# Economies with Public Goods

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## Abstract

A public good is one for which there is non-rivalry in consumption, that is, if the good is consumed by individual *i*, this does not preclude individual *j* from consuming it. When there is neither exclusion nor free disposal a public good becomes a collective decision whose consequences affect the whole of society. Pure public goods are those whose quantity consumed by each member of the society is identical. It should be noted that a public good is a special sort of externality.

## Keywords

Utility Function Public Good Optimal Decision Constant Return Private Good
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## References

- Good introductions to the topics dealt with in this chapter are: J.J. Laffont, (1988)
*Fundamentals of Public Economic*, Introduction and Chapter 2 (MIT Press) and W. Thomson, ‘Lecture on Public Goods’, mimeo, University de Rochester, Sections 1–6.Google Scholar - The articles in which the topics dealt with here were developed for the first time in a modern way are: P.A. Samuelson (1954), ‘The Pure Theory of Public Expenditure’,
*Review of Economics and Statistics*, 36, pp. 387–9Google Scholar - and D.K. Foley (1970), ‘Lindahl’s Solution and the Core of an Economy with Public Goods’,
*Econometrica*, 38, no. 1 pp. 66–72.CrossRefGoogle Scholar - The classical surveys on public goods and Lindahl’s equilibrium are: J.C. Milleron (1972), ‘Theory of Value with Public Goods: A Survey Article’,
*Journal of Economic Theory*, 15, pp. 419–77CrossRefGoogle Scholar - and D.J. Roberts (1974), ‘The Lindahl Solution for Economies with Public Goods’,
*Journal of Public Economics*, 3, pp. 23–42.CrossRefGoogle Scholar - Both papers present proofs for the existence of Lindahl’s equilibrium where it is required that all consumers hold strictly positively endowments of public goods. The existence of Lindahl’s equilibrium without this assumption has been established by C. Herrero and A. Villar (1991), ‘Vector Mappings with Diagonal Images’,
*Mathematical Social Sciences*, 122, pp. 57–67.CrossRefGoogle Scholar - The generalization of the Lindahl—Bowen—Samuelson condition to allow boundary allocations is analyzed in D.E. Campbell and M. Truchon (1988), ‘Boundary Optima and the Theory of Public Goods Supply’,
*Journal of Public Economics*, 35, pp. 241–9; and J.P. Conley and D. Diamantaras, ‘Generalized Samuelson Conditions and Welfare Theorems for Nonsmooth Economies’, Working Paper, University of Illinois.CrossRefGoogle Scholar - The second welfare theorem in economies with public goods is proved in M.A. Khan and R. Vohra (1987), ‘An Extension of the Second Welfare Theorem to Economies with Nonconvexities and Public Goods’,
*Quarterly Journal of Economics*, pp. 223–41.Google Scholar - The non-equivalence between the core and Lindahl’s equilibrium was first demonstrated by T. Muench (1972), ‘The Core and the Lindahl Equilibrium of an Economy with Public Goods’,
*Journal of Economic Theory*, 4, pp. 241–55.CrossRefGoogle Scholar - Sufficient conditions for the convergence of the core to the Lindahl allocation in economies with pure public goods are studied in J.P. Conley (1994), ‘Convergence Theorems on the Core of a Public Goods Economy: Sufficient Conditions’,
*Journal of Economic Theory*, 62, no. 1, pp. 161–85CrossRefGoogle Scholar - and M. Wooders (1991), ‘On Large Games and Competitive Markets. 1 Theory. 2 Applications’. University of Bonn, 303, DPB-195–6.Google Scholar
- The ratio equilibria were first proposed in M. Kaneko (1977), ‘The Ratio Equilibrium and a Voting Game in a Public Good Economy’
*Journal of Economic Theory*, vol. 16, pp. 123–36.CrossRefGoogle Scholar - The assumptions on the technology used above have been generalized by D. Diamantaras and S. Wilkie (1994), ‘A Generalization of Kaneko’s Ratio Equilibrium for Economies with Private and Public Goods’,
*Journal of Economic Theory*, vol. 62 no. 2, pp. 499–512.CrossRefGoogle Scholar - Whereas the cost-share equilibria were proposed in A. Mas-Colell and J. Silvestre (1989), ‘Cost-Share Equilibria: A Lindahlian Approach’,
*Journal of Economic Theory*, vol. 47 no. 2, pp. 239–56.CrossRefGoogle Scholar - The relationship between the core and cost-share equilibria (under the assumption of non-increasing returns to scale) is studied in S. Weber and H. Wiesmeth (1991), ‘The Equivalence of Core and Cost-Share in an Economy with a Public Good’,
*Journal of Economic Theory*, vol. 54, pp. 190–7.CrossRefGoogle Scholar - Other authors have proposed different solution concepts. A list which is by no means exhaustive includes: A. Mas-Colell (1980), ‘Efficiency and Decentralization in the Pure Theory of Public Goods’,
*Quarterly Journal of Economics*, vol. XCIV, no. 4, pp. 625–641CrossRefGoogle Scholar - H. Moulin (1992), ‘All Sorry to Disagree: A General Principle for the Provision of Nonrival Goods’,
*Scandinavian Journal of Economics*, vol. 94 no. 1 pp. 37–51CrossRefGoogle Scholar - F. Vega-Redondo (1987), ‘Efficiency and Non-Linear Pricing in Non-Convex Environments with Externalities: A Generalization of the Lindahl Equilibrium Concept’,
*Journal of Economic Theory*, vol. 41, no. 1 pp. 54–67.CrossRefGoogle Scholar - A panoramic view of other concepts of equilibrium can be found in the surveys of Inman and Oakland in A.J. Auerbach and M. Feldstein (eds) (1987),
*Handbook of Public Economics*(New York: Elsevier), chs 9 and 12Google Scholar - H. Moulin (1988),
*Axioms of Cooperative Decision-Making*, Econometric Society Monographs no, 15 (Cambridge University Press); and W. Thomson ‘Monotonic Allocation Rules in Economies with Public Goods’, Mimeo, University of Rochester.CrossRefGoogle Scholar

## Copyright information

© Luis C. Corchón 1996