Not really an algebra field, but seen as you asked nicely:
An individual’s utility function is represented by
U(x) = 3ln(x), where x, his total wealth including the value of his stamp collection, is £300,000.
There is a 2% probability of theft or fire, which would make his collection, worth £20,000 worthless.
The utility function of an insurance company is represented by
U(x) = ln (x + 100,000)
where x denotes the value of the company’s assets which are currently valued at £1,000,000.
Show that the individual would be prepared to accept a
policy where he would pay a premium of £300 and the first
£500 of a claim, so that the insurance company would pay
out an amount in excess of £500.