Consider a version of the Spence signalling model for which the data are

Type marginal product proportion of population cost of y units of signal

L 1 q cL(y) = 2y

H 2 1 q cH(y) = y

(a) Find a wage schedule that induces a separating equilibrium. Are both agents always better off in the separating equilibrium than in a world with no signalling?

(b) Find a wage schedule that induces a pooling equilibrium where all agents acquire the signal.

(c) Suppose that the signal, y, is quantity of education, and consider a government policy that subsidizes the acquisition of education. In particular, assume the policy allows any individual to obtain any amount of education freely. Is a separating equilibrium still possible?