Publicly Funded Education and Human Capital in the Presence of a Convex-Concave Education Function

This study investigates an aggregative optimal growth model in which short-lived individuals obtain their labour skill through education. The process of human capital formation is described by an increasing, convex-concave education function relating the success rate to the educational expenditure per student. The cost of education is publicly funded by an income tax imposed on adult workers. Despite the apparent regularity and rationality of this idealized economy, it is shown that the existence of the steady state of the model is not guaranteed. In fact, the steady state only exists for carefully chosen social time rates of preference. However, the steady state, if it exists, is unique and in terms of local stability, a saddle point.