buletin ştiin ific - Facultatea de Stiinte Economice - Universitatea din ...

Some Potential Econophysics’ Models for Real Economic Convergenceln p ( x)= −α ln x + C , (2)where the constant α is called exponent of the power law, and C is constant and mostlyuninteresting (once α is fixed, it is determined by the requirement of normalisation to 1), or inthe case of taking the exponential of both sides, this is equivalent to:p ( x ) = C x− α(3)(a power-law distribution occurs in an extraordinarily diverse range of phenomena such asFinance, Macroeconomics, Demography’s urbanism and, why not, even in real economicconvergence). [18]a fractal and chaos analysis originating as Benoite Mandelbrot pointed out that the change in theprice of the stock market has a fractal structure for certain range of time interval [19, 20], andcharacterized as a self-similar structure expressed as:x ( t ) = Ct D (4)where D is a fractal dimension, calculated by the box counting method.(the fractal structure isspecial case of a chaos and chaotic behaviour is very common in a non-linear system as for aneconomic system; whether the process is chaotic or not can be determined by sign of Lyapunovindex λ defined as:λ = 1/ n Σ log | F ′(t ) | (5)and when λ is positive (negative) then the process is chaotic (non- chaotic). [21]Modern Econophysics has developed a new learning system for econophysicists, a systemconsisting of several parts:1) Basic Mathematics,2) Basic Econometrics3) Echonophysics, including chaos and fractals concepts,4) Virtual market,and reviewing concepts concerning to each part: Mathematical representation and analysis of theeconomic data for Basic Econometrics; the chaos and fractal including the Lyapunov index andthe fractal dimension for Econophysics; the Sato-Takayasu model and simulation for Virtualmarket.[21]Today, there still are some weaknesses in the Econophysics’ models approaches in realeconomic convergence:- a lack of awareness of work that has been done within economics itself;- a resistance to more rigorous and robust statistical methodology;- a belief that universal empirical regularities can be found in many areas of economic activity;- an inadequate, theoretical model which is being used to explain somehow relative the diversityof the empirical phenomena.5. Final RemarksIn a comparison to classical Economics new sciences like Econophysics and its newmodels have revealed that heterogeneous in economic and social reality must be explained withhomogeneous in their theory and this is the most important improvement of the quality in theclassical science and research. The main role of the Physics and its methods, like StatisticalPhysics or Quantum Physics for the beginning, was to unify and simplify classical Economics.The contemporary models of Econophysics improve the quality of classical Economics,Econometrics and even Physics and extend their themes, fields and final interpretations. Thepower of prediction or the higher level of exactness of the Econophysics’ models remains themost important difference between this new and powerful science and classical Economics’ andEconometrics’ thinking. The complex studies of Econophysics try to capture the universal buttemporary laws, from data manifested differently in different parts of the same body of naturalphenomena, where information about population are made from more individuals than 10 23 units60