Mr. Onyango's current wealth consists of his home, which is worth Kshs. 5,000,000 and a Kshs. 2,000,000 in savings earned at 7% in a savings 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 (Kshs) Probability

0 0.98

500,000 0.01

1,000,000 0.005

5,000,000 0.005

insurance agent has quoted the following premiums:

Amount of Insurance (Kshs) Premium (Kshs)

3,000,000 30 + AVL1

4,000,000 27 + AVL2

5,000,000 24 + AVL3

Where AVL = Actuarial value of loss = Expected value of the Insurer's loss.

Mr. Onyango 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 is logarithmic; that is U (W) = ln (W).

a.Given that the insurance company agrees with Mr. Onyango's estimate of his losses, should he renew his policy give reasons:

(1)

For the full value of his house (2 mark)

(2) For Kshs. 4,000,000 (2 mark)

(3) For Kshs. 3,000,000 (2 mark)

(4)Should he cancel it? (2 mark)

b.Suppose Mr. Onyango has Kshs. 3200000 in a savings account. Based on utility theory assumptions would this change his insurance decision and why?(8 marks)

c.If Mr. Onyango has Kshs. 2,000,000 in savings and if his utility function is U (W) = -200000

1. Should he renew his home insurance and if yes, for what amount of coverage and what other factors should he consider?(8marks)