There are four levels of ability for workers: excellent, good, ok and bad.

Excellent workers produce goods worth $10000 and have outside options of $6000, good workers produce goods worth $8000 and have outside options worth $5000, ok workers produce goods worth $6000 and have outside options worth $4000 bad workers produce goods worth $4000 and have outside options worth $3000.

In the workforce, 10% are excellent, 30% are good, 50% are ok and 10% are bad.

Workers know their own ability, but firms cannot observe ability.

1. a) What is the profit maximizing wage firms should offer to workers?

2. b) Now firms are able to observe if a worker is bad or not, but not if he is ok, good or excellent. How do your answers to a) change if the firm can offer different wages to bad workers and other workers?

3. c) How much would firms pay at most for information that reveals each workers type?