Early state formation in a Malthusian economy

This study develops a Malthusian growth model with early state formation and interstate competition. It explores how states' tax capacity and provision of productive public goods shape population dynamics and interstate competition. Each state has an optimal tax rate, increasing in the elasticity of agricultural output with respect to public goods. Without interstate competition, population either converges to a Malthusian trap or grows steadily depending on this elasticity. With interstate competition, states either coexist or only one survives. Population of any surviving state first rises and then falls with its tax rate, capturing the rise and fall of the state.