Unfortunately, oil spills are not uncommon. For example, in August 2016, two tankers ran into each other off the coast of Japan, causing an oil spill. In January 2017, two different tankers ran into each other off the coast of India, causing another. The environmental consequences of these accidents, which can be very costly, include clean-up and site restoration costs, legal fees, punitive damages, and compensation for people whose livelihoods have been adversely affected. Suppose a firm (the contractee) contracts with an oil tanker company (the contractor) to transport refined petroleum products for \(€ 8\) million. The contractor is fully liable for damages from any oil spills. The total cost of an oil spill is \(€ 20\) million, and the probability of a spill is \(\delta\).

a. What is the value of \(\delta\) that would make a riskneutral contractor indifferent to accepting or rejecting the contract? For what values of \(\delta\) would the contractor accept the contract?

b. If the true probability of a spill is \(2 \%\), the contractor is risk averse, and fair insurance is offered, how much insurance would the contractor buy?

c. If the contractee partially compensates the riskneutral contractor so that the latter would have to pay only \(40 \%\) of the cost of an oil spill, what value of \(\delta\) would make the contractor indifferent to accepting or rejecting the contract? What does this say about the relationship between liability and acceptance?

d. If the true probability of a spill is \(2 \%\), the contractor is risk averse, fair insurance is offered, and the contractor is partially compensated as in part \(\mathrm{c}\), how much fair insurance will the contractor now buy?