The income distribution, like all those that exist in reality, will be assumed to have a median value that is below its mean. Lastly, a distinguishing feature of the analysis is that the value of key variables will be determined by the political system rather than exogenously or through a benevolent social planner. While political systems are undoubtedly complex, we will establish a benchmark by considering the case of majority vote. This is a system in which public education is financed solely by district level funds. There is no redistribution across districts, only within a district.
All redistribution is intergenerational.
This system is analytically similar to a purely private system of education. It is also extremely inegalitarian. Children from poor families who live in poor districts will have access to less funding for education than do children who live in wealthier districts. To some extent, increasing the economic heterogeneity of the district can reduce inequality within this system. This may be difficult to achieve since individuals will tend to move to districts where their income is not greater than district mean income.