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Consequently, it is expedient that representative taxpayer be considered as the agent, whose preferences are considered while the regional leader determines his behavior. Moreover it is possible that the whole household comprising three generations be regarded as economic agent and it might be assumed that such enlarged household system in the region be homogeneous9:

( 3)

where c – the amount of representative household public goods consumption;

Ls – household labor supply for private sector (it will be assumed that the number of public sector employees and their labor time be exogenously given and each enlarged household has similar number of workers);

E – budget expenditure for public goods provision;

th– vector of tax variables used in the model for the household budget constraint;

– wages value which is determined by labor market or by other factors,

Budget constraint for household goes as follows:

,

, (4)

where

W –wages in the private sector;

Ld – aggregate labor demand of the firms;

B – the variable comprising the sum of budget allowances, pensions and public sector wages received by the family members;

Th – total amount of taxes paid by representative household.

The fact that total tax amount is included in the budget constraint doesn’t mean that the taxes should be considered lump-sum. It is possible that income tax and sales tax be included in the model as:

( 5)

Then budget constraint for the household will be as follows:

(6)

where

w – after-tax private sector wages,

tw – personal income tax rate,

ts – effective rate of taxes levied on consumption (in particular – sales tax rate),

th + (tw, ts) – vector of household tax variables.

Now let’s return to function P (∙) If it can be assumed that special group interests are limited by regional big business interests in the model, then this function will represent expected disposable income utility received by enterprise owners inclusive, generally speaking, of sheltered income regarding possibility of tax breach exposure. Besides, legal tax evasion could be possible and its degree may depend upon budget policy transparency. In a simplified case an assumption can be made that income tax return be correct, then disposable after-tax net income will manifest itself as function P (∙) value. In order to simplify the model it’s advisable a short-term period be considered and our assumption be derived from aggregate production function of the regional large business enterprise, which goes as follows:

( 7)

where Ld – enterprise labor demand.

Assume the competitive market, then prices would be considered exogeneously given. To simplify set the product price as unity.

In this case

(8)

where

tf – vector of tax variables used for enterprise profit calculation,

Tf – aggregate tax liabilities of the firm (it may be not lump-sum as in the household case)

FC – enterprise fixed costs.

If regional labor market competition is imperfect, w might be considered as function of L.Besides, as it was mentioned above, it is not obligatory that the market determine wage value. Within a more complicated task performed, it is possible to regard unemployment level value as a function variable estimating the Federal Center attitude towards the policy pursued by the regional authorities. But in the preliminary analysis of the model of interbudgetary transfers influence upon the regional authorities’ decisions P (∙) function will be omitted and only household utility for creating labor demand and wages level will be analyzed under assumption of exogenously given values of labor demand and wages.

It is also possible that the model get more complicated by regarding production function to be dependent upon public goods provision level.

S (∙) can be considered as bureaucrats utility function depending on public goods production level and/or special groups income. Its value might be determined by a possibility that the officials will take discretionary decisions10. In the introduction it was mentioned which factors may exert an influence upon function value defining the Federal Center estimation given to the regional leader performance. But at present stage of model analysis this influence won’t be regarded.

Therefore, the system describing regional leader’s behavior comprises regional leader’s objective function (1). The variables of this function are based upon objective functions of the groups, whose interests must be considered by a regional leader striving for power maintenance or growth, i.e. functions (3), (7) and S (∙), F (∙) functions, which were not detailed at the formal level, as well as budget constraints described in equations (2) and (5). In the preliminary analysis the Federal Center influence won’t be regarded exclusive of federal authorities influence exerted upon transfers amount received by the region.

Therefore, regional authorities’ objective function will be regarded as follows:

(9)

Besides, in the simplified model it will be assumed that S entirely depends upon Z, i.e. upon the sum expended on officials’ interests, the amount of which is defined by the regional leader. Consequently, regional leader’s objective function goes as follows:

(10)

As long as even after such simplifications the model tends to be rather complicated, it is necessary that a series of further simplifications be performed in order to determine the influence exerted by intergovernmental grants allocation methods upon regional leader’s behavior.

Now the situation when the regional leader can change only tax revenues collected in the region and received by the regional or local budget as well as expenditures on public goods provision value will be analyzed. Both wages level and labor demand are exogenously given (the latter is considered by households as exogenous for it is defined on the basis of enterprise profit maximization) as well as pecuniary reward value of the regional government officials is also exogenously defined.

In this case Z and, consequently, S (Z), as well as B prove to be constants and for that reason the will be regarded in neither utility function nor budget restriction11. Then the leader maximizes the following function:

(11)

subject to E = T + Tr, (12)

where T = Tf + Th

Then

(13)

subject to

(14)

If it is assumed that enterprise taxation level is not varied by the regional leader12, then

(15)

In this case if Tf as well as other constants is not considered in regional leader’s budget constraint, then T = Th.

Labor demand is uniquely determined by exogenously given wages and profit which follows from the maximization condition. If it is assumed that there is no labor deficit, then it is possible to define household labor amount, i.e.

(16)

P (∙) value can also be uniquely defined and region leader’s final objective function will comprise it as a constant.

Then, as long as household labor amount and wages are sharply defined, it is necessary that a new notation be introduced

(17)

Then household budget constraint goes as follows:

(18)

If c is substituted in the household utility function (regarding L as uniquely determined), we get.

If it is assumed that household system be homogeneous, regional leader’s utility function comes to be as follows:

(19)

where ;

– fixed value of after-tax (disposable) income received by enterprise owners.

The task can also be formulated as maximization of some regional leader’s utility function U (E,T), subject to the condition of E = T + Tr.

The analysis of a simplified model of regional fiscal behavior under regional authorities utility function of Cobb-Douglas type

In order to define the influence exerted by the basic features of intergovernmental transfers system upon regional fiscal policy a simplified variant of one of the model types described above should be analyzed. It might be assumed that objective function be dependent only upon two variables: regional consolidated budget expenditure amount (positively) and tax revenues received by the regional budget (negatively) both determined by selected level of regional and local tax rates as well as by shared federal tax revenues received by the regional and local budget:

( 20)

where E – the RF Subject consolidated budget expenditures (as an indicator reflecting level of public goods provision in the region),

T – tax revenues of the RF Subject consolidated budget (regional and local tax revenues as well as revenues from federal shared taxes received by regional and local budgets)13.

Regarding utility function as mentioned above, we can assume that public transfers (cash or in-kind) are not included into regional budget expenditures and budget revenues are based on tax payments leading to reduction in public goods consumption experienced by economic agents other than the state. According to this assumption the formula can be regarded as a problem similar to the>14. For example, Williams assumed15 that local communities possess indifference curves of choice between private and public goods similar to individual indifference curves. The formula (20) can be shaped as follows:

( 21)

where Y – regional disposable income.

Such formula makes it possible to consider that tax growth leads to reduction in disposable income as well as in private goods consumption. This type of objective function will be analyzed below16. As it was demonstrated above, the equation (20) results from more general assumptions about regional authorities behavior, therefore, the choice between regional budget revenues and expenditures will be regarded as some general model comprising different groups taking an interest in it. However the conclusions we arrive at below prove to be true for a simple model describing consumer’s choice based on transfer formula of a certain type.

The regional authorities maximize utility function (20) or (21) along with budget constraint (22) consisting in the assumption that expenditures can’t exceed the sum of revenue amount and the amount of federal transfer received:

≤ +Tr ( 22)

And the transfer from the federal budget is calculated by the federal fiscal authorities in proportion of y to the gap between regional budget revenues and expenditures. According to the coefficient value the gap range between revenue and expenditure side is based upon either actual (reported) expenditure amount or regional expenditure needs. It is in the same manner that coefficient value determines the weight of actual budget revenues or revenue capacity in calculating the revenue item in the regional expenditures less revenues gap calculation.

17 ( 23)

where Tr – financial aid value received by the region from the federal budget (FFAR transfers, subventions, state subsidies, mutual settlements, etc.)

T – regional tax revenues (regional, local as well as federal tax revenues received by regional budget). In order to simplify the calculation it might be assumed that lump-sum taxes are used;

E – regional budget expenditures;

– regional fiscal capacity calculated according to tax income.

– regional expenditure needs standards (some 'normative' expenditures calculated by the federal fiscal authorities concerning estimates of regional expenditure needs and federal priorities in regional development).

In the countries with multi-leveled budgetary system it is formally declared that intergovernmental equalization programs implemented are aimed at equalizing the ability of sub-national governments to provide public goods. Those programs if looked at from the economist point of view are based on the estimates of subnational jurisdictions' fiscal capacity and/or their expenditure needs. But in practice interbudgetary equalization mechanisms (inclusive of FFAR allocation methodology used in Russia at the present moment) are aimed at filling (at a certain ratio) the gap between regional revenues and expenditures rather than at equalizing the potential level of public services provision. Besides, both fiscal capacity and expenditure needs estimates are based (to some extent) on actual revenues and expenditures figures.

This fact makes it possible to devise financial aid allocation formula as (23). Coefficients α and value in regard to some particular equalization program can be interpreted as the degree of actual budget execution data influence exerted upon regional fiscal capacity and expenditure needs calculation. As well as coefficient value shows intergovernmental financial aid influence exerted upon recipients’ gap between certain estimates of budget expenditures and revenues.

Conformably to Russia it means that at present actual function of equalization transfers received by the regions from the federal fund for financial assistance to regions doesn’t consist in regional minimum level of public goods provision equalization in terms of public goods provision or budget revenues but in filling up the gap between expenditures set by legislation and potential (calculated according to the Federal Center data) budget revenues. In practice expenditure responsibilities and potential revenue calculation to more or less extent (in different years)18 depended upon both actual revenues along with expenditure value and expenditure needs as well as fiscal capacity estimates. If other kinds of federal financial aid could be considered in addition to FFAR transfers, then it would be possible to state that actual budget revenues of Federal subject and expenditures regarded within financial aid allocation methodology be more important than tax capacity and expenditure needs values19.

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