Decreasing average cost in private schools, existence of majority voting equilibrium, and a policy analysis for Turkey

The existing models of mixed public–private school systems usually capture only the decreasing average cost faced by public schools, whereas empirical studies find evidence of it for private schools as well. Motivated by this, an equilibrium model of a mixed public–private school system is studied in this paper, whereby private schools also face decreasing average cost over enrollment. In the model, households, heterogeneous with respect to exogenously specified income and child’s ability, choose among a public and a private school. Private school charges tuition whereas public school is free. Public school spending is financed by income tax revenue collected from all households and the tax rate is determined via majority voting. Achievement of a child depends on its ability and education spending. Under the assumptions on the parameters of the model, a joint lognormal distribution of income and ability, and a Cobb–Douglas utility, majority voting equilibrium is numerically shown to exist. The model is calibrated to match certain statistics from the 2013 Turkish data. Using the calibrated model, we compare the benchmark for a mixed public–private school system with a pure public school system to understand the impact of shutting down some of the private schools in Turkey following the July 15 coup attempt. We find that mean achievement and variance of achievement after high school is $$0.039\%$$ 0.039 % higher and $$0.013\%$$ 0.013 % lower respectively in a pure public school system.