School Locations and Vacancies: A Constrained Logit Equilibrium Model

A partial static competitive equilibrium theory is presented and the corresponding constrained logit model specified for a given scenario of policies, which yields the expected equilibrium locations, prices of schools, and students' school choices. Rational students differentiated by socioeconomic cluster demand vacancies at different schools after assessing the school quality, price, and transport costs. Students also interact among them by their valuation of who attends each school (a consumer externality). Schools and vacancies are supplied by different suppliers: private and private-subsidized providers choose school locations and type (quality, capacity, prices); public schools provide free education to fulfill demand under fixed total budgets. Producers face production economies. The Nash demand–supply equilibrium is studied with regard to the existence and uniqueness of the solution, which is solved by a fixed-point algorithm to find a unique solution. The model is applicable to assess different scenarios of regulations and subsidies, as is shown in a test example using data from Santiago, Chile.