There are two types of workers, "quicks" and "slows." Productivity equals 2 for quicks, and 1 for slows. λ (between zero and one) equals the fraction of workers who are slows in the population. Workers may invest in a signal of their ability (a credential of some kind) before applying for jobs, at cost ½•y for quicks, and cost y for slows. All firms pay workers their productivity (if there is signaling), or their expected productivity (if there is no signaling). Workers are employed for only a single period after being hired.
For what values of λ and y will signaling occur (a separating equilibrium)? For what values of λ and y will signaling not occur (a pooling equilibrium)? Briefly explain.
Hint: remember the concept of Nash Equilibrium from your economics classes and employ it here. For signaling to work, each quick and slow must have no incentive to change their behavior individually, given that others are not changing their behavior.