8 A manager needs a new website for his business. He does not know how difficult this task is: it can take either T = 1 months or T = 3 months, both with equal probability. The manager would like to ensure that the project is done, but minimise the expected payment. He goes to see an IT contractor, who knows the length of time it will take to finish the project. The contractor's utility function is u(T, m) = -107 + m, where m is the remuneration. His reservation utility is 0. (a) The gullible manager believes everything he is told. The contrac- tor however is truthful only when it pays. The manager asks the contractor how long the project will take, and offers a contract that gives the contractor at least his reservation utility. How much will the manager offer if he is told T = 1 or T = 3? How much will he actually pay if T = 1 or T = 3? What is the true expected payment of the manager? (b) Before meeting the contractor, the manager is informed that some people could be lying to him. His first thought is to offer a pair of contracts my and my so that the contractor will choose me if T = 1 and my if T = 3. Why does this not reduce the expected payment? (c) His next idea is to require the contractor to come into the office for a minimum amount of time 7. He knows that the contractor has disutility of 10 for every amount of time spent working on the project but only a disutility of 5 for an amount of time spent idle in the office. So, the contractor's utility is u(T, T, m) = -10T + m TZT -107 - 5(T - T) +m T