Question

Neighbors Ron and Deborah live in adjacent houses but are undecided as to whether to pave a shared driveway that offers equal access to each of their houses. The driveway is usable but unpaved. It is long and tree lined and does have some rustic charm. Ron has recently bought a new car and wants a paved approach road/ driveway to protect his new car from unnecessary wear and tear. Ron had approached Deborah about sharing the cost of the project that is estimated to be $40,000. Deborah seems ambivalent and often talks about the rustic appeal and old charm of the existing road. Ron believes that secretly, Deborah also wants the road done but is unwilling to share the cost. Ron agonized over having to pay the entire paving cost but stopped short of doing it. He reckons that the value of the paved road to him is about $30,000, and if Deborah is like him, the paved road should be worth $30,000 to her as well. It seems unfair to him that he alone pays for it, while it should be really be shared 50:50. By himself, he has decided to suffer through and not do it at all. You are friends with Deborah and Ron respects you. As a last resort, you have been approached by Ron to act as a mediator to find a mutually acceptable solution. Consider each question independently and carefully: 1. You approach Deborah and assess that there is a 40% chance that she is just like Ron, only not admitting that in order to extract concession. However there is a 60% chance that she really likes the rustic charm of the unpaved road and the value of the paved road is only $8000 to her. a. Should the road be built at all with this information? (1 points) 2. Suppose you know that even if Deborah likes the rustic charm, her value of the paved road is really $20,000 because she is allergic to dust. a. Should you recommend that the road be built with this information? (1 points) b. Suppose you could know Deborah's true type, how will you allocate the cost? Why? (1 point) c. If you did not know Deborah's true type but only have the probability information of her type and her value estimate as in Part 2, would you decide to build, and if so, what would be the cost sharing arrangement between the two neighbors that you believe would be acceptable to them? (2 points) [Hint: You may consider a mixed strategy where the road is built with a finite probability]

Answer 1

Solution to 1.

We will calculate the value extimated value of road for Deborah

Value of Road for Deborah	Value for her	probability	Value
She like the paved road	30,000	40%	12,000
She like the unpaved road	8,000	60%	4,800
			16,800

Value is 16,800 which is less than 50% of estimated cost of 40,000.

No, So road will not build with the informatio given.

Solution to 2. a.

Value of road for Deborah:

Value of Raod for Deborah	Value for her	probability	Value
She like the paved road	30,000	40%	12,000
She like the unpaved road	20,000	60%	12,000
			24,000

Value is 24,000 which is higher than 50% of estimated cost of 40,000.

Yes, So road will be build with the information given.

Solution to 2. b.

We can allocate cost of 40,000 to 20,000 each. As it is equal for both and both have value of 20,000 or more.

Solution to 2. c.

we can allocate 40,000 into following

Maximum Ron 30,000

Maximum Deborah 24,000

we can allocate 40,000 in the ratio of 30,000:24,000

So Ron will pay = $22,222 & Deborah will pay 17,778