Related calculation problems
Page 2 of 5 ACCT42115-WE01
1. Maryam must select a decision from three alternatives, labelled 𝑎1, 𝑎2, 𝑎3. The
outcome she receives depends on which of four equally likely states occurs. The
states are denoted 𝑠1, 𝑠2, 𝑠3, 𝑠4. The table below presents the cash outcomes for
Maryam conditional on the state of the world and decision.
𝒔𝟏 𝒔𝟐 𝒔𝟑 𝒔𝟒
𝒂𝟏 6 6 9 2
𝒂𝟐 1 14 1 0
𝒂𝟑 5 0 25 1
(a) If Maryam is risk neutral, what is the upper limit on how much she would be
willing to pay for perfect information on the prevailing state prior to selecting
her decision?
(20 marks)
(b) Bobby has the same choice as Maryam, but his preferences are well
described by the utility function 𝑈 = √𝐶, where 𝐶 is the cash outcome.
(i) Which action is optimal for Bobby in the absence of information on the
state? Support your answer with suitable calculations. Comment on the
difference between the preferences of Mary and Bobby with respect to
optimal actions in the absence of prior information on the state.
(15 marks)
(ii) An information system can be acquired that will imperfectly signal the
state prior to selection of a decision. The system partitions the set of
states into {{𝑠1, 𝑠2}{𝑠3, 𝑠4}}. State the fineness principle and apply it to
individual decisions by Maryam and Bobby to acquire the information
system. You need not perform any calculations.
(20 marks)
(iii) What is the expected utility of the imperfect information system for
Bobby? Support your answer with suitable calculations.
(25 marks)
(iv) If the information system costs 4, should Maryam purchase it? Support
your answer with suitable calculations.
(20 marks)
Page 3 of 5 ACCT42115-WE01
2. A public company is operated by Olive, its Chief Executive Officer (CEO), whose
impact on the company’s aggregate cash inflows is set out in the following table.
𝑠𝑖 , 𝑖 = 1,2,3 are random uncontrollable states of nature, and 𝑎𝑗 , 𝑗 = 1,2 are two
possible actions Olive can take.
𝒔𝟏 𝒔𝟐 𝒔𝟑
𝒂𝟏 20000 50000 20000
𝒂𝟐 20000 50000 50000
𝒑(𝒔𝒊) 0.2 0.4 0.4
The numbers in the final row of the table are the probabilities of the three states.
You may assume that the shareholders of the company are risk neutral. However,
Olive is both risk and effort averse, with the utility function √𝐼(. ) − 𝑒, where 𝐼(. ) is
Olive’s salary function and 𝑒 is Olive’s effort level. For 𝑎1, 𝑒 = 5 and for 𝑎2, 𝑒 = 20.
She must receive expected utility of at least 100 to induce her to work for the
company.
(a) Compute the first-best optimal salary, assuming cooperative behaviour.
(25 marks)
(b) Now assuming Olive acts non-cooperatively, compute the agency cost
suffered by the shareholders if no information is made public.
(20 marks)
(c) By how much is the agency cost reduced if the aggregate cash flow is
published ex post? Support your answer with suitable calculations.
(35 marks)
(d) Compare and contrast the sources of value for ex post decision-influencing
and ex ante decision-facilitating information in a one-period agency
framework.
(20 marks)
Please turn over
