Question

On each of two days, Alan and Daisy can jointly undertake a project that yields a profit of $150 per day. They alternately make proposals (at most one per day), starting with Daisy, about how to split this amount. If a proposal is rejected, they don’t work on the project that day; if it is accepted, the agreement applies to that day and the remaining day (if any) . Suppose, first, that both Alan and Daisy have no outside option (they can earn nothing outside). They both want to maximize their own total income over the two days.

(a) Determine the outcome (how they will split the profit) of this bargaining situation, carefully explaining your logic.

(b) Now suppose that Daisy can earn $70 a day outside (but Alan still cannot earn anything outside). Determine the bargaining outcome now.

(c) Explain why the bargaining outcomes are different in parts a and b above.

Answer 1

a) As on the first day both of them do not have any outside option to work , they will desperately want to work in the project to make money . So they will make a decision jointly that both of them agrees and eliminate the chance of rejection of the proposal. So they will split the amount $150 between them, i.e, $75 each.

b) Now Daisy have an outside option of $70 but Alan still cannot earn anything outside. So desperation of being part of the project for Alan is much higher than Daisy. So Daisy will use this opportunity to claim higher amount than $75 that she was getting first day. And If Alan rejects that offer then he will left out with nothing but Daisy would still have $70. So It is most likely for Alan to accept Daisy's proposal.

c) Here the main reason for the different outcomes are Rational thinking of a Person. As both of them wanted to maximize their own total income they chose to be rational about it. At the first day as both of them didn't have any income outside they were dependent at the project so made a fair deal between them so that no one complains about it. But the situation changed next day when Daisy had income outside ,she was not bound to make any fair deal anymore so she demanded more money than equal distribution. Alan knew that if he don't agree with the proposal then Daisy will still gain $70 from outside but he would left with zero. So the only rational option for him was to go with the proposal.