(a)Given the utility function ,

(i)Graph the function, assuming.(5 marks)

(ii)Explain if the function exhibits positive marginal utility and what is the attitude towards risk of an individual who has such a utility function. (5 marks)

(b)Mr. Sanitizer's current wealth consists of his home, which is worth $50,000 and $20,000 in savings, which are earning 7% 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 fire, storm and so on, during the period covered by the renewal:

Value of Loss ($) Probability

0 0.98

5,000 0.01

10,000 0.005

50,000 0.005

His insurance agent has quoted the following premiums:

Amount of Insurance ($) Premium ($)

30,000 280

40,000 327

50,000 374

Mr Sanitizer expects neither to save nor to dissave during the coming year, and he does not expect his home to change appreciably in value over this period. His utility for wealth at the end of the period covered by the renewal if logarithmic; that is, U (w) = In (w).

(i)Give that the insurance company agrees with Mr Sanitizer's estimate of his losses, under with policy should he renew this insurance ($30,000, $40,000 or for the $50,000) or shall he cancel it.(10 marks)

(ii)Suppose Mr Sanitizer has $320,000 in his savings account. Would this change his insurance decision?(10 marks)

Hints: Assume Mr Sanitizer earns 7% on savings and that premium are paid at the beginning of the year.