3. In a simplified bargaining model of marriage, the couple jointly maximizes the following utility function: U=[Um - Tm]*[U T] Where U=c; for i=m,f Subject to Y= c+cf, where Y is total family income And Um > Tm & U Tf a. Solve the first order conditions for the couple's joint utility maximization problem to find the relationship between U-T and Um-Tm for the couple, given the income constraint. (Hint: The c; are the choice variables. Substitute U=c; in to the couple's utility function and treat the price of both cm and cf as 1.) b. What is UT? Give two examples from class notes or readings of events that would increase the value of T and explain why Te increases in these cases. Be as specific as possible about your examples. f c. What events or factors would increase T in this model? m d. Empirically, why do we need look for "external environmental parameters" to change Tf and Tm? What sort of bias are we hoping to avoid? e. How would Uf change if Tf increased in this model? Explain why. If Y also remained constant, what would happen to c, and cm?