2. [40 Points] An economy has two types of workers, Qualified and Unqualified. You must hire workers without observing their type and pay them before knowing their actual output. In your firm, a worker who is hired as a qualified worker is paid a wage of 100 units and the wage for an unqualified worker is 60 units.

a. [25 Points] Consider the following screening mechanism: Anyone who is educated to level N is considered as a Qualified worker, and anyone who is educated to level N/2 is considered as unqualified. Assume that the unit cost of education for a Qualified worker is 5, whereas for an Unqualified worker, it is 10. (These costs are measured in the same unit as the wages). The alternative (fallback) option for a Qualified worker pays 60 and requires 4 levels of education. The alternative (fallback) option for the Unqualified worker pays 30 and requires 2 levels of education.

1. What is the minimum level of N that will achieve a separating equilibrium? (N must be an integer.)

2. What is the equilibrium payoff to each type of workers if N is set to the lowest number that would achieve a separating equilibrium?

b. [10 Points] Assume that the population consists of 50% Qualified and 50% Unqualified workers. Now suppose you drop the screening mechanism and pool the Qualified and Unqualified workers.

1. Find the pooled wage that you will need to offer.

2. Considering both types of workers, who will gain and who will lose from dropping the screening mechanism and moving to a pooling equilibrium?

c. [5 Points] Suppose you are a Qualified worker in this economy and you start off at the pooling equilibrium you found in part b.

1. Would asking for a raise be a best response strategy for you? If so, identify exactly the argument you would make to your employer which would guarantee you the raise that you will be asking, i.e. state how much of a raise you would ask and how you would convince the employer to accept.

2. What will be the equilibrium outcome if all qualified workers follow their best-response strategy?