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Sarah and Josh are contemplating marriage, and in the event that they marry their utility possibility frontier is given by x+y=12, where x and y,
Sarah and Josh are contemplating marriage, and in the event that they marry their utility possibility frontier is given by x+y=12, where x and y, respectively, denote the utility levels that Sarah and Josh attain in their married state. Their respective outside options generate a utility of X=0 for Sarah and Y=4 for Josh.
- Graph the region of feasible utility combinations in marriage, which presumably is a cooperative endeavor.
- Define the notion of Pareto efficiency. Why might we expect the outcome here to be Pareto efficient?
- If Sarah could unilaterally decide the allocation of utilities, what allocation would she choose? And what allocation would Josh choose?
- Describe (with the help of a diagram) the nature of the Nash bargaining solution (NBS), where both Sarah and Josh influence the outcome.
- Compute the utilities of Sarah and Josh in the NBS by graphing the Nash product. Based on your solution, can you predict whether Sarah and Josh will opt to marry?
- Redo part e when X=4 and X=8 (assuming that Y is fixed at 4).
- Using the solutions you have computed, graph Sarahs utility in the NBS as a function of her threat utility. On the same figure, also graph Joshs utility in the NBS. What do these graphs
say to you?
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