ECN6510 Topic 2 Past Questions
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ECN6510
Topic 2 Past Questions
1. (a) An individual, who has a utility function given by U = w1/ 2 , has wealth (w) of £150 and faces the prospect of a loss of £85 with a probability of 0.3 and a probability of 0.7 that he/she will not incur the loss.
(i) Explain what is meant by risk aversion and whether this individual is risk averse. [10%]
(ii) Calculate the maximum premium the individual will pay to insure against this loss. [20%]
(iii) Explain what is meant by fair insurance and calculate the fair insurance premium. [20%]
(b) Assume an economy is comprised of two types of individuals characterised by high risk and low risk such that the high risk individuals experience a relatively high probability of losing wealth due to an adverse event occurring. Formally analyse the conditions under which (i) a pooling equilibrium and (ii) a separating equilibrium arise in the market for insurance against the loss in wealth associated with the occurrence of the adverse event. [50%]
2. (a) Explain what is meant by full and fair insurance and comment on whether it is likely to arise in practice. [20%]
(b) Using a diagram, compare the fair insurance premium with the maximum premium that a risk averse individual is willing to pay for insurance. [20%]
(c) In the context of asymmetric information, analyse the problems faced by insurance companies in designing insurance contracts for high risk and low risk individuals. [60%]
3. (a) An individual has wealth (”) of £160 and faces the prospect of a loss of £80 with a probability of 0.1. The individual has a utility function given by U = w1/2 . Explain what is meant by risk aversion and explain whether or not this individual is risk averse. [20%]
(b) What is the maximum premium the individual described in part (a) will pay for insurance against this loss? [10%]
(c) Explain what is meant by a fair insurance premium and calculate the difference between the fair premium and the maximum premium that the individual is willing to pay. [10%]
(d) Formally analyse the problems faced by insurance companies in designing insurance contracts when faced with a population comprising different types of individuals. [60%]
4. Assume two types of risk averse individuals characterised by high risk and low risk respectively. There are C low risk individuals and β high risk individuals in the population. There are two states of nature, good and bad. In the good state, wealth is w0 and, in the bad state, wealth equals w0 - L where L > 0 . The probability of experiencing the bad state is pi where i = H, L , pH > pL . An insurance company which is only concerned with expected profits is considering providing insurance to the two types of individuals.
(a) Assuming the insurance company can ascertain whether an individual is high or low risk, explain what type of insurance contract the company will offer. [50%]
(b) How is your answer to part (a) affected if the insurance company is no longer able to ascertain whether an individual is high or low risk? [50%]
2023-08-01