Bilokon O.M., Chevganova V.Ya., Zotsenko M.M.

 Poltava National Technical University Named After Jury Kondratyuk

THE WELL-BEING  OF ECONOMIC AGENT AND THE MODEL OF THE LIFE CYCLE CONCEPT .

 

The decision of an investor depends on the life cycle stage of the object of investment. Therefore the improvement of the economic agent’s  market position trend methods of analysis, life cycle concept generalization and  theoretical substantiation are timely. The investment capitals movement processes  are considered as the nonlinear phenomena in open dissipative systems. The description of the similar phenomena determines the generalized approaches of synergy –  theory of self-organizing. Calculating experiment, the  life cycle concept  base model  being theoretically proved for which, is accepted as the scientific research method.

Theoretical methods of scientific abstraction and the deductive method enabled us to assume the abstract notion “ the well-being of the economic agent” as a vital resource availability at a certain time, corresponding integrated result of the agent’s market behaviour  and entry conditions.

The continuous function of the agent’s well-being   $ (e, i, t)  is accepted, where: e,i – external and internal factors which are conservative and  do not change in the short-term periods. In this case well-being is only dependent  on the factor of time t. The inclination of the function is a ratio Δ $ = ($1-$0) to Δt = (t1-t0).

The method of the theoretical analysis enabled us to divide the  function of well-being into two (supply and flow) processes, and to formulate cause and effect conditions  and laws as differential equations.

Cause and effect conditions in the supply process are in the statement: the  greater  well-being reserve is, it will give more opportunities for its changes. This law combined with the supply process and well-being changes in time is formulated as:

                                                                                                              (1)

 

Infinitesimal change of well-being at an infinitesimal time interval is proportional to the well-being itself with coefficient of proportionality C.

The general solution to the differential equation looks like:

                                                            (2)

Coefficient C is not a flexible in time (conservative) characteristic, the parameter of the economic agent, it displays the subjective propensity of the agent’s actions  in the supply process.

Graphically  formula (2) is displayed in fig. 1. At C> 0 the agent is inclined to increase  the well-being reserve in time. At C=0 the agent is inclined to conserve the well-being reserve. At C <0 the agent is inclined to use the well-being reserve.

Cause and effect conditions in the flow process are  in the statement: the  greater the rate of well-being $  reproduction b is, it will give more opportunities for its changes. The law combined with the flow process and well-being changes is formulated as:

                                       (3)

Infinitesimal change of well-being at an infinitesimal time interval is proportional to rate of well-being reproduction  with coefficient of proportionality b.

The general solution for the differential equation is a multiplicative model:

                                            (4)

Coefficient b is not a flexible in time parameter  of the economic agent, it displays the subjective propensity of the agent’s actions in the process of well-being reproduction .

Graphically  formula (4) is displayed  in fig. 2. At b=1 the agent  recreates well-being in time evenly. At b> 1 the agent is inclined to the well-being reproduction rate intensification . At 0 <b <1 the agent is inclined to the well-being reproduction rate slowing down . At b=0 the agent is inclined  not to recreate well-being. At b <0 the agent is inclined to withdraw well-being.

 

                                  

                                                       Fig. 1                                                                Fig. 2.

 

The method of theoretical synthesis enabled the authors to formulate the generalized law of well-being changes  in time:

                                                         (5)

Infinitesimal  well-being change at an infinitesimal time interval  is proportional to well-being and its reproduction rate.

The general solution to the differential  equation is submitted as the exponential-multiplicative formula:

                                                      (6)

The formula(6) diagrams are displayed in fig. 3 (a,â,c).

       

              Fig. 3 (à) b <0                                          Fig. 3 (b) 0 <b <1                               Fig. 3 (c) b> 1

The presented theoretical grounds enable us to accept the exponential-multiplicative  economic-mathematical model hypothesis as the base model for the life cycle concept of the economic agent.

References:

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