Hi, I think I've done this right, however, i need to know if I have as there is no point me thinking I am right if I'm not, obviously.
U(x) = 2ln(x)
Initial Wealth = 500,000
Books = 10,000
Total Wealth = 510,000
Pr(complete loss of books) = 0.02
Pr(no loss) = 0.98
U(x) = ln(x + 200,000)
Assets = 2,000,000
1 - The insurer initially offers the dealer a quote of £250. Find out if the dealer would accept this offer.
2 - Find the maximum offer the dealer would accept.
3 - The dealer offers to pay £201, find out if the insurer would accept this lower price.
E[U(a-x)] = (2ln(510000)*0.98)+(2ln(500000)*0.02)
E[U(a-x)] = 26.2835
26.2835 = 2ln(510000-P)
exp(13.14177) = 510000 - P
P = £201.948
As the initial offer is greater than P the initial offer would be rejected.
The maximum quote the dealer would accept is £201.94 (rounding down as up would be more than the maximum)
Insurer without insuring
U(x) = ln(2,000,000 + 200,000)
U(x) = ln(2,200,000)
U(x) = 14.60396792
U(x) = (ln(2,200,000 + 201) * 0.98) + (ln(2,200,000 + 201 - 10,000) * 0.02)
U(x) = 14.60396817
Utility function with insuring is greater than not insuring so the insurance company would accept the dealers quote of £201.
Does this method seem to be the right one? Are my conclusions correct?