3. (35 points) Neal, Ron, and Joe are bargaining over a unit of a resource. Denote...

 

 

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3. (35 points) Neal, Ron, and Joe are bargaining over a unit of a resource. Denote Neal by N, Ron by R, and Joe by J. We can model their outcome using the Nash bargaining solution. To remind you, the Nash bargaining solution is argmax log(ui uoi) Suppose that the threat point for all three is zero and the welfare weights are identical, i.e. YN YR = YJ = 1.0. Let xy be the share of the good that Neal gets, xR be the share of the good that Ron gets, and xj be the share of the good that Joe gets. Since there is a single unit of the resource, the amount that Joe gets is equal to one minus the amounts that Neal and Ron get. In other words, xy = 1 - XN-XR- i (a) (15 points) Suppose that utility is lincar, so that if x = 0.25, UN = 0.25 and so on. Find the split of the resource. That is, find the amount of the resource that Neal, Ron, and Joe each get. 3. (35 points) Neal, Ron, and Joe are bargaining over a unit of a resource. Denote Neal by N, Ron by R, and Joe by J. We can model their outcome using the Nash bargaining solution. To remind you, the Nash bargaining solution is argmax log(ui uoi) Suppose that the threat point for all three is zero and the welfare weights are identical, i.e. YN YR = YJ = 1.0. Let xy be the share of the good that Neal gets, xR be the share of the good that Ron gets, and xj be the share of the good that Joe gets. Since there is a single unit of the resource, the amount that Joe gets is equal to one minus the amounts that Neal and Ron get. In other words, xy = 1 - XN-XR- i (a) (15 points) Suppose that utility is lincar, so that if x = 0.25, UN = 0.25 and so on. Find the split of the resource. That is, find the amount of the resource that Neal, Ron, and Joe each get.

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Finding the Split of the Resource with Linear Utility We are given that the Nash bargaining solution ... View the full answer