% ) and isuniform. Then the mean real values of probability  P  mean : will be  P  high mean < 99%. P  low mean > 1%, Real low probability will be higher than the preliminary one.Real high probability will be lower than the preliminary one.The unsolved problems may be solved.1.1.5. MiscellaneousLiterature reviewThe search of the term “uncertainty principle” in economic   literature found in titles or keywords offers no examples in the predominant meaning of this paper.The classical review in Schoemaker (1982) and the most recent (one month before Harin2005, the first feature paper on this idea) review in Quiggin and Chambers (2005) do notmention this idea. The author’s review of RePEc from 1969 does not find this idea either.Similar or supporting works are, e.g., Quiggin (2005), Capuano (2006), Hey (2005), Chay etal (2005), Novarese (2002).3   Questions, generalization and analogiesAt the present, the name and wording of the principle are open to questioning. Advices arewelcomed.Generally, this principle may be treated and referred to as “Future   uncertainty principle” or “Principle of future’s uncertainty” or “Principle of uncertain future” or “Principle of hiddenuncertainties,” etc.The economic uncertainty principle may be, to some extent, treated in terms of incomplete or asymmetric information.There are evident analogies between Heisenberg’s uncertainty principle and Einstein’sgeneral and specific theories of relativity on one hand and the economic uncertainty principle onthe other hand. There is an evident influence of the great physicians on the new principle.Moreover, the economic uncertainty principle can be, to some extent, the consequence of Heisenberg’s uncertainty principle. Indeed, one cannot simultaneously measure both impulseand position better than with uncertainty  ∆  p ×  ∆  x ≥    ћ / 2 where  ∆  p - impulse uncertainty,  ∆  x - position uncertainty, ћ - Planck's constant divided by 2 π .This fact, along with actual impossibility to know all reasons and srcins of future events,can give rise to future events’ uncertainties.The situation, when comparing the economic theory without and with the economicuncertainty principle, is in a sense analogous to the situation when comparing classical andquantum physics. Classical physics does not consider Heisenberg’s uncertainty principle whichis one of the cornerstones of quantum physics. The “classical” economic theory does notconsider the economic uncertainty principle.Consider two processes:a process which is a basic one for economics – a choice of an outcome which probability is  P  ,anda process which is a basic one for physics – a scattering on a barrier which the heightis  H  .In the both cases, when the uncertainty is essential:for high  P  and  H  the choice and the scattering are lower than those of the classical theory;for low  P  and  H  the choice and the scattering are higher than those of the classical theory.4
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