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Provision of public goods in a large economy
Economics Letters 61 (1998) 229–234
Provision of public goods in a large economy Mark Gradstein* Ben-Gurion University and the University of Pennsylvania, Pennsylvania, USA Received 13 April 1998; accepted 25 June 1998
Abstract In this paper, I consider a large economy with a private and a public good where the distribution of costs (but not the individual costs) associated with the provision of the public good is known. A simple tax-subsidy policy, whereby all contributors get a subsidy funded by a tax on non-contributors, is shown to attain the first best allocation provided that the socially optimal amount of the public good is independent of the distribution of individual costs. 1998 Published by Elsevier Science S.A. All rights reserved. Keywords: Provision of public goods JEL classification: H4
1. Introduction It is well known that private provision of public goods is inefficient, and that inefficiency can only be aggravated in a large economy—see Andreoni, 1988; Fries et al., 1991 and Gradstein, 1992, for some recent studies of private provision of public goods in a large economy. Government intervention might therefore be needed to restore the first best allocation. This is easily achieved when information (on individual tastes, production technology, etc.) is complete, and the set of policy instruments is unlimited. For example, the government can attain the first best by imposing Lindahl taxes, and such policy benefits everyone. A more delicate situation emerges when information is partial. For instance, while the distribution of some characteristics in the population may be known, each individual’s characteristics may be not. In this case, government policies cannot be conditioned on individual characteristics, although they may possibly depend on individual actions. Furthermore, they must be coercive in the sense that some *Corresponding author. Tel.: 11-215-8985692; fax: 11-215-5732057; e-mail: [email protected] 1 The mechanism design literature, which seeks means of attaining efficient allocations under incomplete information, has yielded many negative results resulting in the impossibility of voluntary and efficient provision of public goods, thus implying necessity of coercive intervention to attain efficiency—see Laffont and Maskin, 1979; Myerson and Satterhwaite, 1983 and Rob, 1989, for some of the most directly related literature. Coercion can be avoided with some specific assumptions on the feasible set of economic environments, see Gradstein, 1994, or under specific allocation of property rights, see Neeman, 1994. 0165-1765 / 98 / $ – see front matter 1998 Published by Elsevier Science S.A. All rights reserved. PII: S0165-1765( 98 )00159-1
M. Gradstein / Economics Letters 61 (1998) 229 – 234
230
individuals have to be forced to comply with the policy. For instance, Lindahl taxes require information on preferences and incomes that individuals are not generally willing to reveal.1 In this paper, I consider a large economy where the cost associated with one’s contribution to the public good is privately known, and the government acts knowing only the distribution of these costs in the population. A simple tax-subsidy policy is exhibited, where all contributors get a subsidy funded by a tax on non-contributors, which attains the first best allocation provided that the socially optimal amount of the public good is independent of the distribution of individual costs. Since some individuals may oppose this policy, it turns out that its implementation may involve coercion; and its political feasibility in a democratic regime hinges on the existence of a sufficiently large supporting coalition. These results are shown to hold under a variety of assumptions about the technology of public goods provision, in particular, they hold whether the public good is continuous or discrete.
2. The basic model Consider an economy of individuals whose measure is the unit interval. There are two goods one of which (X) is purely public and another (Y) private. Each individual is endowed with one indivisible unit of the private good the value of which is c i . These values are assumed to be individually specific and privately known; their distribution, G(c), however, is assumed to be common knowledge. The support of this distribution is assumed to be the unit interval, and the distribution function is assumed to be continuously differentiable. Individuals can participate in the provision of the public good by contributing the private good. Letting q denote the proportion of contributing individuals, X 5 H(q) is the amount of the public good produced. H is the production function assumed to be monotonic with H(0) 5 0; more detailed technology assumptions are laid down below. Let z i denote individual i’s decision variable, such that z i 5 1 is the decision to contribute to the provision of the public good, and z i 5 0 denotes the decision to refrain from contribution. We assume that individual tastes are identical and representable by an additively separable utility function, which, after taking into account the budget constraint can be written as follows: V(X) 1 Y 5V(H(q)) 1 1 2 c i z i
(1)
where V is assumed to be monotonic and concave.2 Note that, with our assumptions, c i can also be interpreted as the opportunity cost of a contribution to the public good; we refer to it below as a contribution cost. We distinguish the following production technologies for the provision of the public good.
2.1. Continuous public goods In this case, the production function satisfies the standard concavity assumption, H0,0. In the social optimum, only individuals with sufficiently low costs contribute to the provision of the public 2
This paper considers standard pure public goods, without the ‘joy of giving’ component (see Andreoni, 1989, for a comprehensive study of the latter), although the main results could be extended to account for that possibility.
M. Gradstein / Economics Letters 61 (1998) 229 – 234
231
good. Letting c 0 denote the socially optimal threshold level such that only individuals with a contribution cost below c 0 make a contribution, this threshold maximizes the social welfare function (a constant which represents the amount of the private good in the economy is omitted throughout)
E
c0 0
[V(H(G(c ))) 2 c]dG(c) 1
0
E
1
c0
0
0
[V(H(G(c )))]dG(c) 5V(H(G(c )) 2
E
c0
cdG(c)
(2)
0
The social welfare is given by the difference between the social value of the public good and the total contribution costs. Differentiation of (2) with respect to c 0 reveals the following first order condition: 2 c 0 1V 9(H(G(c 0 )))H9(G(c 0 )) 5 0
(3)
and our assumptions guarantee that the second order condition is satisfied. Assuming that V 9(H(1))H9(1),1 guarantees the existence of a unique internal solution. In equilibrium, each individual decides whether or not to contribute to the provision of the public good on his own. Since in our large economy the level of the public good is unaffected by a single individual’s contribution decision, it is clear that at equilibrium all individuals have an incentive to free ride. Hence the equilibrium proportion of contributors to the public good, and therefore the amount of the public good, H(q*), equal 0. In contrast, the socially optimal amount, given by (3), is strictly positive.
2.2. Discrete public goods One particular type of public goods, which has received a considerable attention in the literature, has a production function of the following nature: the good is provided if and only if a certain minimal requirement on the proportion of participants is met. This is the case for referendum voting and, more generally, for any public choice procedure which requires a quorum of participants. Public goods with this feature have recently been studied in several theoretical and empirical papers—see, for instance, Dawes, 1980; Nitzan and Romano, 1990; Palfrey and Rosenthal, 1988, 1991; Van de Kragt et al., 1983; Schelling, 1978, contains examples of this kind of a public good. Let g denote the minimal proportion of individuals required for the provision of the above described public good. By arbitrarily choosing the scale, the production function can be described as follows: H(q)50 if q,g, and H(q)51 if q$g. Let V(1)5v be the value assigned by the individuals to the public good; then the first–best social optimum requires that the public good will only be provided if v2
E
c0
cdG(c) . 0
(4)
0
where c 0 5 G 21 (g ) in which case individuals whose cost is less than c 0 contribute.
(5)
M. Gradstein / Economics Letters 61 (1998) 229 – 234
232
At equilibrium, on the other hand, the same considerations as before ensure that the proportion of contributors is zero and therefore suboptimal.
3. Government intervention Since the government lacks sufficient information on the individual costs, it cannot simply pick the ‘correct’ low cost contributors as required by the social welfare maximization. Therefore, I consider a tax / subsidy scheme under which each contributor is given a subsidy of s, and each non-contributor is taxed by the amount of t. I also impose the requirement of a balanced budget. Efficiency requires that the equilibrium of the game implies the socially optimal cutoff point c 0 .3 Note that the tax–subsidy scheme preserves the social optimality condition because of the absence of income effects. Budget balance thus implies: sG(c 0 ) 5 t[1 2 G(c 0 )]
(6)
For c 0 to constitute the equilibrium contribution threshold, the c 0 individual type must be indifferent between making a contribution and refraining from contributing. In other words, the following should hold true: V(H(G(c 0 ))) 2 c 0 1 s 5V(H(G(c 0 ))) 2 t
(7)
That is, s 1 t 5 c0
(79)
Combining (6) and (79) we get t 5 c 0 G(c 0 ), s 5 c 0 [1 2 G(c 0 )]
(8)
where c 0 is given by (3). In Eq. (8) is determined the (unique) tax–subsidy rates needed to implement the first best allocation. Under this policy, the tax on non-contributors is the threshold contribution cost weighed by the fraction of the population which contributes, and the subsidy to contributors is the threshold cost weighed by the fraction of non-contributors. Since a higher socially optimal threshold implies both a higher threshold cost and a greater fraction of contributors, the tax increases as the socially optimal threshold increases. In contrast, the subsidy may go either way. It definitely increases with c 0 for c 0 close to 0 and definitely falls with c 0 for c 0 close to 1. Note that the optimal policy depends not on personal characteristics, nor on the production function, but only on individual actions, and its economic logic can be traced to Pigovian corrective subsidies. The individual utilities under this scheme are as follows: V(H(G(c 0 ))) 2 c 0 G(c 0 ) for non 2 contributors V(H(G(c 0 ))) 2 c i 1 c 0 [1 2 G(c 0 )] for contributors 3
Brito et al., 1991, study such policy in a related context.
(9)
M. Gradstein / Economics Letters 61 (1998) 229 – 234
233
The equilibrium utility level is a decreasing function of the contribution cost; in particular, since the contribution cost of all contributors is less than the threshold socially optimal cost, at equilibrium the contributors (individuals with low costs) are better off than the non-contributors. Furthermore, some individuals—notably, the non-contributors who are required to pay taxes—may become worse off with this policy. Turning to the discrete public good case considered at the end of the previous section, suppose that (4) is satisfied. Then at equilibrium the individual type c 0 —as determined by (5)—has to be indifferent between contributing or not, and the budget balance condition (6) is to be respected. As in the case of the standard public good, this gives rise to (79). Combining (5) and (79) we obtain t 5 G 21 (g )g, s 5 G 21 (g )(1 2 g )
(10)
as a (unique) tax / subsidy policy implementing the first best allocation. The individual equilibrium utilities are v 2 G 21 (g )g for non 2 contributors v 2 c i 1 G 21 (g )(1 2 g ) for contributors
(11)
Again, the contributors are better off than the non-contributors. In addition, provided that v is small, some individuals (in particular, non-contributors) may be worse off than they would be without government intervention. This is the case, for instance, if the cost distribution is uniform and g 2 / 2,v,g 2 . Then efficiency requires that the public good should be produced, but all noncontributors end up being worse off. The adoption of this policy, therefore, hinges on the existence of a winning coalition of low cost individuals who approve it. This, however, is not always ensured. Suppose that the public choice is made by a simple majority, such that the tax-subsidy policy is adopted only if it is preferred to the private provision by at least 50% of the individuals. In this example, all non-contributors vote against the policy, and if g ,1 / 2, their vote is decisive. Hence, the suggested policy is not always politically feasible. In a recent paper, Ledyard and Palfrey, 1994, present an alternative, more sophisticated mechanism which, in a related context, solves the problem of political feasibility. Also note that the policy we suggest does not achieve the first best whenever the socially optimal amount of the public good depends on the distribution of individual costs, the reason being that the policy itself affects the optimal amount of the public good. It does, however, achieve this goal whenever the socially optimal cutoff is not changed when this policy is introduced. This holds for any preferences under which the optimal amount of the public good is independent of the distribution of the individual characteristics, which as is proved in Bergstrom and Cornes, 1983, is satisfied for preferences given by A(X)Yi 1Bi (X), where and A and Bi are monotonic and concave functions, of which (1) is a special case.
4. Concluding remarks This paper presents a corrective policy for the provision of public goods when the individual contribution costs are unknown, and the government policy depends on individual actions. The recent
234
M. Gradstein / Economics Letters 61 (1998) 229 – 234
literature implies that a policy yielding voluntary and efficient provision of public goods does not exist, hence some coercion has to be exercised. Here it is shown that a simple tax–subsidy policy yielding the first best solution can be devised, provided that the socially optimal amount of the public good is independent of the distribution of individual characteristics. Since this policy does not represent a Pareto improvement relative to private provision, its political feasibility hinges on the existence of a sufficiently large supporting coalition.
References Andreoni, J., 1988. Privately provided public goods in a large economy: The limits of altruism. Journal of Public Economics 35, 57–73. Andreoni, J., 1989. Giving with impure altruism: applications to charity and Ricardian equivalence. Journal of Political Economy 97, 1447–1458. Bergstrom, T.C., Cornes, R.C., 1983. Independence of allocative efficiency from distribution in the theory of public goods. Econometrica 51, 1753–1765. Brito, D.L., Sheshinski, E., Intriligator, M.D., 1991. Externalities and compulsory vaccinations. Journal of Public Economics 45, 69–90. Dawes, R.M., 1980. Social dilemmas. Annual Review of Psychology 31, 169–193. Fries, T.L., Golding, E., Romano, R., 1991. Private provision of public goods and the failure of the neutrality property in large finite economies. International Economic Review 32, 147–157. Gradstein, M., 1992. Time dynamics and incomplete information in the private provision of public goods. Journal of Political Economy 100, 581–597. Gradstein, M., 1994. Efficient provision of a discrete public good. International Economic Review 35, 877–898. Laffont, J.J., Maskin E., A differential approach to expected utility maximizing mechanisms. In: Laffont, J.J. (ed.), Aggregation and Revelation of Preferences, North-Holland, Amsterdam, 1979. Ledyard, J.O., Palfrey, T.R., 1994. Voting and lottery drafts as efficient public goods mechanisms. Review of Economic Studies 61, 327–356. Myerson, R.B., Satterhwaite, M.A., 1983. Efficient mechanisms for bilateral trading. Journal of Economic Theory 28, 265–281. Neeman, Z., Property rights and efficiency of public-good mechanisms under asymmetric information, mimeo, 1994. Nitzan, S., Romano, R., 1990. Private provision of a discrete public good with uncertain cost. Journal of Public Economics 42, 357–370. Palfrey, T.R., Rosenthal, H., 1988. Private incentives in social dilemmas: The effects of incomplete information and altruism. Journal of Public Economics 35, 309–332. Palfrey, T.R., Rosenthal, H., 1991. Testing for effects of cheap-talk in a public good game with private information. Games and Economic Behavior 3, 183–220. Rob, R., 1989. Pollution claim settlements under private information. Journal of Economic Theory 47, 307–333. Schelling, T.C., Micromotives and Macrobehavior, W.W. Norton, NY, 1978. Van de Kragt, A.J.C., Orbell, J.M., Dawes, R., 1983. The minimal contributing set as a solution to public goods problem. American Political Science Review 77, 112–121.
Provision of public goods in a large economy Mark Gradstein* Ben-Gurion University and the University of Pennsylvania, Pennsylvania, USA Received 13 April 1998; accepted 25 June 1998
Abstract In this paper, I consider a large economy with a private and a public good where the distribution of costs (but not the individual costs) associated with the provision of the public good is known. A simple tax-subsidy policy, whereby all contributors get a subsidy funded by a tax on non-contributors, is shown to attain the first best allocation provided that the socially optimal amount of the public good is independent of the distribution of individual costs. 1998 Published by Elsevier Science S.A. All rights reserved. Keywords: Provision of public goods JEL classification: H4
1. Introduction It is well known that private provision of public goods is inefficient, and that inefficiency can only be aggravated in a large economy—see Andreoni, 1988; Fries et al., 1991 and Gradstein, 1992, for some recent studies of private provision of public goods in a large economy. Government intervention might therefore be needed to restore the first best allocation. This is easily achieved when information (on individual tastes, production technology, etc.) is complete, and the set of policy instruments is unlimited. For example, the government can attain the first best by imposing Lindahl taxes, and such policy benefits everyone. A more delicate situation emerges when information is partial. For instance, while the distribution of some characteristics in the population may be known, each individual’s characteristics may be not. In this case, government policies cannot be conditioned on individual characteristics, although they may possibly depend on individual actions. Furthermore, they must be coercive in the sense that some *Corresponding author. Tel.: 11-215-8985692; fax: 11-215-5732057; e-mail: [email protected] 1 The mechanism design literature, which seeks means of attaining efficient allocations under incomplete information, has yielded many negative results resulting in the impossibility of voluntary and efficient provision of public goods, thus implying necessity of coercive intervention to attain efficiency—see Laffont and Maskin, 1979; Myerson and Satterhwaite, 1983 and Rob, 1989, for some of the most directly related literature. Coercion can be avoided with some specific assumptions on the feasible set of economic environments, see Gradstein, 1994, or under specific allocation of property rights, see Neeman, 1994. 0165-1765 / 98 / $ – see front matter 1998 Published by Elsevier Science S.A. All rights reserved. PII: S0165-1765( 98 )00159-1
M. Gradstein / Economics Letters 61 (1998) 229 – 234
230
individuals have to be forced to comply with the policy. For instance, Lindahl taxes require information on preferences and incomes that individuals are not generally willing to reveal.1 In this paper, I consider a large economy where the cost associated with one’s contribution to the public good is privately known, and the government acts knowing only the distribution of these costs in the population. A simple tax-subsidy policy is exhibited, where all contributors get a subsidy funded by a tax on non-contributors, which attains the first best allocation provided that the socially optimal amount of the public good is independent of the distribution of individual costs. Since some individuals may oppose this policy, it turns out that its implementation may involve coercion; and its political feasibility in a democratic regime hinges on the existence of a sufficiently large supporting coalition. These results are shown to hold under a variety of assumptions about the technology of public goods provision, in particular, they hold whether the public good is continuous or discrete.
2. The basic model Consider an economy of individuals whose measure is the unit interval. There are two goods one of which (X) is purely public and another (Y) private. Each individual is endowed with one indivisible unit of the private good the value of which is c i . These values are assumed to be individually specific and privately known; their distribution, G(c), however, is assumed to be common knowledge. The support of this distribution is assumed to be the unit interval, and the distribution function is assumed to be continuously differentiable. Individuals can participate in the provision of the public good by contributing the private good. Letting q denote the proportion of contributing individuals, X 5 H(q) is the amount of the public good produced. H is the production function assumed to be monotonic with H(0) 5 0; more detailed technology assumptions are laid down below. Let z i denote individual i’s decision variable, such that z i 5 1 is the decision to contribute to the provision of the public good, and z i 5 0 denotes the decision to refrain from contribution. We assume that individual tastes are identical and representable by an additively separable utility function, which, after taking into account the budget constraint can be written as follows: V(X) 1 Y 5V(H(q)) 1 1 2 c i z i
(1)
where V is assumed to be monotonic and concave.2 Note that, with our assumptions, c i can also be interpreted as the opportunity cost of a contribution to the public good; we refer to it below as a contribution cost. We distinguish the following production technologies for the provision of the public good.
2.1. Continuous public goods In this case, the production function satisfies the standard concavity assumption, H0,0. In the social optimum, only individuals with sufficiently low costs contribute to the provision of the public 2
This paper considers standard pure public goods, without the ‘joy of giving’ component (see Andreoni, 1989, for a comprehensive study of the latter), although the main results could be extended to account for that possibility.
M. Gradstein / Economics Letters 61 (1998) 229 – 234
231
good. Letting c 0 denote the socially optimal threshold level such that only individuals with a contribution cost below c 0 make a contribution, this threshold maximizes the social welfare function (a constant which represents the amount of the private good in the economy is omitted throughout)
E
c0 0
[V(H(G(c ))) 2 c]dG(c) 1
0
E
1
c0
0
0
[V(H(G(c )))]dG(c) 5V(H(G(c )) 2
E
c0
cdG(c)
(2)
0
The social welfare is given by the difference between the social value of the public good and the total contribution costs. Differentiation of (2) with respect to c 0 reveals the following first order condition: 2 c 0 1V 9(H(G(c 0 )))H9(G(c 0 )) 5 0
(3)
and our assumptions guarantee that the second order condition is satisfied. Assuming that V 9(H(1))H9(1),1 guarantees the existence of a unique internal solution. In equilibrium, each individual decides whether or not to contribute to the provision of the public good on his own. Since in our large economy the level of the public good is unaffected by a single individual’s contribution decision, it is clear that at equilibrium all individuals have an incentive to free ride. Hence the equilibrium proportion of contributors to the public good, and therefore the amount of the public good, H(q*), equal 0. In contrast, the socially optimal amount, given by (3), is strictly positive.
2.2. Discrete public goods One particular type of public goods, which has received a considerable attention in the literature, has a production function of the following nature: the good is provided if and only if a certain minimal requirement on the proportion of participants is met. This is the case for referendum voting and, more generally, for any public choice procedure which requires a quorum of participants. Public goods with this feature have recently been studied in several theoretical and empirical papers—see, for instance, Dawes, 1980; Nitzan and Romano, 1990; Palfrey and Rosenthal, 1988, 1991; Van de Kragt et al., 1983; Schelling, 1978, contains examples of this kind of a public good. Let g denote the minimal proportion of individuals required for the provision of the above described public good. By arbitrarily choosing the scale, the production function can be described as follows: H(q)50 if q,g, and H(q)51 if q$g. Let V(1)5v be the value assigned by the individuals to the public good; then the first–best social optimum requires that the public good will only be provided if v2
E
c0
cdG(c) . 0
(4)
0
where c 0 5 G 21 (g ) in which case individuals whose cost is less than c 0 contribute.
(5)
M. Gradstein / Economics Letters 61 (1998) 229 – 234
232
At equilibrium, on the other hand, the same considerations as before ensure that the proportion of contributors is zero and therefore suboptimal.
3. Government intervention Since the government lacks sufficient information on the individual costs, it cannot simply pick the ‘correct’ low cost contributors as required by the social welfare maximization. Therefore, I consider a tax / subsidy scheme under which each contributor is given a subsidy of s, and each non-contributor is taxed by the amount of t. I also impose the requirement of a balanced budget. Efficiency requires that the equilibrium of the game implies the socially optimal cutoff point c 0 .3 Note that the tax–subsidy scheme preserves the social optimality condition because of the absence of income effects. Budget balance thus implies: sG(c 0 ) 5 t[1 2 G(c 0 )]
(6)
For c 0 to constitute the equilibrium contribution threshold, the c 0 individual type must be indifferent between making a contribution and refraining from contributing. In other words, the following should hold true: V(H(G(c 0 ))) 2 c 0 1 s 5V(H(G(c 0 ))) 2 t
(7)
That is, s 1 t 5 c0
(79)
Combining (6) and (79) we get t 5 c 0 G(c 0 ), s 5 c 0 [1 2 G(c 0 )]
(8)
where c 0 is given by (3). In Eq. (8) is determined the (unique) tax–subsidy rates needed to implement the first best allocation. Under this policy, the tax on non-contributors is the threshold contribution cost weighed by the fraction of the population which contributes, and the subsidy to contributors is the threshold cost weighed by the fraction of non-contributors. Since a higher socially optimal threshold implies both a higher threshold cost and a greater fraction of contributors, the tax increases as the socially optimal threshold increases. In contrast, the subsidy may go either way. It definitely increases with c 0 for c 0 close to 0 and definitely falls with c 0 for c 0 close to 1. Note that the optimal policy depends not on personal characteristics, nor on the production function, but only on individual actions, and its economic logic can be traced to Pigovian corrective subsidies. The individual utilities under this scheme are as follows: V(H(G(c 0 ))) 2 c 0 G(c 0 ) for non 2 contributors V(H(G(c 0 ))) 2 c i 1 c 0 [1 2 G(c 0 )] for contributors 3
Brito et al., 1991, study such policy in a related context.
(9)
M. Gradstein / Economics Letters 61 (1998) 229 – 234
233
The equilibrium utility level is a decreasing function of the contribution cost; in particular, since the contribution cost of all contributors is less than the threshold socially optimal cost, at equilibrium the contributors (individuals with low costs) are better off than the non-contributors. Furthermore, some individuals—notably, the non-contributors who are required to pay taxes—may become worse off with this policy. Turning to the discrete public good case considered at the end of the previous section, suppose that (4) is satisfied. Then at equilibrium the individual type c 0 —as determined by (5)—has to be indifferent between contributing or not, and the budget balance condition (6) is to be respected. As in the case of the standard public good, this gives rise to (79). Combining (5) and (79) we obtain t 5 G 21 (g )g, s 5 G 21 (g )(1 2 g )
(10)
as a (unique) tax / subsidy policy implementing the first best allocation. The individual equilibrium utilities are v 2 G 21 (g )g for non 2 contributors v 2 c i 1 G 21 (g )(1 2 g ) for contributors
(11)
Again, the contributors are better off than the non-contributors. In addition, provided that v is small, some individuals (in particular, non-contributors) may be worse off than they would be without government intervention. This is the case, for instance, if the cost distribution is uniform and g 2 / 2,v,g 2 . Then efficiency requires that the public good should be produced, but all noncontributors end up being worse off. The adoption of this policy, therefore, hinges on the existence of a winning coalition of low cost individuals who approve it. This, however, is not always ensured. Suppose that the public choice is made by a simple majority, such that the tax-subsidy policy is adopted only if it is preferred to the private provision by at least 50% of the individuals. In this example, all non-contributors vote against the policy, and if g ,1 / 2, their vote is decisive. Hence, the suggested policy is not always politically feasible. In a recent paper, Ledyard and Palfrey, 1994, present an alternative, more sophisticated mechanism which, in a related context, solves the problem of political feasibility. Also note that the policy we suggest does not achieve the first best whenever the socially optimal amount of the public good depends on the distribution of individual costs, the reason being that the policy itself affects the optimal amount of the public good. It does, however, achieve this goal whenever the socially optimal cutoff is not changed when this policy is introduced. This holds for any preferences under which the optimal amount of the public good is independent of the distribution of the individual characteristics, which as is proved in Bergstrom and Cornes, 1983, is satisfied for preferences given by A(X)Yi 1Bi (X), where and A and Bi are monotonic and concave functions, of which (1) is a special case.
4. Concluding remarks This paper presents a corrective policy for the provision of public goods when the individual contribution costs are unknown, and the government policy depends on individual actions. The recent
234
M. Gradstein / Economics Letters 61 (1998) 229 – 234
literature implies that a policy yielding voluntary and efficient provision of public goods does not exist, hence some coercion has to be exercised. Here it is shown that a simple tax–subsidy policy yielding the first best solution can be devised, provided that the socially optimal amount of the public good is independent of the distribution of individual characteristics. Since this policy does not represent a Pareto improvement relative to private provision, its political feasibility hinges on the existence of a sufficiently large supporting coalition.
References Andreoni, J., 1988. Privately provided public goods in a large economy: The limits of altruism. Journal of Public Economics 35, 57–73. Andreoni, J., 1989. Giving with impure altruism: applications to charity and Ricardian equivalence. Journal of Political Economy 97, 1447–1458. Bergstrom, T.C., Cornes, R.C., 1983. Independence of allocative efficiency from distribution in the theory of public goods. Econometrica 51, 1753–1765. Brito, D.L., Sheshinski, E., Intriligator, M.D., 1991. Externalities and compulsory vaccinations. Journal of Public Economics 45, 69–90. Dawes, R.M., 1980. Social dilemmas. Annual Review of Psychology 31, 169–193. Fries, T.L., Golding, E., Romano, R., 1991. Private provision of public goods and the failure of the neutrality property in large finite economies. International Economic Review 32, 147–157. Gradstein, M., 1992. Time dynamics and incomplete information in the private provision of public goods. Journal of Political Economy 100, 581–597. Gradstein, M., 1994. Efficient provision of a discrete public good. International Economic Review 35, 877–898. Laffont, J.J., Maskin E., A differential approach to expected utility maximizing mechanisms. In: Laffont, J.J. (ed.), Aggregation and Revelation of Preferences, North-Holland, Amsterdam, 1979. Ledyard, J.O., Palfrey, T.R., 1994. Voting and lottery drafts as efficient public goods mechanisms. Review of Economic Studies 61, 327–356. Myerson, R.B., Satterhwaite, M.A., 1983. Efficient mechanisms for bilateral trading. Journal of Economic Theory 28, 265–281. Neeman, Z., Property rights and efficiency of public-good mechanisms under asymmetric information, mimeo, 1994. Nitzan, S., Romano, R., 1990. Private provision of a discrete public good with uncertain cost. Journal of Public Economics 42, 357–370. Palfrey, T.R., Rosenthal, H., 1988. Private incentives in social dilemmas: The effects of incomplete information and altruism. Journal of Public Economics 35, 309–332. Palfrey, T.R., Rosenthal, H., 1991. Testing for effects of cheap-talk in a public good game with private information. Games and Economic Behavior 3, 183–220. Rob, R., 1989. Pollution claim settlements under private information. Journal of Economic Theory 47, 307–333. Schelling, T.C., Micromotives and Macrobehavior, W.W. Norton, NY, 1978. Van de Kragt, A.J.C., Orbell, J.M., Dawes, R., 1983. The minimal contributing set as a solution to public goods problem. American Political Science Review 77, 112–121.