Explain if the function a negative exponential has a positive marginal utility and what is the

attitude towards risk of an individual who has such a utility function. (5

marks)

(b) Tom current wealth consists of his home, which is worth $60,000 and

$10,000 in savings, which are earning 6% in a saving account. His one-year

homeowner's insurance is up for renewal, and he has the following estimates of

the potential losses on his house owing to hazards, during the period

covered by the renewal:

Value of Loss ($) Probability

0 0.98

2,000 0.01

9,000 0.005

60,000 0.005

His insurance agent has quoted the following premiums:

Amount of Insurance ($) Premium ($)

20,000 280

30,000 327

40,000 374

The utility for wealth at the end of the period covered by the renewal if logarithmic; that is.

(i) Give that the insurance company agrees with Mr Tom's estimate of his

losses, under with policy should he renew this insurance ($20,000, $30,000 or for

the $40,000) or shall he cancel it. (10 marks)

(ii) Suppose Mr Tom has $310,000 in his savings account. Would this change

his insurance decision? (10 marks)

Mr Tom gets 6% on savings and premiums are paid at start of the period.