Abstract
In the literature of local public finance, one of the well-known properties of optimal matching grant programs is that the matching grant rate should increase as the degree of benefit spillovers of public goods increases. This paper presents the reexamination of properties of optimal matching grant programs using the model of Bjorvatn and Schjelderup (Int Tax Public Financ 9:111–120, 2002). The result formally captures a property of matching grants that the optimal matching grant rate might decrease with the degree of spillover externalities.
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Notes
In the capital tax competition literature, an optimal subsidy program to correct an inefficient resource allocation has been studied previously by Wildasin (1989) and DePater and Myers (1994). The framework used in this paper is similar in some respects to those studies, but their interests are not on the effects of changes in \(\beta\) and \(n\) on the optimal subsidy rate.
Assuming \(\partial \epsilon/\partial \beta=0\), 21 can be obtained by taking derivatives of \(m\) with respect to \(\beta\) as \(\partial m/\partial \beta=[n-1-\epsilon n+(1-\beta)[1+\beta(n-1)](\partial \epsilon/\partial \beta)]/[1+\beta(n-1)]^2\).
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Acknowledgements
The author would like to thank David Wildasin, William Hoyt, Marco Castaneda, James Marton, Pierre Picard, Nobuhiro Okuno, Dan Sasaki, Toshihiro Matsumura, Toshihiro Ihori, Masayoshi Hayashi, and John Carruthers for helpful comments. The author also thanks the anonymous referees and the editor, Roger Stough, who made suggestions for which the author is grateful. The research has been supported by grants from the Shikishima foundation, Japan Society for the Promotion of Science, and Japan Center for Economic Research. The author is very grateful to Martin School of Public Policy and Administration for its support.
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This research was carried out while the author was on leave at the University of Kentucky. An earlier version of this paper was presented at the University of Kentucky, Institute of Statistical Research, University of Tokyo, and the 43rd Annual meeting of Western Regional Science Association.