(a) Consider the following version of Spence's signalling model. The productivity of a

worker in a given job is Z. A worker can be of high ability (Z = 2) or low ability (Z = 1),

with equal probability. Each worker chooses a level of education e >= 0. The total cost

of obtaining education level e is e²/(Z^1/2). The worker's wage is equal to her expected

productivity.

(i) Find the the lowest education level supporting a separating perfect Bayesian

equilibrium.

(ii) Are high-ability workers (of type Z = 2) better off in the separating equilibrium

described in part (i) or in the pooling perfect Bayesian equilibrium in which no one

gets education?