Q. Suppose there are two types of men and two types of women (Good/Bad), and assume further that same-sex marriage is not allowed in this society. The payoffs of the marriage are given by the table below:

Good Wife Bad Wife
Good Husband (2,2) (-1/2,1)
Bad Husband (1/2, -1) (-1,-1)

Suppose the percentage of good wives is a, and of good husbands is b, and b > a. Further assume that people have no idea of their spouse's type before they get married, and one's type is independent of the spouse's type. Single people receive a payoff of 0. Assume people cannot get divorced.

a) What is the socially efficient allocation of wives and husbands in this society (the percentage of each combination of marriages that maximizes social welfare)? Compute the efficient total social welfare.

b) Given the random way in which marriages are formed, what will be the distribution of types of marriages? Compute the total social welfare, and show that it is lower than under the efficient allocation.

Now assume people can get divorced unilaterally.

c) What is the divorce rate if transaction costs are zero? What if transaction costs are high enough that husbands and wives cannot bargain?

d) Can this model explain the fact that unilateral divorce law increased the divorce rate temporarily? What about the fact that long run divorce rates remained the same?

e) Now assume there are 10, 000 couples that get married each year. Before the unilateral divorce law, inefficient marriages divorce after one year of bargaining. Assume bargaining itself doesn't affect payoffs. What are the short run and long run effects of a unilateral divorce law?