Equation help

surferbarney0729

I understand the idea of the questio, but am perplexed as what to put in the equation to get it to equal $38906.20

Here is the question and answer
Your utility function is U = ln(2C) where C is the amount of consumption you have in
any given period. Your income is $40,000 per year and there is a 2% chance that you
will be involved in a catastrophic accident that will cost you $30,000 next year

I have solved the first parts, and EU is 11.262, but the last section is confusing me

What is the most that you would be willing to pay for insurance, given your utility
function?
To answer this question, first go back to the original utility to determine how much
money would yield the same utility as the expected utility of taking the risk. The wealth
that would yield utility of 11.262 solves ln(2W) = .98ln(80,000) + .02ln(20,000), so W =
exp(.98ln(80,000) + .02ln(20,000))/2 ≈ $38,906.20. You are indifferent between the risky
situation and certain wealth of $38,906.20 because they yield the same utility. Therefore,
you should be willing to pay $40,000 – 38,906.20 = $1,093.80 for insurance.

Any help on what my equation needs to look like to get 38,906.20?

alan2

It looks to me like you solved it. Can you clarify what your question is?

By the way, you are looking at expected utility. I could argue that the more correct method is utility of expected consumption. In that case I would be willing to pay $600.