Early State Formation and Interstate Competition in a Malthusian Economy

Chu, Angus C. and Wang, Xilin and Xu, Rongxin (2025): Early State Formation and Interstate Competition in a Malthusian Economy.

Abstract

This study develops a Malthusian growth model with early state formation and interstate competition. It explores how the capacity of early states to collect tax revenue and provide productive public goods affects their population dynamics and interstate competition. We find that there is an optimal tax rate for each state that is increasing in the elasticity of agricultural output with respect to productive public goods. Without interstate competition, there is a threshold value for this elasticity below (equal) which the population converges to a steady state (grows at a constant rate) in the long run. With interstate competition, there is a lower threshold value for the above mentioned elasticity below (equal) which competing states coexist (only one state survives) in the long run. Whether we consider productive public goods as a flow or stock variable, the population-maximizing tax rate for each state is increasing in its elasticity of agricultural output with respect to productive public goods. We use historical data to provide empirical evidence for this theoretical result.

• Item Type: MPRA Paper
• Language: English
• Keywords: Public goods; interstate competition; Malthusian growth theory
• Subjects: E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E60 - General; H - Public Economics > H2 - Taxation, Subsidies, and Revenue > H20 - General; H - Public Economics > H5 - National Government Expenditures and Related Policies > H56 - National Security and War; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O43 - Institutions and Growth

References

Ahlerup, P., and Olsson, O., 2012. The roots of ethnic diversity. Journal of Economic Growth, 17, 71-102.

Alsan, M., 2015. The effect of the tsetse fly on African development. American Economic Review, 105, 382-410.

Ashraf, Q., and Galor, O., 2011. Dynamics and stagnation in the Malthusian epoch. American Economic Review, 101, 2003-2041.

Ashraf, Q., and Galor, O., 2013. The "Out of Africa" hypothesis, human genetic diversity, and comparative economic development. American Economic Review, 103, 1-46.

Ashraf, Q., and Galor, O., 2018. The macrogenoeconomics of comparative development. Journal of Economic Literature, 56, 1119-1155.

Barro, R., 1990. Government spending in a simple model of endogenous growth. Journal of Political Economy, 98, S103-S125.

Barro, R., and Sala-i-Martin, X., 1992. Public finance in models of economic growth. Review of Economic Studies, 59, 645-61.

Bockstette, V., Chanda, A., and Putterman, L., 2002. States and markets: The advantage of an early start. Journal of Economic Growth, 7, 347-369.

Borcan, O., Olsson, O., and Putterman, L., 2018. State history and economic development: Evidence from six millennia. Journal of Economic Growth, 23, 1-40.

Brander, J. A., and Taylor, M. S., 1998. The simple economics of Easter Island: A Ricardo-Malthus model of renewable resource use. American Economic Review, 88, 119-138.

Chanda, A., and Putterman, L., 2007. Early starts, reversals and catch-up in the process of economic development. Scandinavian Journal of Economics, 109, 387-413.

Chatterjee, S., and Turnovsky, S.J., 2012. Infrastructure and inequality. European Economic Review, 56, 1730-1745.

Chu, A., 2010. Nation states vs. united empire: Effects of political competition on economic growth. Public Choice, 145, 181-195.

Chu, A., 2025. Human Origins and Evolution in a Malthusian Economy. World Scientific Publishing.

Chu, A., Peretto, P., and Furukawa, Y., 2024. Political fragmentation versus a unified empire in a Malthusian economy. Journal of Economic Behavior and Organization, 222, 284-293.

Collins, J., Baer, B., and Weber, E. J., 2014. Economic growth and evolution: Parental preference for quality and quantity of offspring. Macroeconomic Dynamics, 18, 1773-1796.

Dalgaard, C.-J., and Strulik, H., 2015. The physiological foundations of the wealth of nations. Journal of Economic Growth, 20, 37-73.

de la Croix, D., and Dottori, D., 2008. Easter Island's collapse: A tale of a population race. Journal of Economic Growth, 13, 27-55.

Ehrlich, I., and Lui, F., 1997. The problem of population and growth: A review of the literature from Malthus to contemporary models of endogenous population and endogenous growth. Journal of Economic Dynamics and Control, 21, 205-242.

Futagami, K., Iwaisako, T., and Ohdoi, R., 2008. Debt policy rule, productive government spending, and multiple growth paths. Macroeconomic Dynamics, 12, 445-462.

Futagami, K., and Mino, K., 1995. Public capital and patterns of growth in the presence of threshold externalities. Journal of Economics, 61, 123-146.

Futagami, K., Morita, Y., and Shibata, A., 1993. Dynamic analysis of an endogenous growth model with public capital. Scandinavian Journal of Economics, 95, 607-625.

Galor, O., 2005. From stagnation to growth: Unified growth theory. Handbook of Economic Growth, 1, 171-293.

Galor, O., 2011. Unified Growth Theory. Princeton University Press.

Galor, O., 2022. The Journey of Humanity: The Origins of Wealth and Inequality. Dutton.

Galor, O., and Michalopoulos, S., 2012. Evolution and the growth process: Natural selection of entrepreneurial traits. Journal of Economic Theory, 147, 759-780.

Galor, O., and Moav, O., 2002. Natural selection and the origin of economic growth. Quarterly Journal of Economics, 117, 1133-1191.

Galor, O., and Ozak, O., 2016. The agricultural origins of time preference. American Economic Review, 106, 3064-3103.

Glomm, G., and Ravikumar, B., 1994. Public investment in infrastructure in a simple growth model. Journal of Economics Dynamics and Control, 18, 1173-1188.

Glomm, G., and Ravikumar, B., 1997. Productive government expenditures and long-run growth. Journal of Economic Dynamics and Control, 21, 183-204

Hirshleifer, J., 1991. The paradox of power. Economics and Politics, 3, 177-200.

Hirshleifer, J., 2000. The macrotechnology of conflict. Journal of Conflict Resolution, 44, 773-792.

Lagerlof, N.-P., 2007. Long-run trends in human body mass. Macroeconomic Dynamics, 11, 367-387.

Lagerlof, N.-P., 2014. Population, technology and fragmentation: The European miracle revisited. Journal of Development Economics, 108, 87-105.

Lagerlof, N.-P., 2021. Multiple steady statehood: The roles of productive and extractive capacities. Journal of Economic Growth, 26, 113-152.

Le Fur, T., and Wasmer, E., 2025. Fighting for resources: A unified growth model of the Great Divergence. Journal of Economic Growth, forthcoming.

Maebayashi, N., Hori, T., and Futagami, K., 2017. Dynamic analysis of reductions in public debt in an endogenous growth model with public capital. Macroeconomic Dynamics, 21, 1454-1483.

Malpede, M., 2023. Malaria and economic activity: Evidence from US agriculture. American Journal of Agricultural Economics, 105, 1516-1542.

Malthus, T.R., 1798. An Essay on the Principle of Population. Oxford World's Classics.

Mayshar, J., Moav, O., and Pascali, L., 2022. The origin of the state: Land productivity or appropriability?. Journal of Political Economy, 130, 1091-1144.

Putterman, L., and Trainor, C., 2006. Agricultural Transition Year Country Data Set. Brown University.

Svizzero, S., and Tisdell, C., 2014. Inequality and wealth creation in ancient history: Malthus' theory reconsidered. Economics and Sociology, 7, 222-239.

Turnovsky, S.J., 1996. Optimal tax, debt, and expenditure policies in a growing economy. Journal of Public Economics, 60, 21-44.

Turnovsky, S.J., 2000. Fiscal policy, elastic labor supply, and endogenous growth. Journal of Monetary Economics, 45, 185-210.