4. Consider the Nash bargaining model. Suppose that there are two players, the size of the "pie" is 1. (a) Suppose the utilities from a split of the pie given by (x1,x2) are u1(x1)=x1,u2(x2)= x2. The disagreement points are (d1,d2)=(0.1,0.2). Compute the Nash bargaining solution. (b) Suppose now the utility of the first player is given by u(x1)=x12, and the utility of the second one is given by u2(x2)=x2. The disagreement points are (d1,d2)=(0,0). How does the change in utility affect the outcome relative to a version of this problem we saw in class? (c) Suppose that (x1,x2) are u1(x1)=x1,u2(x2)=x2, and that (d1,d2)=(0,0), but the first player has more bargaining power: now the Nash bargaining solution looks like maxx1,x2(x1d1)(x2d2)1, for say, =43 (this is how to capture the fact that one side has not only a better disagreement point, but is also has more power). What is the solution now? How is the solution related to their bargaining power? (d) Finally, suppose that u1(x)=u2(x)=x, and that (d1,d2)=(0.1,0.2), and =0.6. Compute the solution. 4. Consider the Nash bargaining model. Suppose that there are two players, the size of the "pie" is 1. (a) Suppose the utilities from a split of the pie given by (x1,x2) are u1(x1)=x1,u2(x2)= x2. The disagreement points are (d1,d2)=(0.1,0.2). Compute the Nash bargaining solution. (b) Suppose now the utility of the first player is given by u(x1)=x12, and the utility of the second one is given by u2(x2)=x2. The disagreement points are (d1,d2)=(0,0). How does the change in utility affect the outcome relative to a version of this problem we saw in class? (c) Suppose that (x1,x2) are u1(x1)=x1,u2(x2)=x2, and that (d1,d2)=(0,0), but the first player has more bargaining power: now the Nash bargaining solution looks like maxx1,x2(x1d1)(x2d2)1, for say, =43 (this is how to capture the fact that one side has not only a better disagreement point, but is also has more power). What is the solution now? How is the solution related to their bargaining power? (d) Finally, suppose that u1(x)=u2(x)=x, and that (d1,d2)=(0.1,0.2), and =0.6. Compute the solution