# Optimal provision of a public good with costly exclusion

## Author

Listed:
• Gravel, Nicolas
• Poitevin, Michel

## Abstract

We examine the problem of providing a non-rival and excludable public good to individuals with the same preferences and differing contributing capacities. Exclusion from the public good is costly in the sense that if two different quantities of the public good are consumed in the community, then the sum of the costs of providing the two quantities must be borne. By contrast, costless exclusion only requires the cost of the largest quantity consumed of the public good to be financed. We show that despite its important cost, providing public goods in different quantities is often part of any optimal provision of public good when the public authority is imperfectly informed about the agents' contributive capacities. In the specific situation where individuals have an additively separable logarithmic utility function, we provide a complete characterization of the optimal exclusion structure in the two-type case. We also show that the preference for such a costly exclusion is more likely when the heterogeneity in the population or income is large, and when the aversion to utility inequality is important.

## Suggested Citation

• Gravel, Nicolas & Poitevin, Michel, 2019. "Optimal provision of a public good with costly exclusion," Games and Economic Behavior, Elsevier, vol. 117(C), pages 451-460.
• Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:451-460
DOI: 10.1016/j.geb.2019.07.009
as

File URL: http://www.sciencedirect.com/science/article/pii/S0899825619301071

File URL: https://libkey.io/10.1016/j.geb.2019.07.009?utm_source=ideas
LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
---><---

As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

## References listed on IDEAS

as
1. Hellwig, Martin F., 2005. "A utilitarian approach to the provision and pricing of excludable public goods," Journal of Public Economics, Elsevier, vol. 89(11-12), pages 1981-2003, December.
2. Gravel, Nicolas & Poitevin, Michel, 2006. "The progressivity of equalization payments in federations," Journal of Public Economics, Elsevier, vol. 90(8-9), pages 1725-1743, September.
3. Hanming Fang & Peter Norman, 2010. "Optimal Provision of Multiple Excludable Public Goods," American Economic Journal: Microeconomics, American Economic Association, vol. 2(4), pages 1-37, November.
4. Hellwig, Martin F., 2007. "The provision and pricing of excludable public goods: Ramsey-Boiteux pricing versus bundling," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 511-540, April.
5. Peter Norman, 2004. "Efficient Mechanisms for Public Goods with Use Exclusions," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 1163-1188.
6. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
7. Hervé Moulin, 1994. "Serial Cost-Sharing of Excludable Public Goods," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 305-325.
8. Martin F. Hellwig, 2003. "Public-Good Provision with Many Participants," Review of Economic Studies, Oxford University Press, vol. 70(3), pages 589-614.
9. Fraser, Clive D., 1996. "On the provision of excludable public goods," Journal of Public Economics, Elsevier, vol. 60(1), pages 111-130, April.
Full references (including those not matched with items on IDEAS)

## Most related items

These are the items that most often cite the same works as this one and are cited by the same works as this one.
1. Hanming Fang & Peter Norman, 2014. "Toward an efficiency rationale for the public provision of private goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 375-408, June.
2. Hellwig, Martin F., 2007. "The provision and pricing of excludable public goods: Ramsey-Boiteux pricing versus bundling," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 511-540, April.
3. Hanming Fang & Peter Norman, 2010. "Optimal Provision of Multiple Excludable Public Goods," American Economic Journal: Microeconomics, American Economic Association, vol. 2(4), pages 1-37, November.
4. Hellwig, Martin F., 2005. "A utilitarian approach to the provision and pricing of excludable public goods," Journal of Public Economics, Elsevier, vol. 89(11-12), pages 1981-2003, December.
5. Martin Hellwig, 2004. "Optimal Income Taxation, Public-Goods Provision and Public-Sector Pricing: A Contribution to the Foundations of Public Economics," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2004_14, Max Planck Institute for Research on Collective Goods.
6. Stefan Behringer, 2005. "The Provision of a Public Good with a direct Provision Technology and Large Number of Agents," JEPS Working Papers 05-007, JEPS.
7. Maniquet, François & Sprumont, Yves, 2010. "Sharing the cost of a public good: An incentive-constrained axiomatic approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 275-302, January.
8. Stefano Galavotti, 2014. "Reducing Inefficiency in Public Good Provision Through Linking," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(3), pages 427-466, June.
9. Martin Hellwig & Felix Bierbrauer, 2009. "Public Good Provision in a Large Economy," 2009 Meeting Papers 1062, Society for Economic Dynamics.
10. Fang,H. & Norman,P., 2003. "An efficiency rationale for bundling of public goods," Working papers 19, Wisconsin Madison - Social Systems.
11. Grüner, Hans Peter & Koriyama, Yukio, 2012. "Public goods, participation constraints, and democracy: A possibility theorem," Games and Economic Behavior, Elsevier, vol. 75(1), pages 152-167.
12. Hines Jr., James R., 2000. "What is benefit taxation?," Journal of Public Economics, Elsevier, vol. 75(3), pages 483-492, March.
13. Gary-Bobo, Robert J. & Jaaidane, Touria, 2000. "Polling mechanisms and the demand revelation problem," Journal of Public Economics, Elsevier, vol. 76(2), pages 203-238, May.
14. Bierbrauer, Felix & Winkelmann, Justus, 2020. "All or nothing: State capacity and optimal public goods provision," Journal of Economic Theory, Elsevier, vol. 185(C).
15. Bierbrauer, Felix & Netzer, Nick, 2016. "Mechanism design and intentions," Journal of Economic Theory, Elsevier, vol. 163(C), pages 557-603.
16. Han, Seungjin, 2015. "Robust competitive auctions," Economics Letters, Elsevier, vol. 136(C), pages 207-210.
17. Rong, Kang, 2014. "Proportional individual rationality and the provision of a public good in a large economy," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 187-196.
18. Hans Gersbach, 2010. "Democratic Provision of Divisible Public Goods," CESifo Working Paper Series 2939, CESifo.
19. Takuya Obara & Shuichi Tsugawa & Shunsuke Managi, 2021. "$$\lambda$$ λ envy-free pricing for impure public good," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 11-25, April.
20. Felix Bierbrauer, 2010. "An incomplete contracts perspective on the provision and pricing of excludable public goods," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2010_01, Max Planck Institute for Research on Collective Goods.

### Keywords

Mechanism design; Asymmetric information; Public goods; Costly exclusion;
All these keywords.

### JEL classification:

• D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
• H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:451-460. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.