6 Self-fullling expectations In question 5, we assumed that the probabilities that members of groups A and B were qualied were different to each other. Consider now the same problem, except now that these probabilities are endogenous and depend on the decisions of the candidates. In particular, a candidate of either group rst observes a cost c that is drawn from the interval [0,1] according to the uniform distribution. After observing their individual cost c, a candidate decides whether or not to invest. If she invests, she becomes qualied for sure. If she does not invest, she remains unqualied. A candidate gets a payoff of 3/2 if she is hired and 0 if she is not hired. The rm does not observe if the candidate invested or not, but the rm does observe the result of a test, which can be L, M, or H and has the same properties as we assumed in question 5. As before, the rm also observes the identity of the candidate. Notice that members of group A are exante identical to members of group B. (a) Show that there exists a (Bayesian Nash) equilibrium where the rm discriminates against members of group B. (b) Suppose that, starting from the discriminatory equilibrium we found in part (a), we introduce regulation that prohibits discrimination. What will be the effect of this policy? Once the policy is lifted, what do you think will happen