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Equation utility function help

  1. Oct 24, 2012 #1
    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

    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?
  2. jcsd
  3. Oct 27, 2012 #2
    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.
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