A Married couple with children is considering divorce. They are negotiating about two elements of the divorce: the level of child support that will be paid to the partner who keeps the children, and level of child support that will be paid to the partner of the children who keeps the children, and the amount of time that the children will spend with each partner. Whoever has the children would prefer more child support from the other partner and more time with the children. Furthermore, the partner who keeps the children believes that as the amount of child support increases, the value of more time with the children declines relative to the value of child support. Draw a typical indifference curve for the partner who keeps the children with the level of child support on the horizontal axis and the amount of time that the children spend with this partner on the vertical axis. Is this indifference curve convex to origin? Why or why not?
Suppose that the partner who keeps the children has this utility function u=cv, where c = the weekly level of child support and v = the number of days per week that the children spend with this partner. Suppose that initially the weekly support level is $100, and the number of days per week spent with this partner is 4. What is the utility to this partner from week spent with partner is 4. What is the utility to this partner from that arrangement? If the other partner wishes to reduce the weekly support to $80, how many more days with the children must the child-keeping partner have in order to maintain utility at the previous level?