Evgeny V. Popov, Ph.D., (Dr.Sc.), Economical Theory Department, Institute of Economics, Ural Branch of Russian Academy of Sciences, Moskovskaya str., 29, Ekaterinburg, AL 620014, Russia and Lyudmila N. Popova, Ph.D., Institute of Management of the Ural State University, Lenins str., 13b, Ekaterinburg, 620014, Russia.
The aim of this investigation is the elaboration of the minieconomical institutions evolution model on the base of the mathematical formalization of diffusion processes and received author’s empirical results.
The process of the economical institutions growth may be observed more informative in comparison with other systems on the firm level – level of minieconomical systems[1]. In this case, the business project which is the base of first investments may be determined as an initial economical institute of the firm. From the other side the institutes of firm management may be seemed as the long term equilibrium institutes.
Institutional structure of the firm activity may be possible divide on the four main management functions (planning, organizing, stimulating and controlling) which cover the four main resources (labor, financial, material and informational) on the three levels of activity (analytical, industrial and communicational). Such quantification of the firm activity allows dividing the about fifty minieconomical institutions with difference functional contents[2].
The dynamic of the economical institutions growth may be represented as dependence of the whole transactional costs C from the time t and functional content x of economical institutions:
C = C (x, t)
It is known that the growth of the concentration of some substance (in our case it is the transactional costs of the economical institutions formation) in any environment is writing as the Fick’s diffusion law:
∂C / ∂t = D ( ∂2C / ∂x2 ),
where D is the diffusion coefficient. In our case the diffusion coefficient is the coefficient of ratio between the whole transactional costs time dynamics and the distribution of these costs under the space of economical institutions functional contents.
The standard solution of the diffusion equation is determining the following distribution of the whole transactional costs C from time t in the space x for economical institutions functional contents:
∞
C(x,t) = Σ (2C0 / π n) Sin ( π n x /d) exp ( - π2 n2 D t / d2 ),
n = 1
where C0 is the initial value of the whole transactional costs (for example, it is the cost of the preparing the business project of the firm); d is the “wide” of the economical institutions functional contents (for example, it is the bounder conditions for used resources which are formed the analyzing institutional structure).
The last solution caused to the following non simple conclusions.
Firstly, the time and functional distribution of transactional cost is describes by the wave (sine curve in mathematical language) dependence. Secondly, the value of transactional costs is decreasing in case of absence of internal influence.
The both conclusions may be explained by the introduction of hypothesis about the presence of economical institution life time, and as consequence the opening of transactional costs sine curve.
[1] Popov E.V. Minieconomics as a Separate Part of Microeconomics //Atlantic Economic Journal. 2005. Vol. 33. No.3. P.133.
[2] Popov E.V. Market Potential of the Firm //International Advances in Economic Research. 2004. Vol. 10. No. 4. P.337.