An equilibrium model with mixed federal structures
Shlomo Weber, V. L. Makarov, A. V. Savvateev
This paper examines the problem of meeting an inelastic demand for public goods of club type in an economy with a finite number of agents, who exhibit different preferences regarding the choice of public projects. The choice problem is assumed to be multidimensional as there are several dimensions of a societal decision.
From the formal point of view, the problem can be summarized as follows. There are n players, identified by points in a multidimensional space, who should be partitioned into a finite number of groups under the requirement that there exists no nonempty subset S of players, each member of which strictly prefers (in terms of utilities) group S to the group he was initially allocated.
Utilities which are inversely related to costs consist of two parts: monetary part (inversely proportional to the group’s size), and the transportation part (distance from the location of a player to the point minimizing aggregate transportation cost within his group).
One cannot hope for a general result of existence of stable coalition structure even in a uni-dimensional setting. However, by allowing formation of several coalition structures, each pursuing a different facet of public decision, we obtain a very general existence result. Formally, this means that for each coalition there exists a balanced
system of weights assigned to each of the dimensions of the public project.
equilibrium, regions, federal structures, monetary contribution, equal share
519.83, MSC 91-02, 91A40
1. Alesina A., Spolaore E. On the number and size of nations. Quarterly Journal of Economics, 1997, vol. 113, pp. 1027–1056.
2. Alesina A., Angeloni I. and Etro F. International unions / American Economic Review, 2005, vol. 95, pp. 602–15.
3. Bogomolnaia A., Le Breton M., Savvateev A., Weber S. Stability of jurisdiction structures under the equal share and median rules. Economic Theory, 2008, vol. 3, pp. 523–543.
4. Casella A. The role of market size in the formation of jurisdictions. Review of Economic Studies, 2001, vol. 68, pp. 83–108.
5. Danilov V.I. On the Scarf theorem (in Russian). Economics and Mathematical Methods, 1999, vol. 35, no. 3, pp. 137–139.
6. Haimanko O., Le Breton M. and Weber S. Transfers in a polarized country: bridging the gap between efficiency and stability. Journal of Public Economics, 2004, vol. 89, pp. 1277–1303.
7. J´ehiel P. and Scotchmer S. Constitutional rules of exclusion in jurisdiction formation. Review of Economic Studies, 2001, vol. 68, pp. 393–413.
8. Makarov V.L. Calculus of Institutions (in Russian). Economics and Mathematical Methods, 2003, vol. 39, no. 2, pp. 14–32.9. Scarf H.E. The core of an N-person game. Econometrica, 1967, vol. 35, pp. 50-69.
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