# Equation utility function help

1. Oct 24, 2012

### 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