Scenario 1: wh = $4U,w = $20, and c = $15 ::> college education pays off . whw;=20>15=c ::> high ability people go to college (low ability people can't go] ::> separating equilibrium: firms can differentiate workers Scenario 1w;1 = $4D,w = $20, and c = $15 and i9 = 0.5 ::> ayg. wage is W = 0.5040) + (J.5[2(J) = 30 ::> college education still pays off but... ::> ayg. wage is higher than high ability wage minus the costly signal whc=25 high ability people do not go to college (they prefer the ayg. wage) ::> pooling equilibrium: firms pay average wage to all workers Example 1: Wh = $40, w, = $20, and c = $15 and 0 = 0.5 (1) c = 15 (1 - 0)P = 10 ==> both equilibria are possible (point y) Pooling equilibrium: all workers earn w = 30 (total welfare: W = 0 + 30) Separating equilibrium: w/ = 20 only separating equilibrium is possible (point 2') - lowability workers earn w; = 20 30 - Total welfare: W = {J + 356 + 20(1 6) = 27.5 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 cr = $2. Questions 07 How much do firms pay to each worker type when they cannot differentiate them? (a) W = $20 and W, = $16 (b) w, = $2 and w, = $5 (c) w = $17 (d) w = $18 Questions 08 Consider the wage for both types of workers and the high-ability workers' college cost, C . For which values of 8 (the proportion of high-ability workers in the population) do the high-ability workers prefer the separating equilibrium over the pooling equilibrium? (a) Any 8 > 1/2 (b) Any 8 12 (b) Ch = 0 and any Wh > 16 (c) Any ch > 3 and Wh = 20 (d) Any C