Signaling when education is productive. there are two groups of workers: h types (higher productivity) and l types (lower productivity). let ch(e) denote a type h worker’s cost function for obtaining education and let cl(e) denote the cost function for a type l worker, where: cl(e) = 0.5 · e 2 (10) ch(e) = 0.25 · e 2 . (11) mh = 4e is the marginal product of labor for a type h worker and ml = 2e is the marginal product for a type l worker. by assumption, the marginal product of labor for each type depends on the amount of education received. a fraction p = 0.4 are type h and the rest of the workers are type l. as usual, the utility that a worker receives from working is the wage minus cost: u(e) = w(e) − c(e) (12) answer the following:
(a) clearly define a pooling equilibrium for this problem.
(b) solve for all values of ¯e that are consistent with a pooling equilibrium. show your work.
(c) clearly define a separating equilibrium for this problem.
(d) solve for all values of ¯e that are consistent with a separating equilibrium. show your work.