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Transfers or public good provision? A political allocation perspective
economics letters Economics
ELSEVIER
Letters
45 (1994) 451-457
Transfers or public good provision? A political allocation perspective Shmuel Nitzan Department of Economics,
Bar-Ilan University, 52900 Ramat-Gan,
Received 18 November
1993; accepted
7 February
Israel
1994
Abstract Employing an extended rent-seeking model this paper focuses on the problem faced by an optimizing politician of allocating a given budget among monetary transfers to individuals, monetary transfers to groups and public-good transfers to groups. JEL
classification: D72
1. Introduction
The objective of this paper is to identify circumstances that give rise to specific patterns of government spending. The proposed approach is based on an extended rent-seeking model. Although this model is rather restrictive, it is an appropriate vehicle for a first investigation of the complicated issue at hand. The literature on rent seeking has investigated rent dissipation when (i) there is but a single potential beneficiary of the rent, (ii) the rent is indivisibly allocated and therefore the contest is for the entire rent, and (iii) the rent exhibits private good characteristics.’ A number of studies have departed from these assumptions. Katz et al. (1990), Long and Vousden (1987) and Ursprung (1990) analyzed situations where groups compete for the supply of a public good. Competition by groups for a private-good transfer is analyzed in Nitzan (1991). In Gradstein and Nitzan (1989) the assumption of individual rent seeking is retained, but there are multiple contests. In general, the political process of rent or transfer allocation may be such that none of the initial three assumptions need hold. There may be multiple rents to be allocated, the transfers may have either public or private good characteristics and they may be allocated to individuals or groups of individuals. In the current paper I focus on the following problem faced by a politician: how to allocate 1 See the review
of the literature
in Hillman
0165-1765/94/$07.00 0 1994 Elsevier SSDI 0165-1765(94)00446-9
Science
(1989, ch. 6). B.V. All rights reserved
452
S. Nitzan I Economics Letters 45 (1994) 451-457
a given budget among the three possible types of transfers (monetary transfers to individuals, monetary transfers to groups and public-good transfers to groups). It is shown that the politician’s equilibrium strategy entails selection of an extreme type of portfolio of transfers consisting of just one type of transfer. The main proposition specifies the condition determining the nature of the preferred type of transfer in terms of the environmental parameters: the distribution of potential individual beneficiaries of the rents, the number of groups competing, the rule used to distribute private good transfers within groups, and the individual valuation of the local public good. Consider a politician who has the discretion to allocate a fixed budget. N individuals are divided into t groups that stand to benefit from the transfers, which may take the form of private or public goods. The equilibrium on which the analysis focuses is the outcome of a two-stage (N + 1)-player game in which the politician appropriates a fraction of the transferseeking expenditures. In the first stage of the game he acts as a Stackelberg leader taking into account the reactions of the transfer seekers in determining how to allocate the rent to maximize his expected income. In the second stage, the N risk-neutral individuals decide upon their expenditures. This extended multiple transfer-setting-transfer-seeking game is described in section 2. Section 3 characterizes the equilibrium allocation of transfers. The paper concludes with a brief summary.
2. The model A politician has discretion over the allocation of a given budget, So. The budget can be divided into m components for which individuals or groups may compete. The politician’s sole objective is to maximize total transfer-seeking expenditures because he receives a certain fraction, (Y, of these resources.’ Suppose that there exist t well-defined coalitions seeking the transfer. The number of the divisible individuals in group i, i E I, Z = { 1, . . . , t}, is n(i) and the rule for distributing a of the transfer is equally transfer among the members of a winning group is f”; a proportion shared by the group members and the remainder is shared according to the principle ‘to each according to his relative effort’. Confronted with the t groups and given their size distribution, n(l), . . . , n(t), and the common sharing rule, f”, the politician designs a three-element system of transfers. First, he divides the budget So into m components, that is, he selects an m-tuple S = (S,, . . . , S,) such he decides whether each comthat Sj > 0, i = 1, . . . , m, and S, + * * . + S, = So. Secondly, ponent S, is to be a private (monetary) transfer or a local public good transfer. In the former case, Sj is shared by the members of the winning group according to the rule f”. In the latter case, each individual in the group securing the public good provision values it at &Sj. 6 is the common individual monetary equivalent valuation of one dollar spent on the public-good transfer. Note that in our stylized model there is just one public good, S, is sufficient to produce the public good for a single group only, independent of its size, and 6 is a constant independent of Sj. * For a discussion
of rent dissipation
by a politician,
see Appelbaum
and Katz (1986).
453
S. Nitzan I Economics Letters 45 (1994) 451-457
Let sj be a decision variable indicating whether Sj is a private-good transfer (sj = 1) or a public-good transfer (sj = -1). The m-tuple (si, . . . , sm) is the second element of the transfer portfolio. Finally, the politician has to associate with each component Sj the set of groups competing for it. This subset of contesting groups is denoted Gj, Gj C I. The number of groups in G, is on the denoted tj, tj = IG,l, and the number of individuals in Gj, the individual contestants transfer Sj, is denoted Nj, Nj = CiEc n(i). If G, = I, Nj = N = ci,, n(i) is the total number of potential individual transfer seekers and t: = t. The m-tuple G = (G,, . . . , G,) is the third element of the rent allocation system. Given the parameters n(l), . . , n(t), f”, S” and S, the politician selects a portfolio of transfers [(S,? . . . , S,), (~1,. . . , s,), (G,, . . . , G,)] that maximizes total expenditure on transfer seeking in the m independent contests. Being a leader in the two-stage transfer-setting-transfer-seeking game, he takes into account the total expenditures at the Nash equilibria of the independent subgames corresponding to the contests characterized by the typical triples (Sj, si, G;). Consider the contest (Si, si, Gi). If sj = 1, the t, contesting groups in G, confront the opportunity of winning the monetary transfer S,. The success probability of each group participating in contest j is given by the value of its transfer-seeking outlays relative to the outlays made by all groups engaged in contest j. Given f” and assuming risk neutrality one obtains the game studied in Nitzan (1991). The total transfer-seeking outlays at the Nash equilibrium of this game are given by3 X’ = X(S,, 1, G,) = S,
[( 1 - a)A$ + t/a - l] N, ’
If sj = - 1, the groups compete for a public-good transfer. The equilibrium public-good transfer seeking is given by [see Katz et al. (1990)] X’=X(S,,
expenditure
on the
(I. - 1)
-1, G,) =+““i.
I
The transfer allocation following problem:
pattern
chosen by the politician is thus determined
by the solution
to the
mrllxc a[X’ +x2 + . ’ . + Xrn] = y*(sO, 6, a, n(l), . . . ) n(t)) . ,.
s.t. (i) m I 1 and for j = 1, _ . . , m , (ii) sj > 0 and 2 S, = So
,
j=l
(iii) s, E (1, -l}
,
(iv) G, C Z and
3 Henceforth the analysis focuses on interior equilibria assuming that individuals to carry out the desired
level of the transfer-seeking
activity.
always have sufficient
resources
454
S. Nitzan
I Economics
Letters 45 (1994) 451-457
The constraints (i), (ii), (iii) and (iv) relate, respectively, to the basic requirements of the three elements of the transfer-allocation system. The fifth constraint relates the equilibrium outlays in contest j to the control variables S,, s, and G,. The function y*(S, 6, a, n(l), . . . , n(t)) is the indirect utility function of the politician.4
3. Equilibrium
transfer setting
Given the functional form of X’(Sj, sj, Gj), it is clear that if two contests, r and I/, (S,, s,, G,) and (Sy, s,, G,), differ essentially in their first component, i.e. either s, = s, = -1 and D, = D,, where Dj = [( 1 - a)Nj + tja - l]/Nj, or s, = sy = -1 and t, = t,, then the sum of their equilibrium expenditures, X’ + X”, is equal to the equilibrium outlays in the contest (S, + S,, s,, G,) or in the contest (S, + S,, s,, G,). This property justifies the assumption that the politician economizes on the number of contests, that is, he does not design contests whose essential difference is only in the first component. He will then never divide his budget into more than two components. Furthermore, if he divides his budget into two components he will design a two-element system of contests with one private-good contest and one public-good contest. In general, the politician does not divide his budget and his problem reduces to the choice between the private and public transfer-seeking contests that yield the largest outlays. His decision hinges on the relationship between N, t, f”, SSfl and the distribution of individuals across the existing groups.
Proposition 1. Let (m *, S* , s*, G*) be a solution to the politician’s problem. ifm*= 2, ST zs;.
Then m * 5 2, and
Proof. Suppose, to the contrary, that m* L 3, or m* = 2 and ST = sz. Since, by assumption, the optimal system of transfers does not contain contests differing essentially in their first component, there are at least two contests, r and V, satisfying either ST = s*, = 1 and D, # Dy or ST = s*, = -1 and t, # t,. With no loss of generality, let D, > Dy in the former case and t, > t, in the latter case. By (1) and (2), in either case X’ + X” < X(ST + St, ST, GT), which contradicts the optimality of (m*, S*, s*, G*). Q.E.D. By Proposition 1, the politician chooses to divide his budget into at most two components. Denote by (So, 1, G,) the monetary transfer contest yielding the maximal equilibrium transfernumbers of contesting groups and seeking outlays, given the budget So. The corresponding individual transfer seekers are t, and N,.5 By (2), (So, - 1, Z) is the contest on the provision of the public good yielding maximal transfer-seeking expenditures. If the politician divides the budget, then part of it, p, becomes a monetary transfer and the residual, 1 - p, is allocated to the provision of the public good. Proposition 1 implies that the problem the politician faces can be rewritten as follows: 4 Since, by assumption, (Y is a constant which does not affect the solution of the politician’s problem, it is deleted from the set of parameters determining the form of the indirect utility function. in both N, and t, and, therefore, the contest (S”, 1, Z) ‘Notice that when a 5 l/t, X(S,, 1, G,) IS increasing maximizes the equilibrium expenditure on monetary transfer seeking. In such a case N, = N and t, = t.
4.55
S. Nitzan I Economics Letters 4.5 (1994) 451-457
mp”” s.t.
4Xp + X(l-p)l ,
(i) 0 I p 51
@) x = PS”Kl - m + ta - 11and P N (iii)
x
_
(1
=
(1 - P)=“(t - 1)
P)
t
Clearly, if XP ZXcl_p, Hence
or
[(l - a)N, + t,a - l] ~ s(t - 1) N, =t’
p*, of the reduced
the solution
problem
is given by:
Proposition 2.
1, =o, =
l[OJI The indirect
if 6 5 ~ t (t
_
1)
[Cl- 44 + t,a- 11= NI
B
7
utility
function
of the politician
thus takes the following
czS’[(l - a)N, + tla - l] y*(SO, 6, a, n(l),
. . . , n(t))
=
Nl aGSO(t - 1) t
’
,
form:
if6
Since the objective function is linear in p, we obtain a corner solution - when 6 differs from the critical value B the politician does not divide his budget. Since B is decreasing in a, ceteris paribus, he is more likely to prefer provision of a public good when the transfer-seeking environment is more egalitarian - a is larger. The reason is the following: as a increases, the free-riding incentives within the contesting groups become stronger. Consequently, the total transfer-seeking outlays associated with a private-good transfer, and, in turn, the fraction of these outlays that reach the politician, is reduced. A sufficient reduction in these expected benefits will induce the politician to allocate his budget to the alternative option, the provision of the local public good. In more egalitarian societies he is therefore more inclined to provide the local public good.6’7
‘When N[ = N and t, = t, the effect of both t and N on B is ambiguous. ’ Proposition 1 implies that when each individual is indifferent between receiving one dollar or seeing that dollar transformed into the public good (6 = l), which means that the effectivity of one dollar spent on the provision of a local public good to group i is n(i) times higher than the effectivity of transferring one dollar to that group, the politician creates a private (public) good transfer-seeking game if a is smaller (larger) than
456
S. Nitzan
I Economics
Letters
45 (1994) 451-457
By (l), X(S,, 1, G,) is decreasing in a. If the politician can determine the rule f ‘, he will maximize a by setting a = 0. That is, he will prefer the sharing rule based on the principle ‘to each according to his relative effort’. This sharing rule minimizes the free-riding incentives within the groups competing for the private-good transfer, and thus maximizes the value of the resources reaching the politician when he chooses to set up such a private-good, transferseeking game. With a = 0, X(Sj, 1, G,) is independent of tj and is increasing in N,. Consequently, the feasible private-food transfer contest yielding the maximal equilibrium outlays is (SO, 1, Z) and X(S”, 1, Z) = S (N - 1)/N. By Proposition 2, when the politician designs the transfer allocation system determining both p and a, he will prefer the monetary transfer if the individual valuation of one dollar spent on the provision of the local public good is sufficiently small, namely if 6 < t(N - l)/ (t - l)N. This condition is necessarily satisfied when 6 I 1 since t(N - l)l(t - l)N 2 1. In such a case transfer sharing will be based on the principle ‘to each according to his relative effort’. By (I), X(Sj, 1, G,> is increasing in t. If the politician can determine the partition of the total population into contesting groups, he will maximize X(Sj, 1, G,) by setting t, = N. That is, from the politician’s standpoint, since he is interested in eliminating the free-riding incentives, individual rather than collective transfer seeking is always advantageous. In such a case the maximal equilibrium outlays are equal to S”(N - 1)/N. By Proposition 2, the politician will prefer to make a monetary transfer (p * = 1) if 6 < 1, and he will prefer the provision of a local public good (p * = 0) when 6 > 1.
4. Summary Politicians often have discretion regarding the manner in which they can allocate their political prizes. This paper investigated the relationship between equilibrium political transfer allocation and the transfer-seeking environment as described by the distribution of potential beneficiaries of the transfers across the groups, the rule used to share monetary transfers, and the relative value of a dollar spent on the provision of a local public good. In our stylized setting the politician usually selects an extreme strategy that entails either offering the entire budget as a private-good transfer or using it to provide a local public good to one of the contesting groups. The principal result is the condition that determines which of the two extreme strategies is chosen. If the politician can control the sharing rule within groups, he prefers the rule based on the principle ‘to each according to his relative effort’, since this rule minimizes the free-riding incentives within the groups, and thus maximizes the value of the transfer to the politician. If he can control the number of groups contesting the transfers, he would attempt to increase that number, since, from his viewpoint, t = N is optimal; in that case free-riding incentives are eliminated, regardless of whether the politician chooses the transfer or the provision of the public good.
References Appelbaum, Economic
Eli and Eliakim Katz, Journal 97, 685-699.
1986, Seeking
rents
by setting
rents:
The political
economy
of rent seeking,
S. Nitzan I Economics Letters 45 (1994) 451-457 Gradstein, Mark and Shmuel Nitzan, 1989, Advantageous multiple rent seeking, Mathematical Modelling 12, 511-518. Hillman, Arye L., 1989, The political economy of protection (Harwood Academic Publishers, London and New York). Katz, Eliakim, Shmuel Nitzan and Jacob Rosenberg, 1990, Rent seeking for pure public goods, Public Choice 65, 49-60. Long, Ngo Van and Neil Vousden, 1987, Risk averse rent seeking with shared rents, Economic Journal 97, 971-985. Nitzan, Shmuel, 1991, Collective rent dissipation, Economic Journal 101, 1522-1534. Ursprung, Heinrich W., 1990, Public goods, rent dissipation and candidate competition, Economics and Politics 2, 115-132.
ELSEVIER
Letters
45 (1994) 451-457
Transfers or public good provision? A political allocation perspective Shmuel Nitzan Department of Economics,
Bar-Ilan University, 52900 Ramat-Gan,
Received 18 November
1993; accepted
7 February
Israel
1994
Abstract Employing an extended rent-seeking model this paper focuses on the problem faced by an optimizing politician of allocating a given budget among monetary transfers to individuals, monetary transfers to groups and public-good transfers to groups. JEL
classification: D72
1. Introduction
The objective of this paper is to identify circumstances that give rise to specific patterns of government spending. The proposed approach is based on an extended rent-seeking model. Although this model is rather restrictive, it is an appropriate vehicle for a first investigation of the complicated issue at hand. The literature on rent seeking has investigated rent dissipation when (i) there is but a single potential beneficiary of the rent, (ii) the rent is indivisibly allocated and therefore the contest is for the entire rent, and (iii) the rent exhibits private good characteristics.’ A number of studies have departed from these assumptions. Katz et al. (1990), Long and Vousden (1987) and Ursprung (1990) analyzed situations where groups compete for the supply of a public good. Competition by groups for a private-good transfer is analyzed in Nitzan (1991). In Gradstein and Nitzan (1989) the assumption of individual rent seeking is retained, but there are multiple contests. In general, the political process of rent or transfer allocation may be such that none of the initial three assumptions need hold. There may be multiple rents to be allocated, the transfers may have either public or private good characteristics and they may be allocated to individuals or groups of individuals. In the current paper I focus on the following problem faced by a politician: how to allocate 1 See the review
of the literature
in Hillman
0165-1765/94/$07.00 0 1994 Elsevier SSDI 0165-1765(94)00446-9
Science
(1989, ch. 6). B.V. All rights reserved
452
S. Nitzan I Economics Letters 45 (1994) 451-457
a given budget among the three possible types of transfers (monetary transfers to individuals, monetary transfers to groups and public-good transfers to groups). It is shown that the politician’s equilibrium strategy entails selection of an extreme type of portfolio of transfers consisting of just one type of transfer. The main proposition specifies the condition determining the nature of the preferred type of transfer in terms of the environmental parameters: the distribution of potential individual beneficiaries of the rents, the number of groups competing, the rule used to distribute private good transfers within groups, and the individual valuation of the local public good. Consider a politician who has the discretion to allocate a fixed budget. N individuals are divided into t groups that stand to benefit from the transfers, which may take the form of private or public goods. The equilibrium on which the analysis focuses is the outcome of a two-stage (N + 1)-player game in which the politician appropriates a fraction of the transferseeking expenditures. In the first stage of the game he acts as a Stackelberg leader taking into account the reactions of the transfer seekers in determining how to allocate the rent to maximize his expected income. In the second stage, the N risk-neutral individuals decide upon their expenditures. This extended multiple transfer-setting-transfer-seeking game is described in section 2. Section 3 characterizes the equilibrium allocation of transfers. The paper concludes with a brief summary.
2. The model A politician has discretion over the allocation of a given budget, So. The budget can be divided into m components for which individuals or groups may compete. The politician’s sole objective is to maximize total transfer-seeking expenditures because he receives a certain fraction, (Y, of these resources.’ Suppose that there exist t well-defined coalitions seeking the transfer. The number of the divisible individuals in group i, i E I, Z = { 1, . . . , t}, is n(i) and the rule for distributing a of the transfer is equally transfer among the members of a winning group is f”; a proportion shared by the group members and the remainder is shared according to the principle ‘to each according to his relative effort’. Confronted with the t groups and given their size distribution, n(l), . . . , n(t), and the common sharing rule, f”, the politician designs a three-element system of transfers. First, he divides the budget So into m components, that is, he selects an m-tuple S = (S,, . . . , S,) such he decides whether each comthat Sj > 0, i = 1, . . . , m, and S, + * * . + S, = So. Secondly, ponent S, is to be a private (monetary) transfer or a local public good transfer. In the former case, Sj is shared by the members of the winning group according to the rule f”. In the latter case, each individual in the group securing the public good provision values it at &Sj. 6 is the common individual monetary equivalent valuation of one dollar spent on the public-good transfer. Note that in our stylized model there is just one public good, S, is sufficient to produce the public good for a single group only, independent of its size, and 6 is a constant independent of Sj. * For a discussion
of rent dissipation
by a politician,
see Appelbaum
and Katz (1986).
453
S. Nitzan I Economics Letters 45 (1994) 451-457
Let sj be a decision variable indicating whether Sj is a private-good transfer (sj = 1) or a public-good transfer (sj = -1). The m-tuple (si, . . . , sm) is the second element of the transfer portfolio. Finally, the politician has to associate with each component Sj the set of groups competing for it. This subset of contesting groups is denoted Gj, Gj C I. The number of groups in G, is on the denoted tj, tj = IG,l, and the number of individuals in Gj, the individual contestants transfer Sj, is denoted Nj, Nj = CiEc n(i). If G, = I, Nj = N = ci,, n(i) is the total number of potential individual transfer seekers and t: = t. The m-tuple G = (G,, . . . , G,) is the third element of the rent allocation system. Given the parameters n(l), . . , n(t), f”, S” and S, the politician selects a portfolio of transfers [(S,? . . . , S,), (~1,. . . , s,), (G,, . . . , G,)] that maximizes total expenditure on transfer seeking in the m independent contests. Being a leader in the two-stage transfer-setting-transfer-seeking game, he takes into account the total expenditures at the Nash equilibria of the independent subgames corresponding to the contests characterized by the typical triples (Sj, si, G;). Consider the contest (Si, si, Gi). If sj = 1, the t, contesting groups in G, confront the opportunity of winning the monetary transfer S,. The success probability of each group participating in contest j is given by the value of its transfer-seeking outlays relative to the outlays made by all groups engaged in contest j. Given f” and assuming risk neutrality one obtains the game studied in Nitzan (1991). The total transfer-seeking outlays at the Nash equilibrium of this game are given by3 X’ = X(S,, 1, G,) = S,
[( 1 - a)A$ + t/a - l] N, ’
If sj = - 1, the groups compete for a public-good transfer. The equilibrium public-good transfer seeking is given by [see Katz et al. (1990)] X’=X(S,,
expenditure
on the
(I. - 1)
-1, G,) =+““i.
I
The transfer allocation following problem:
pattern
chosen by the politician is thus determined
by the solution
to the
mrllxc a[X’ +x2 + . ’ . + Xrn] = y*(sO, 6, a, n(l), . . . ) n(t)) . ,.
s.t. (i) m I 1 and for j = 1, _ . . , m , (ii) sj > 0 and 2 S, = So
,
j=l
(iii) s, E (1, -l}
,
(iv) G, C Z and
3 Henceforth the analysis focuses on interior equilibria assuming that individuals to carry out the desired
level of the transfer-seeking
activity.
always have sufficient
resources
454
S. Nitzan
I Economics
Letters 45 (1994) 451-457
The constraints (i), (ii), (iii) and (iv) relate, respectively, to the basic requirements of the three elements of the transfer-allocation system. The fifth constraint relates the equilibrium outlays in contest j to the control variables S,, s, and G,. The function y*(S, 6, a, n(l), . . . , n(t)) is the indirect utility function of the politician.4
3. Equilibrium
transfer setting
Given the functional form of X’(Sj, sj, Gj), it is clear that if two contests, r and I/, (S,, s,, G,) and (Sy, s,, G,), differ essentially in their first component, i.e. either s, = s, = -1 and D, = D,, where Dj = [( 1 - a)Nj + tja - l]/Nj, or s, = sy = -1 and t, = t,, then the sum of their equilibrium expenditures, X’ + X”, is equal to the equilibrium outlays in the contest (S, + S,, s,, G,) or in the contest (S, + S,, s,, G,). This property justifies the assumption that the politician economizes on the number of contests, that is, he does not design contests whose essential difference is only in the first component. He will then never divide his budget into more than two components. Furthermore, if he divides his budget into two components he will design a two-element system of contests with one private-good contest and one public-good contest. In general, the politician does not divide his budget and his problem reduces to the choice between the private and public transfer-seeking contests that yield the largest outlays. His decision hinges on the relationship between N, t, f”, SSfl and the distribution of individuals across the existing groups.
Proposition 1. Let (m *, S* , s*, G*) be a solution to the politician’s problem. ifm*= 2, ST zs;.
Then m * 5 2, and
Proof. Suppose, to the contrary, that m* L 3, or m* = 2 and ST = sz. Since, by assumption, the optimal system of transfers does not contain contests differing essentially in their first component, there are at least two contests, r and V, satisfying either ST = s*, = 1 and D, # Dy or ST = s*, = -1 and t, # t,. With no loss of generality, let D, > Dy in the former case and t, > t, in the latter case. By (1) and (2), in either case X’ + X” < X(ST + St, ST, GT), which contradicts the optimality of (m*, S*, s*, G*). Q.E.D. By Proposition 1, the politician chooses to divide his budget into at most two components. Denote by (So, 1, G,) the monetary transfer contest yielding the maximal equilibrium transfernumbers of contesting groups and seeking outlays, given the budget So. The corresponding individual transfer seekers are t, and N,.5 By (2), (So, - 1, Z) is the contest on the provision of the public good yielding maximal transfer-seeking expenditures. If the politician divides the budget, then part of it, p, becomes a monetary transfer and the residual, 1 - p, is allocated to the provision of the public good. Proposition 1 implies that the problem the politician faces can be rewritten as follows: 4 Since, by assumption, (Y is a constant which does not affect the solution of the politician’s problem, it is deleted from the set of parameters determining the form of the indirect utility function. in both N, and t, and, therefore, the contest (S”, 1, Z) ‘Notice that when a 5 l/t, X(S,, 1, G,) IS increasing maximizes the equilibrium expenditure on monetary transfer seeking. In such a case N, = N and t, = t.
4.55
S. Nitzan I Economics Letters 4.5 (1994) 451-457
mp”” s.t.
4Xp + X(l-p)l ,
(i) 0 I p 51
@) x = PS”Kl - m + ta - 11and P N (iii)
x
_
(1
=
(1 - P)=“(t - 1)
P)
t
Clearly, if XP ZXcl_p, Hence
or
[(l - a)N, + t,a - l] ~ s(t - 1) N, =t’
p*, of the reduced
the solution
problem
is given by:
Proposition 2.
1, =o, =
l[OJI The indirect
if 6 5 ~ t (t
_
1)
[Cl- 44 + t,a- 11= NI
B
7
utility
function
of the politician
thus takes the following
czS’[(l - a)N, + tla - l] y*(SO, 6, a, n(l),
. . . , n(t))
=
Nl aGSO(t - 1) t
’
,
form:
if6
Since the objective function is linear in p, we obtain a corner solution - when 6 differs from the critical value B the politician does not divide his budget. Since B is decreasing in a, ceteris paribus, he is more likely to prefer provision of a public good when the transfer-seeking environment is more egalitarian - a is larger. The reason is the following: as a increases, the free-riding incentives within the contesting groups become stronger. Consequently, the total transfer-seeking outlays associated with a private-good transfer, and, in turn, the fraction of these outlays that reach the politician, is reduced. A sufficient reduction in these expected benefits will induce the politician to allocate his budget to the alternative option, the provision of the local public good. In more egalitarian societies he is therefore more inclined to provide the local public good.6’7
‘When N[ = N and t, = t, the effect of both t and N on B is ambiguous. ’ Proposition 1 implies that when each individual is indifferent between receiving one dollar or seeing that dollar transformed into the public good (6 = l), which means that the effectivity of one dollar spent on the provision of a local public good to group i is n(i) times higher than the effectivity of transferring one dollar to that group, the politician creates a private (public) good transfer-seeking game if a is smaller (larger) than
456
S. Nitzan
I Economics
Letters
45 (1994) 451-457
By (l), X(S,, 1, G,) is decreasing in a. If the politician can determine the rule f ‘, he will maximize a by setting a = 0. That is, he will prefer the sharing rule based on the principle ‘to each according to his relative effort’. This sharing rule minimizes the free-riding incentives within the groups competing for the private-good transfer, and thus maximizes the value of the resources reaching the politician when he chooses to set up such a private-good, transferseeking game. With a = 0, X(Sj, 1, G,) is independent of tj and is increasing in N,. Consequently, the feasible private-food transfer contest yielding the maximal equilibrium outlays is (SO, 1, Z) and X(S”, 1, Z) = S (N - 1)/N. By Proposition 2, when the politician designs the transfer allocation system determining both p and a, he will prefer the monetary transfer if the individual valuation of one dollar spent on the provision of the local public good is sufficiently small, namely if 6 < t(N - l)/ (t - l)N. This condition is necessarily satisfied when 6 I 1 since t(N - l)l(t - l)N 2 1. In such a case transfer sharing will be based on the principle ‘to each according to his relative effort’. By (I), X(Sj, 1, G,> is increasing in t. If the politician can determine the partition of the total population into contesting groups, he will maximize X(Sj, 1, G,) by setting t, = N. That is, from the politician’s standpoint, since he is interested in eliminating the free-riding incentives, individual rather than collective transfer seeking is always advantageous. In such a case the maximal equilibrium outlays are equal to S”(N - 1)/N. By Proposition 2, the politician will prefer to make a monetary transfer (p * = 1) if 6 < 1, and he will prefer the provision of a local public good (p * = 0) when 6 > 1.
4. Summary Politicians often have discretion regarding the manner in which they can allocate their political prizes. This paper investigated the relationship between equilibrium political transfer allocation and the transfer-seeking environment as described by the distribution of potential beneficiaries of the transfers across the groups, the rule used to share monetary transfers, and the relative value of a dollar spent on the provision of a local public good. In our stylized setting the politician usually selects an extreme strategy that entails either offering the entire budget as a private-good transfer or using it to provide a local public good to one of the contesting groups. The principal result is the condition that determines which of the two extreme strategies is chosen. If the politician can control the sharing rule within groups, he prefers the rule based on the principle ‘to each according to his relative effort’, since this rule minimizes the free-riding incentives within the groups, and thus maximizes the value of the transfer to the politician. If he can control the number of groups contesting the transfers, he would attempt to increase that number, since, from his viewpoint, t = N is optimal; in that case free-riding incentives are eliminated, regardless of whether the politician chooses the transfer or the provision of the public good.
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