Thus, the region has neither incentive to reduce taxes expecting transfer increase nor anti-incentives to foster own revenues growth for fear of transfer amount reduction. At the same time if α and γ values are big enough, then along with expenditure growth objective function value proves to be increasing without adequate tax growth reducing corresponding utility value for budget restriction comes soften on account of transfer value increase. It is in the same manner that expenditure reduction should lead to transfer decrease, which must be compensated by regional tax growth. Thus, choosing budget expenditures and tax values regional authorities gain incentives to regional expenditure increase on account of federal compensation for the gap between regional revenues and expenditure. As a result, optimum decision of the regional authorities could be characterized by the following relation between tax and expenditure marginal utilities:

UE=UT (1 - αγ) (30)

It means that in the optimum point marginal utility of expenditure growth is αγ times lower than marginal loss inflicted by tax burden increase. Given the assumed objective function convexity properties, the optimum will be achieved under high expenditures level andhigh own taxes level. In other words tax burden reduction compensating for regional expenditure decrease should be αγ times less than the latter.

On the contrary, when coefficient β is positive and coefficient α= 0, the transfers allocation mechanism is orientated to 'normative' expenditures amount and, if both β and γ values are big enough, to actual regional own revenues. Consequently tax reduction results in utility gain caused by tax burden decrease and absence of adequate utility loss attained by a less expenditure reduction on account of transfer growth, the latter partially compensating for regional public revenues decrease. It is in the same manner that expenditure growth by the amount less than corresponding regional revenues increase be caused by tax growth for alongside with that the transfer amount is decreasing. Thus, UE (1 - βγ) = UT, i.e. marginal utility of regional expenditures in the optimum point βγ times exceeds marginal loss inflicted by tax growth. It means that in order to compensate for utility decrease during expenditure reduction it is necessary that taxes be βγ times reduced. In this case, if the utility function has the assumed properties, the optimum will be achieved in low expenditure value and tax value point.

Solving the problem of utility maximization (21) within constraints (22) and (2323) we’ll get the following equations for optimum E* and T* dependent upon problem factors as well as for м that is Lagrange multiplier within constraint (27):

( 31)

( 32)

(33)

Thus, regional authorities’ optimum choice depends upon the rules applied to regional transfer allocation. Further on analyzing equations (31) – (32) we’ll arrive at a number of conclusions regarding the influence of IGFR structure exerted upon regional authorities’ fiscal behavior performed by the choice of this or that tax burden and budget expenditure level.

From equations (31) – (32) it can be concluded that optimum value of regional budget expenditure and tax amount are positively dependent upon Y. Alongside with that corresponding private derivative for T* is determined by the α value and is independent from transfer allocation structure, i.e. the higher α weight within objective function is assigned to private goods the less tax growth can be observed along with income increase. At the same time partial derivative E* with respect to Y also depends upon correlation between a and b. It means that along with Y growth optimum expenditure value is increasing according to ratio of α to β, and to be more exact according to marginal rate of substitution of expenditures for taxes in the optimum point: MRSET. The greater the marginal rate of substitution is, the more regional public expenditures increase along with Y growth.

Now, let us analyze, how the modification of different factors constituting the model and determining the transfers allocation mechanism exerts its influence upon regional authorities’ optimal choice. Changes in the Y value lead to proportional changes in transfer amount. If transfer allocation methodology is not determined by regional budget actual expenditures and tax revenues, the effect produced by changes in γ proves to be similar to the changes in lump-sum grant effect in the simplified model of choice between public and private goods, which leads to growth of public goods provision along with tax decrease (expenditure and tax value modification is dependent upon only income effect, see Fig. 1). In general within analyzed model the transfer amount is determined by the choice of regional authorities between budget revenues and expenditures, which after γ modification, besides income effect can cause a shift along indifference curve with simultaneous tax revenue and expenditure change made by regional authorities and attained by additional influence exerted by substitution effect. Therefore, it is not always possible that the sign of expected tax revenue and expenditure change be precisely determined.

Analyzing partial derivatives of optimum tax revenue and expenditure value it should be noted that four most common situations characterized by the parameters' values described below could be pointed out. These situations are defined by A and (α–β)

1. A>0, в>б.

Figure 2

2. A<0, б>в.

Figure 3

Besides, as it is shown in the figures, each of the two situations can be additionally characterized by the intersection point position of budget constraint and bisector relative to asymptote position.

3. A>0, б>в. Under such parameters' relationship the region always proves to be financial aid recipient.

Figure 4

4. A<0, в>б.

Within such relationship of parameters the region always proves to be a donor, i.e. the financial aid amount received is always negative.

Figure 5

Partial derivatives of optimum expenditure and tax value with respect to parameter γ go as follows:

( 34)

( 35)

Three different situations, which perform various results consequent on the change in transfer amount compensating for the gap between regional public revenues and expenditures, prove to be possible α=β, α>β, α<β. And as it was mentioned above, the situations additionally differ from each other depending on the A parameter sign f (A = (1-α)- (1-β).)23 and on following the condition of relationship between regional revenues amount and absolute value of A: Y<|A|/(α-β).

If б=в (inclusive of б=в=0 case), the region always proves to be a transferee under the condition that the part of the transfer calculated on the basis of objective factors within given values of б and в exceeds zero. (А > 0 or γА > 0) In this case transfer amount growth leads to the change in the regional authorities' choice of optimum taxation level and budget expenditure amount determined only by income effect (see Fig.6)

Figure 6

Judging by Fig. 6 we can assume that while changing its position from point 1 to point 2 budget constraint of the regional authorities is shifted to the north-west by the value of the budget constraint intercept change the latter being equal the change in transfer value:: Δ()=.Δγ. The shift proves to be parallel to its initial position (for budget constraint slope still equals 45˚, if б=в) Thus, even if regional decisions on tax revenue and budget expenditures levels exert an influence upon transfer value calculation (б and в do not equal zero), but rules of revenues and expenditures 'normative' values in transfers calculation prove to be symmetrical as long as transfer grows (consequent on value γ increase), the region lacks incentives to disproportional substitution of taxation level for budget expenditures (MRSET=1). It is determined by the fact that for each tax and expenditure value in budget constraint (i.e. the points that can be selected within assumed regional authorities objective function) transfer value remains the same and does not depend upon particular E and T value.

Thus, the model illustrates a well-known fact that when lump-sum (block) grant is received by the region, regional budget expenditures influenced by income effect comes to increase for a value less than the grant amount as well as tax burden level determined by income effect tends to decrease.

It is assumed that when A<0 and б=в the regions with negative transfer amount be considered. These are the regions characterized by fiscal capacity exceeding 'normative' expenditures taken with corresponding equal weights. In this case parameter γ growth (if б=в) causes negative income effect. Alongside with that budget constraint is shifted downwards, which results in tax increase and expenditure reduction.

The assumptions made are not dependent (if б=в) upon a particular type of regional authorities’ objective function. In the regarded case partial derivative of optimum tax value with respect to γ maintains its shape (34). Thus, it is in the same manner with general case that taxes be decreased along with transfer growth (if A>0), but if A<0 within donor region be increased. The derivative for optimum expenditure value with respect to γ looks as follows:

(36)

Thus, partial derivative value is totally determined by the sign of the A. If expenditure 'normatives' exceed regional fiscal capacity, growth if γ results in optimum expenditure increase (and tax revenue reduction), causing the shift from expenditure financing attained by tax revenue to the financing at the account of the grant. I.e. if A>0, regional public expenditures always proves to be growing on account of income effect while transfer is increasing. If A<0, expenditures prove to be reduced while negative transfer growth.

If б≠в, i.e. transfer rules are not symmetrical with regard to weights of revenues and expenditure 'normative' values, then along with γ growth the change in optimum regional tax revenues and budget expenditures is determined by both income effect and substitution effect.

If б≠в within the γ growth, the substitution effect is formally caused by budget constraint turn around point Т0= (characterized by zero transfer value), which leads both to intercept and slope of the budget constraint Е=γ.+∙Т change.

2. Let’s analyze the situation, when б>в. Such relationship between б and в means that transfers calculation methodology is orientated to actual expenditure rather than to actual taxes compared to their 'normative' values. Within such б and в values, if A>0, the region always proves to be the transferee. In this case (see picture 7), if γ value grows in point 1, then after being shifted to point 2 as well as after budget constraint turn optimum decision is achieved in point 3. It is possible that corresponding expenditure and tax changes be decomposed into changes gained by income effect and those attained by substitution effect.

Figure 7

It is obvious that expenditure growth and tax reduction (parallel shift of budget constraint to point 2) be determined by income effect. But unlike the previous case characterized by б and в equality, transfer value increase also leads to budget constraint turn. It means that while applying the rules of transfer calculation based upon actual expenditure rather than upon actual taxes (б>в), the region might add to expenditure value in order to gain the increase in transfer value (so as the transfer amount would be increased). Alongside with that it proves to be necessary that taxes be increased in order to balance the budget (i.e. γ doesn’t equal unity and the transfer is received regardless both expenditure needs 'normative' value and fiscal capacity). The process of budget constraint turn along the level line of regional authorities’ utility function lasts unless the following relationship between marginal utility of expenditure growth and marginal loss inflicted by tax increase is achieved:

(37)

Income effect always proves to be positive for budget expenditures and always negative for tax revenues. Substitution effect is always positive for expenditures and as for taxes substitution effect depends upon the change in the budget constraint slope. Rapid growth of angle coefficient facilitated by an excess of б value over в, i.e. by orientation to actual public expenditures rather than actual taxes, comes to determine positive substitution effect for taxes, otherwise the latter is negative. Therefore, transfer value growth may result in either chosen regional tax revenue increase or decrease.

Figure 8

If A>0 (the region always proves to be financial aid recipient) in the model modification under consideration, characterized by partial derivatives of optimum tax and expenditures values (34) – (35), tax value is always decreasing along with γ value growth (that is with transfer growth) for corresponding derivative is negative. If A<0 the derivative of optimum tax value with respect to γ is always positive. As a result regional authorities’ tax revenue increase is consequent on y growth (if б>в and A<0 the region can be either a donor or a transferee). It proves to be true both for a donor region and a transferee. In the latter case taxation level growth caused by transfer increase is determined by an excess of substitution effect over income effect.

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