4. Suppose that you take $1,000 along for spending money on a trip to New York C

Question

4. Suppose that you take $1,000 along for spending money on a trip to New York City. Your utility from the trip is given by the function U(y) = y1/3 of the amount y you spend. Suppose that there is a 10 percent chance that you will lose $100 during the trip and a 90 percent chance that you will be able to spend all $1000. (a) What is the expected utility of your trip? (b) What is your expected utility if you buy $100 worth of traveler’s checks, as certain insurance against the loss, for an actuarily fair premium of $10? 1 (c) What is the most you would pay from an expected utility point of view for insurance against that loss of $100?

Explanation / Answer

a)

0.9 probability that you will spend all $1000 and 0.1 probability that you will spend $1000-$100= $900

utility = 0.9*10001/3 +0.1*(1000-100)1/3 = 9.9655

b)

if you buy $100 worth traveler’s checks

utility = 1*(1000-10)1/3 =9.9665

c)

let max we can pay x

then accordind to the part a) even w/o insurance , our utility = 9.9655

9.9655 = (1000-x)1/3

1000-x= 989.6856

x= $10.314

thanks

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