A $...$rm earns gross pro...t $($pro$...$t not including the wage$)$ of $100$ from a

low$-$ability worker and $150$ from a high$-$ability worker. A quarter of the

workers are low$-$ability and the rest are high$-$ability.

$($a$)$ If competitive $...$rms have no signals available, what is the equilibrium

wage they would pay?

$($b$)$ Under what conditions on the cost of getting an education for each

type, cL and cH$,$is there a separating equilibrium?

$($c$)$ Suppose cL $=30$ and cH $=0.$ Show that there is a pooling equilibrium

in which both types get an education and explain how much each type

of workers is paid in such equilibrium. Be sure to specify the $...$rm$$s

out$-$of$-$equilibrium beliefs if it were to meet an uneducated worker.