Calculating Willingness to Pay and Minimum Cost for Staying at a Cottage
Roger and Zoë's Vacation Dilemma
Roger and Zoë spend their vacation time at a nice cottage they own in the countryside. Farmer Torti, their neighbor, normally lets his twelve sheep graze in the field next door. The sheep eat quickly and burp loudly, disrupting Roger and Zoë's peaceful vacation. Torti is willing to remove the sheep from the field when Roger and Zoë are there, but his marginal cost of doing so increases with each sheep removed.
Roger and Zoë derive a combined marginal benefit for each sheep Torti removes. They can also opt to stay at a hotel in the city to avoid the sound of burping sheep entirely.
Questions:
a) Calculate the maximum amount Roger and Zoë would be willing to pay to stay at a hotel.
b) Calculate the maximum amount Torti would be willing to pay Roger and Zoë to stay at a hotel.
c) What is the minimum cost of the sound barrier and of going to a hotel that would make it efficient for Roger and Zoë to stay at the cottage without the sound barrier?
d) Describe the circumstances in which Roger and Zoë would stay at the cottage without the sound barrier, stay at the cottage with the sound barrier, and stay at a hotel.
Answers:
a) The maximum amount Roger and Zoë would be willing to pay to go stay at a hotel is $78.
b) The maximum amount Torti would be willing to pay Roger and Zoë to go stay at a hotel is $78.
c) The minimum cost of the sound barrier and going to a hotel that would make it efficient for Roger and Zoë to stay at the cottage without the sound barrier depends on whether the cost of the sound barrier is less than or equal to $78. If it is, they can stay at the cottage without the sound barrier. Otherwise, it would be more efficient for them to go stay at a hotel.
d) Roger and Zoë stay at the cottage without the sound barrier if the cost of the sound barrier is less than or equal to $78. They stay at the cottage with the sound barrier if the cost of the sound barrier is less than or equal to $78 and they prefer the convenience of staying at the cottage. They stay at a hotel if the cost of the sound barrier is greater than $78 or they prefer the comfort and peace of staying at a hotel.