I understand the idea of the questio, but am perplexed as what to put in the equation to get it to equal $38906.20(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Equation help

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