9. Suppose there are two types of workers, low productivity and high productivity. A firm uses a signal of years of education to help determine workers' productivity. Suppose a high productivity worker receives $1,000,000 in lifetime earnings and a low productivity workers receives $700,000 in lifetime earnings.

a. Suppose four years of education creates a separating equilibrium where high productivity workers obtain the signal and low productivity workers do not. What may be the cost of a year of education for a low productivity worker? Briefly explain.

b. In what situation would there be no separating equilibrium where high productivity individuals obtain the signal and low-productivity individuals do not obtain the signal, no matter how many years are picked for the signal? Briefly explain and provide an example.