Abstract
We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost share or ratio equilibrium. Finally, we indicate how it may be exploited to facilitate comparative static analysis of Lindahl and cost share equilibria.
Similar content being viewed by others
References
Atkinson AB, Stiglitz J (1980) Lectures on public economics. McGraw-Hill, New York
Batina RG, Ihori T (2005) Public goods: theory and applications. Springer, Berlin
Boadway RW, Wildasin DE (1984) Public sector economics, 2nd edn. Little, Brown and Company, Boston
Bowen H (1943) The interpretation of voting in the allocation of economic resources. Quart J Econ 58: 27–48
Buchholz W, Peters W (2007) Justifying the Lindahl equilibrium as the outcome of fair cooperation. Public Choice 133: 157–169
Buchholz W, Cornes R, Peters W (2006) Lindahl equilibrium versus voluntary contribution to a public good: the role of the income distribution. FinanzArchiv/Public Finance Anal 62: 28–49
Chiang AC, Wainwright K (2005) Fundamental methods of mathematical economics, 5th edn. McGraw-Hill, Boston
Cornes RC, Sandler T (1996) The theory of externalities, public goods and club goods, 2nd edn. Cambridge University Press, Cambridge
Cornes RC, Hartley R (2007) Aggregative public good games. J Publ Econ Theory 9: 201–219
Danziger L (1976) A graphical representation of the Nash and Lindahl equilibria in an economy with a public good. J Publ Econ 6: 295–303
Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7: 45–98
Hindriks J, Myles GD (2006) Intermediate public economics. MIT Press, Cambridge
Kaneko M (1977) The ratio equilibrium and a voting game in a public good economy. J Econ Theory 16: 123–136
Khan MA, Vohra R (1987) On the existence of Lindahl-Hotelling equilibria. J Publ Econ 34: 143–158
Lindahl E (1919) Die Gerechtigkeit der Besteuerung. Gleerup, Lund
Mas-Colell A, Silvestre J (1989) Cost share equilibria: a Lindahlian approach. J Econ Theory 47: 239–256
Milleron J-C (1972) Theory of value with public goods. J Econ Theory 5: 419–477
Musgrave RA (1959) The theory of public finance. McGraw-Hill, New York
Myles GD (1995) Public economics. Cambridge University Press, Cambridge
Roberts D (1974) The Lindahl solution for economics with public goods. J Publ Econ 3: 23–42
Samuelson PA (1955) Diagrammatic exposition of a theory of public expenditure. Rev Econ Stat 37: 350–356
Sertel M (1994) Manipulating Lindahl equilibria via endowments. Econ Lett 46: 167–171
Sertel M, Yildiz M (1998) The Lindahl solution with changing population and resources. Math Soc Sci 35: 151–163
Shitovitz B, Spiegel M (1998) Cournot–Nash and Lindahl equilibria in pure public good economies. J Econ Theory 83: 1–18
Silvestre J (2003) Wicksell, Lindahl and the theory of public goods. Scand J Econ 105: 527–553
Thomson W (1999) Economies with public goods: an elementary geometric exposition. J Publ Econ Theory 1: 139–176
Uzawa H (2003) Economic theory and global warming. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Buchholz, W., Cornes, R. & Peters, W. Existence, uniqueness and some comparative statics for ratio and Lindahl equilibria. J Econ 95, 167–177 (2008). https://doi.org/10.1007/s00712-008-0024-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00712-008-0024-0