Theoretical Economics Letters, 2016, 6, **-** Published Online August 2016 in SciRes. http://www.scirp.org/journal/tel doi How to cite this paper: Author 1, Author 2 and Author 3 (2016) Paper Title. Theoretical Economics Letters, 6, **-**. http://dx.doi.org/10.4236/***.2016.***** Optimal Formulas for Subnational Tax Revenue Sharing Raul Alberto Ponce Rodriguez * , Ikuho Kochi Departamento de Ciencias Sociales, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, México Email: * rponce@uacj.mx, ikuho.kochi@uacj.mx Received **** 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract We develop an analysis of optimal formulas for subnational tax revenue sharing for two cases of interest: when local public goods (lpg’s) show spillovers and are inter-regional perfect and im- perfect substitutes. Our analysis could be relevant to understand the determinants of feasible competing alternatives for the design of tax revenue sharing systems. Our study shows that: 1) In- ter-regional spillovers should be taken into account in the design of formulas for subnational revenue sharing when lpg’s are perfect inter-regional substitutes but should not be taken into ac- count to supply lpg’s that are imperfect substitutes; 2) The distribution of preferences for lpg’s and population should be considered in formulas for revenue sharing when subnational govern- ments provide both lpg’s that are perfect and imperfect substitutes; 3) For local public goods that are imperfect substitutes, the share of tax revenue is first increasing and then decreasing with in- creases in the population of the district; 4) For perfect substitute-lpg’s, the share of tax revenue in the district is increasing and concave with the district’s population; 5) The distribution of income should not be considered in the design of formulas for lpg’s that are perfect and imperfect substi- tutes. Other empirically relevant comparative analyses are considered in the paper. Keywords Local Public Goods, State and Local Budget and Expenditures, Intergovernmental Transfers, Inter-Regional Externalities, Federalism 1. Introduction Tax revenue sharing seeks to distribute revenue for central and subnational governments from a given tax base. Some of the advantages of tax revenue sharing recognized in the literature include: 1) Tax harmonization be- * Corresponding author.