As in the textbook example, assume there are two types of workers, low- and high-ability, and let 8 = 0.25 be the proportion of high-ability workers in the population. Assume their marginal productivity and, therefore, their wages are wh = $20 and w = $16, and that both types can use college education to signal high ability. The cost of college education for low-ability workers is c, = $5 whereas the cost for high-ability workers is c = $2.Questions 10 Determine a general condition that makes workers want to separate themselves using education as a signal. That is, find a condition that makes high-ability workers want to go to college while low-ability workers do not. Given the wages and costs for both types of workers (W) = 20, w, = 16, C = 2, and c = 5) and the proportion of high-ability workers in the population (8 = 0.50), does the condition hold? What wages are paid to each type of worker? (a) The condition holds; firms pay wh = $20 and w, = $16 (b) The condition holds; firms pay WA = $18 and w, = $11 (c) The condition does not hold; firms pay Wh = $20 and w; = $16 (d) The condition does not hold; firms pay WA = WI = W = $17 Questions 11 Suppose the government gives a $2 subsidy to people who go to college. Does the condition you determined in the previous question hold? What wages are paid to each type of worker? (a) The condition holds; firms pay W, = $20 and w, = $16 (b) The condition holds; firms pay W, = $20 and w, = $13 (c) The condition does not hold; firms pay W, = $20 and w, = $16 (d) The condition does not hold; firms pay WA = W, = W = $17 Questions 12 Compare the equilibria in questions 10 and 11. Which one is more efficient? Which is the most beneficial for high-ability workers? And for the low-ability workers? (a) The separating equilibrium in question 10 is the most beneficial for low-ability workers (b) The separating equilibrium in question 10 is the most efficient in terms of total welfare (c) The pooling equilibrium in question 11 is the most beneficial for high-ability workers (d) The pooling equilibrium in question 11 is the most efficient in terms of total welfare