Mona is going to be out of town for two days and will not be needing her car during this time. Lisa is visiting relatives and is interested in renting her car. The value to Lisa of having the car during this time is $50 per day. Mona figures that the total cost to her of letting Lisa use the car is $20, regardless of how many days Lisa uses it. On the evening before the first of these two days, Mona can send a message to Lisa, offering to rent the car to her for two days for a specified price. Lisa can either accept the offer or reject the offer and make a counteroffer. The only problem is that it takes a full day for a counteroffer to be made and accepted.

Let us consider the Rubinstein bargaining solution to this problem. We start by working back from end. If Lisa rejects the original offer, then the car can only be rented for one day and there will be no time for Mona to make a counteroffer. So if Lisa rejects the original offer, she can offer Mona slightly more than $20 to rent the car for the last day and Mona will accept. In this case, Lisa will get a profit of slightly less than $50−$20 = $30. Mona understands that this is the case. Therefore when Mona makes her original offer, she is aware that Lisa will reject the offer unless it gives Lisa a profit of slightly more than _____________ Mona is aware that the value to Lisa of renting the car for two days is ___________ Therefore the highest price for two days car rental that Lisa will accept is slightly less than ______________ Since Mona’s total costs for renting the car are $20, Mona would make a net profit of slightly less than _____________ and Lisa would make a net profit of slightly more than ____________

(a) Suppose that the story is as before except that Mona will be out of town for three days. The value to Lisa of having the car is again $50 per day and the total cost to Mona of letting Lisa use the car is $20, regardless of how many days Lisa uses it. This time, let us suppose that Lisa makes the first offer. Mona can either accept the offer or refuse it and make a counteroffer. Lisa, in turn, can either accept Mona’s counteroffer or refuse it and make another counteroffer. Each time an offer is rejected and a new offer is made, a day passes and so there is one less day in which the car can be rented. On the evening before the first of these three days, Lisa reasons as follows. “If Mona rejects the offer that I make tonight, then there will be two days left and it will be Mona’s turn to make an offer. If this happens, Mona will get a profit of slightly less than ________________ Since her total costs are $20, Mona will make a profit of $50 if I offer her a price of ____________ for the three days rental.” Since three days of car rental is worth $150 to Lisa, Lisa would make a profit of ________ and Mona would make a profit of $50.

(b) Now suppose that the story is as before except that Mona will be out of town for four days and suppose that Mona makes the first offer. Mona knows that if Lisa rejects her first offer, there will be three days left, it will be Lisa’s turn to make an offer and so Lisa can make a profit of ____________ (See the previous answer.) Having the car for four days is worth $200 to Lisa, so to the highest price that Mona can expect Lisa to accept for the four days is slightly less than __________ In this case, Mona makes a profit of slightly less than __________ and Lisa makes a profit of slightly more than _________