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End of Autumn Semester Examinations 2021/22

ASB-3313 FINANCIAL ECONOMICS

Question 1

a) Manon prefers more money to less and her preferences satisfy the axioms of EUT. She is indifferent between a lottery ticket which gives a 10% chance of winning £5,000 (and 90% chance of nothing) and the certainty of £250.

i. Graph her full set of indifference curves in a Machina triangle with £0, £250 and £5,000 as the pure outcomes. Account for the shape of her indifference curves.

ii. Which of the following two lotteries would Manon prefer?

We are now told that Manon is also indifferent between the certainty of £4,000 and a lottery ticket which gives an 85% chance of winning £5,000.

iii. Derive and graph Manon’s normalised von-Neumann Morgenstern utility function for values between £0 and £5,000.

iv. Describe Manon’s attitude to risk.

b) Explain the difference between first-order and second-order uncertainty. Critically evaluate

the claim that the Ellsberg paradox fatally undermines Expected Utility Theory.

Question 2

a) Consider the following four lotteries:

Explain the concepts of first-order and second-order stochastic dominance. Prove robustly for each lottery whether it first-order or second-order stochastically dominates any of the other lotteries.

b) Distinguish between time consistent and time inconsistent preferences. Provide examples of where time inconsistency arises in the real world. How might certain financial assets allow people to control for their time inconsistency?

Question 3

a) The citizens of Tir-na-Nog face the risk of getting ill. If they do get ill, they must spend $10,000 on medical treatment. There is no other disutility to the illness itself.

Every citizen has a utility function and the same initial wealth of $10,000. However, different citizens have different probabilities of catching the illness. Across the population this probability, , is distributed uniformly between 0 and 1.

i. What is the mean expected utility of the citizens of Tir-na-Nog?

Assume now that the government decides to introduce a voluntary insurance scheme to cover against the illness. The government charges a $5,000 premium for full insurance against the illness.

ii. Assuming that nobody has information about their own individual probability of getting the disease, and only know the distribution of ; what proportion of the citizens will choose to buy the insurance? Does the scheme make a profit or loss? What is the mean expected utility of the citizens of Tir-na-Nog following the introduction of the scheme?

iii. Assuming now that everyone knows their own , but the government still only knows the distribution of ; what proportion of the citizens will now choose to buy the insurance? Does the scheme make a profit or loss?

iv. If instead, the government sets a premium of $7,500, does the scheme make a profit or loss? What is the mean expected utility of the citizens of Tir-na-Nog following the introduction of the scheme?

The government now chooses to make the scheme compulsory.

v. Does the scheme make a profit or loss? What is the mean expected utility of the citizens of Tir-na-Nog following this change?

b) Comment on the results to part (a) in the context of the Hirshleifer effect. In what other circumstances might the value of information not be positive? Illustrate your answer with potential examples from theory or the real world.

Question 4

a) Buddug owns a house worth £100,000, and has no other wealth. The probability that her house will be destroyed by flood is equal to 33% if she doesn’t regularly clear the dykes around her house (e = 0), but this probability falls to 10% if she puts in the effort to clear them (e = 1). If her house is destroyed then she is left with a piece of land that is worth

£25,000.

Her utility function is given by

i. In the absence of insurance, will Buddug put in the effort to clear the dykes? Explain your answer fully.

ii. What is the fair premium for full insurance, assuming that the insurance company can observe that Buddug puts in the effort to clear the dykes? Would Buddug accept this insurance contract?

iii. If Buddug doesn’t put in any effort to clear the dykes, what is the fair premium for full insurance? Would Buddug accept this insurance contract?

iv. Now assume that the insurance company cannot observe whether or not Buddug exerts effort. It chooses to offer partial coverage, of %, at the fair premium. Write down the incentive compatibility constraint for this contract in terms of . Does Buddug choose to exert effort if x = 50? What if x = 60?