Cremer, Helmuth and Maldonado, Dario (2013) Mixed oligopoly in education. TSE Working Paper, n. 13-381, Toulouse

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Abstract

This paper studies oligopolistic competition in education markets when schools can be
private and public and when the quality of education depends on "peer group"effects.
In the first stage of our game schools set their quality and in the second stage they fix
their tuition fees. We examine how the (subgame perfect Nash) equilibrium allocation
(qualities, tuition fees and welfare) is affected by the presence of public schools and
by their relative position in the quality range. When there are no peer group effects,
efficiency is achieved when (at least) all but one school are public. In particular in the
two school case, the impact of a public school is spectacular as we go from a setting
of extreme differentiation to an efficient allocation. However, in the three school case,
a single public school will lower welfare compared to the private equilibrium. We then
introduce a peer group effect which, for any given school is determined by its student
with the highest ability. These PGE do have a significant impact on the results. The
mixed equilibrium is now never efficient. However, welfare continues to be improved if
all but one school are public. Overall, the presence of PGE reduces the effectiveness of
public schools as regulatory tool in an otherwise private education sector.