Question 2 ( 10 points) Consider a firm that is trying to hire workers. There are two types of workers: highproductivity workers have payoff function Ua=w41e2 while low-productivity workers have payoff function Ua=w21e2. Both types of workers have outside option U0=0, and each worker-type occurs with probability 21. The firm has to choose one of three incentive schemes to offer potential workers: i) w=2+e ii) w=2e iii) w=10+4e (Notice that as we go down the list, incentive strength increases while the fixed payment decreases.) The timing of events is: Step 1. The firm chooses an incentive scheme (out of the three schemes specified above) to offer to prospective workers. Step 2. Each type of worker decides whether to accept the offer by the firm. If not, he receives his outside option U0 Step 3. If a worker accepts the offer, he chooses an effort level e, and receives a wage w based on his effort level. 1. (2 points) Which incentive scheme (out of (i), (ii) and (iii)) does a low-productivity worker most prefer? 2. (2 points) Which incentive scheme does a high-productivity worker most prefer? 3. (3 points) Which incentive scheme should the firm offer if it wants to attract only the high-productivity workers? 4. (3 points) What properties of the incentive scheme you chose in (3) allow it to succeed in selecting only the high-productivity workers, while the other two incentive schemes fail to do so? Explain in no more than two sentences