Investigation of privatization and re-privatization processes in the transition economy of Ukraine

Privatization of State Property has become one of the cornerstones of social and economic reforms in Ukraine. Her role in shaping the foundations of a market economy, the creation of a critical mass of effective private owners is undeniable. However, the task of privatization often narrowed to purely fiscal and inconsistency and lack of transparency of privatization processes, their significant politicization provide the basis for a mixed assessment by experts, politicians, civil society, creating conditions for political confrontation, which ultimately prevents the formation of correct privatization strategy.

Especially at this point is to find effective approaches to solving the problem of improving the efficiency of the privatization process and the search for effective social contract, which will allow taking into account the interests of all parties.

A prolonged period of privatization in transition economies Ukraine connected with the problem that initially is chosen economic policy of the state, not by a clear position of the state is not defined rules for other facilities management and there was no synchronization privatization and defining strategic objects determine the time and conditions of privatization. [1]

From the perspective of system analysis and informed decision making for the implementation of the privatization process to apply modeling approach. This means that a decision on the formation and implementation of privatization policies need to visit the appropriate mathematical model on which the decision will be made.

This paper demonstrated a model of privatization in the form of a system of ordinary differential equations of order 1. For calculation based on ratings trajectory forecasts and key variables of the process. In addition, the software used for the forecast for the next three steps.

Thus, in the transition from one species to another property the following problems occur: a significant decline in production resulting in a stop or full stop operation of manufacturing plants, accompanying this recession inflation (which can go into hyperinflation), a significant increase in unemployment, the general decline of social security population and living standards in general, and the deterioration of almost all other macroeconomic indicators. Solution of these problems should find its place in the decisions and plans of the government that decides to implement the privatization process.

It is clear that privatization should be done at a certain finite time interval synchronized with the solutions of other problems of the transition process. It is important to prevent production decline below a certain critical level, which provides an acceptable level of welfare and curb unemployment at a level acceptable to the socio-political point of view. Another objective of privatization may be due to the accumulation of capital privatization with a view to future use for the development of production in the new environment and reduce the budget deficit.

Thus, analysis of the privatization process as a process control shows that the output of this process are the following variables:

- The total volume of production (for a separate branch for several industries or the national economy as a whole);

- Appropriate to the socio-political point of view, the unemployment rate;

- The amount of capital accumulated from the sale of state-owned enterprises to new owners.

As a control input variables can select the number of enterprises subject to privatization per unit time (eg quarterly, half-year or year) and the number of enterprises that are brought to market privatization. The first variable we call the speed of performance or speed of privatization.

The third group of variables that affect the process of privatization, are so-called perturbation, i.e. the input values that are most often affecting the process (which we are going to manage) and is usually difficult or unmanageable manageable. This group comprises the following factors:

- General macroeconomic instability that affects all socio-economic processes in the country and is virtually uncontrollable factor;

- The impact of foreign creditor relies on a decision taken by the government and parliament; this factor has its advantages, but overall the state will have to ultimately accept credit, loans, and interest and not always favorable to the decision of the national economy, which is especially painful for the country as unstable transitional period;

- A rapid change in the legal framework of privatization that leads to chaos and illegal actions on the part of those who sell, and by those who buy the company;

Obviously, the list of negative factors could continue, but just how difficult it can be seen in the model to take into account their impact. Therefore, further analysis will limit ourselves to some generalized integrable perturbation as a Gaussian random process.

Privatization plans as a whole can be seen as a function of time at a certain time interval, which depends on the speed of privatization and variable number of enterprises that are brought to market privatization in the current time. In this case it is important to find a speed of privatization and the current number of enterprises in the privatization market that will ensure compliance with other parameters within specified boundaries.

In the process of transformation from state to private ownership in any industry can be divided into the following three groups of enterprises that affect the progress of the privatization plan:

- Enterprises remaining in state ownership;

- Companies that are transformed into private ownership at the beginning of the time period in question;

- Entities that pass into private ownership during the time period in question.

It is obvious that the second and third group of enterprises play a decisive role in the formation of key macroeconomic indicators of the sector and the whole economy in transition.

In developing the model also relies that the volume of production at enterprises that were privatized at the beginning of the period remaining for simplicity the same as in state enterprises, but with fewer employees. And the volume of production at enterprises of the third group may be different from the first two groups.

As a result of the privatization of state-owned enterprises of the workers released from work and, as the experience, the percentage of released can reach almost 100%. Despite the fact that the workers of state enterprises find work in the second and third groups, this leads to a significant growth rate, which may be open or hidden. Thus, one of the key variables of the mathematical model must be current employment in the privatization process.

Since privatization inevitably accompanied by a decline in production due to quantitative and restructuring of the industry, the second variable that must be considered is the current volume of products within this industry. Third base, you need to enter in the model is the amount of capital that is accumulated from the sale of businesses.

To construct the model is necessary to consider a number of variables that characterize the flow of this process at the industry level. In the process of constructing mathematical models will comply with the methodology proposed in [13]. In order to describe the dynamics of PE, we introduce the following variables:

number of enterprises that are brought to market at the beginning of the privatization implementation of the transition from state to private ownership; current number of enterprises that are brought to market further privatization at time ; introduction of this variable due to both economic and socio-political reasons; period of time during which must be made privatization of the industry; number of enterprises privatized unit time (month, quarter); it is obvious that number of firms privatized in the time interval ; current volume of products produced by private enterprise; number of workers employed at a private company, the company is the second group (for simplicity, it is assumed that the number of workers in all private enterprises the same, that does not affect the generalization of the results); number of workers employed at a state enterprise; performance of the state enterprise privatization at the beginning of the period (assumed constant throughout the period); productivity per worker of state enterprises; productivity per worker private enterprise; current number of enterprises that are created in the private sector at a time ; number of workers at a private company, which is created in the process of privatization; performance of a single private company, which is created in the privatization process; total number of employees in state enterprises at the beginning of the period of privatization; Total current employment in the field at time ; rate of change of total current employment in the field at time ; number of workers who have become unemployed as a result of privatization; number of workers who have become unemployed as a result of privatization without public enterprises that are brought to market further privatization during ; number of private enterprises that are created by the labor of state-owned enterprises to be privatized; number of private enterprises that are created by the labor of state-owned enterprises to be privatized without those state enterprises that additionally submitted for privatization during ; function of the current volume of production for enterprises of all types of property; the rate of change of the current volume of production for enterprises of all types of property; current unemployment caused by the transition to a new form of ownership; initial cost of a state enterprise privatized; current gains of one state enterprise; while gains on a range of public is ; assigned as the function can be predicted based on previous experience of privatization;

current amount of revenue from the sale of state-owned enterprises; Thus, the total amount of proceeds from the sale of state-owned enterprises in the interval is , and taking into account the state-owned enterprises, further submitted to the market, total revenue will

. (1.1)

Be it variable that describes the part of the workers who left the privatized state enterprises and found employment in private enterprises established in the privatization process. The absolute value of the number of workers who find work in the new private enterprises with growth time , calculated by the product . Note that this value increases the total current employment . difference describes the number of workers who are exempt from state enterprises. If ,

then the manpower requirements for new private enterprises (third group) will be fully met by workers who lose their jobs in state enterprises due to their privatization. On the other hand, if there is a less likely situation, ie ,

then the needs of the third group in the labor force will be met by the unemployed in the first two groups. Thus, we can write the following relationship: that a coefficient is

, (1.2)

where.

Write an expression that describes the amount of workers who lose their jobs as a result of privatization of state enterprises in some elemental spell : . This value reduces the total current employment . Thus we can write the following equation for the rate of change of current employment: or , and taking into account (1.2) we obtain . (1.3)

Consider the structure of the differential equation to describe the rate of change of the current production volume in the industry. Increase in volume production in the second group of enterprises is characterized by the product , and a decline in production at enterprises of the first group can be written expression . Increase in volume production at enterprises of the third group by time period can be described by the following equation:

. (1.4)

Thus, the rate of change of the volume of production in the industry as a whole is described by the following differential equation:

. (1.5)

Combining equation (1.1) (in differential form), (1.3) and (1.5), we obtain a system of equations describing the process of privatization of the industry on condition that they produce the same products before and after privatization: , (1.6)

, (1.7)

. (1.8)

Note that the current unemployment rate can be calculated by the expression

. (1.9)

A number of potential businesses you can create by attracting unemployed, calculated by the expression . (1.10) The resulting system of equations can be used to find the optimal (with respect to some chosen criterion) values of variables for the period of time designated for privatization. Obviously, for the formulation of the optimization problem it is necessary to impose restrictions on some variables.

Note that the function (speed of the privatization process) must be piecewise continuous. One of the possible strategies of the privatization process is the simultaneous privatization of the entire set of the industry that are brought to market privatization. However, this strategy is unacceptable to the socio-political and economic point of view because it has the following disadvantages: the rapid and uncontrolled growth of unemployment, a significant decline in production, the low probability of finding the necessary investments for a rapid transition to private ownership and further expansion of production volumes. It is therefore necessary to find a speed of privatization, which would optimize the values of the key variables. Limit the speed of privatization have the form

, (1.11)

and a fixed number of enterprises to be privatized . If you set the level of unemployment through , then the final time share of employment in the area should not be less than on the amount of labor that is released. On this basis, we can write the expression for employment at the end of the term privatization , (1.12)

and a simplified version with a fixed number of enterprises , that are brought to market privatization . (1.13)

Thus the launch of the privatization process must be defined with the following values: . For more complicated version when the number of enterprises to be privatized, is variable, it is necessary function. Restrictions on the proceeds from the sale of businesses . (1.14)

The initial conditions for the basic variables are:

. (1.15)

A mathematical model of the process of privatization, restrictions on the variables and initial conditions can make the formulation of the optimization problem.

Find an (optimal) speed implementation of the privatization process, which is described by a mathematical model , (1.16)

, (1.17)

, (1.18)

(1.19)

that maximizing the total production,

Where class of piecewise continuous functions over the planned privatization period with restrictions

, .

В formulation of this optimization problem is assumed that the market is made privatization a fixed number of enterprises , which does not change throughout the period of implementation of the process, ie , . An alternative formulation of the optimization problem is an option, complicated by the fact that the market for enterprises, which are made for sale, can be expanded during the period .

Consider possible alternative solution to the problem for model (1.17) - (1.19) using Lagrange multipliers. Instead of restricting Add additional variable with boundary conditions and . is the current number of privatized enterprises. By writing the Hamiltonian for this problem (1.28)

where ; introduced as a measure that is maximized; can be interpreted as the shadow price of production area; describes the dynamics of employment and dynamics of privatization market. Conjugated variables, determined by the following differential equations:

Where ; (1.29)

(1.30)

The terms transversality

;

(1.31)

The terms transversality . Thus, we can write that;

;

And terms transversality ,

, , . If і

, so we can get

, (1.32)

Where.

If - growing bent function, then there exists a unique solution of (1.32) defined for each point in time thus a necessary condition is also sufficient for optimality.

In order to get inputs for the model developed software that uses data from past years and forecasts the number of public companies that can be of privatization in these periods. To analyze the operation and was elected a number of times based on 15 values, ie, during the years of the privatization process in Ukraine.

Table 5.1 summarized the characteristics of mathematical models built for the privatization of group A, and features the same stepper projections calculated in these models.

Table 5.1

Type of model	characteristics of the model			Specifications forecast
Type of model			DW	RMSE	MAPE	Theil Coefficient
AR(1)	0,875844	157593,1	0,859390	192,7309	36,96071	0,202947
AR(3)	0,920181	68897,81	1,827690	68,82119	19,98405	0,077099
AR(6)	0,984161	1481,658	2,024068	12,12040	6,491308	0,024747
ARMA(1,1)	0,932531	85639,42	2,304531	61,66583	16,12263	0,050405
ARMA(2,1)	0,965990	38180,54	1,970234	81,16433	12,84269	0,074889
multiple autoregressive	0,758138	319088,5	0,920338	150,9703	33,96408	0,128580

Simulation results are presented in Table 5.1 indicate that all models except the first and last are suitable for modeling as Theil coefficient is measured in hundredths fate. The best model can be considered AR (6) and the set of regression of logarithms of data.

Predict the data for the next 3 years and will demonstrate in Table 5.2

5.1's represent the graph, what is the difference between the known and predicted data.

Figure 5.1 - Prediction 3 years AR (6)

Consequently, the graph shows that the AR (6) predicts fairly close privatization in transition economies Ukraine and we can get input.

The paper analyzes current privatization processes, methods and models to describe the process of privatization. And the algorithm of solving the problem of privatization. We consider the optimal model for our country to nearest privatization process proceeded normally and performed two functions; the state budget was increased and filled with employment. A mathematical model of the process of privatization in the form of differential equations of the first order. The model is used to solve the optimization problem of transformation of ownership at branch level.

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