13. Members of two groups, the blues and the greens, have productivity values that range from $5 to $15/hr. The average productivity of the blues is $6/hr and the corresponding average for the greens is $12/hr. A costless productivity test is known to have the property that it gives the correct productivity value with probability 13, and a random productivity value drawn from the relevant group distribution with probability 23.

a. Assuming labor markets are competitive, how much will a blue with a test value of 9 be paid?

b. How much will a green with the same test value be paid?

c. Is it correct to say that statistical discrimination accounts for why the greens, as a group, are paid more than the blues?