PROBLEM SET 3 1. Suppose there are two types of folks in the world - Slackers and Overachievers. Overachievers are, by nature, more productive than Slackers. However, employers cannot distinguish between these types of workers based on observable characteristics at the time of hiring. Present discounted value of productivity and costs of college education shown below are shown below for both types. Group Overachiever Slacker Value of Proportion Cost of Marginal Of College Product Population Education $200,000 40% $40,000 $120,000 60% $90,000 a. Suppose that employers believe that those with college education are the ones who are overachievers and those without a college education are the ones who are slackers. Under those set of beliefs, what are the wages paid to college graduates and those without college education? Would overachievers choose to get college education or not? Would slackers choose to get college education or not? Is this a signaling equilibrium? If yes, is it a separating equilibrium or pooling equilibrium? b. What is the highest level of tuition (cost of education) that could be charged to overachievers that would maintain a separating equilibrium? c. Suppose that the cost of college rises dramatically to $100,000 for the overachievers and $140,000 for the slackers. Suppose that employers believe that those with college education are the ones who are overachievers and those without a college education are the ones who are slackers with 60% chance and overachievers with 40% chance. Under those set of beliefs, what are the wages paid to college graduates and those without college education? Would overachievers choose to get college education or not? Would slackers choose to get college education or not? Is this a signaling equilibrium? If yes, is it a separating equilibrium or pooling equilibrium?