The Politics of Public Provision of Education: Proofs

Lemma 1 In the (t, g) policy space: (i) The ideal policy of py is (t = 1, g = g∗(1)) and the ideal policy of ry is (t = 0, g = 0) if θ > w wh and otherwise it is (t = t ∗, g = t∗w θ ) for some t∗ ∈ (0, 1). The indifference curves of ry and py are weakly concave and differentiable. For all t0 ∈ [0, 1], an indifference curve of ry(py) that goes through (t0, 0) lies on or above a line that goes through (t0, 0) and has a slope wh −w 1− θ ( wl −w 1− θ ). (ii) The ideal policy of ro is (t = 0, g = 0), and that of po is (t = 1, g = 0). The indifference curves of ro(po) are linear, with a slope w − wh θ ( w − wl θ ).