1- John Doe is a rationale person whose satisfaction or preference for various a
ID: 3217526 • Letter: 1
Question
1- John Doe is a rationale person whose satisfaction or preference for various amounts of money can be expressed as a function U(x) = (x/100)^2, where x is in $. How much satisfaction does $40 bring to John (to the nearest thousandths)? ----
2- John is considering a lottery with a payoff of $80, 40% of the time, and $10, 60% of the time. If John plays this lottery repeatedly, how much will be his long-term average satisfaction? -----
3- If we limit the range of U(x) between 0 and 1.0, then we can use this function to represent John’s utility (i.e. U(x) becomes his utility function). How does his utility function look like?
a.Convex
b.Concave
c. Straight line
4- What does U(x) show about John’s incremental satisfaction with respect to x?
a.Incremental satisfaction increases with increasing x
b.Incremental satisfaction decreases with increasing x
c.Incremental satisfaction is exactly equal to increase in x
5-The shape of John's utility function shows that he is willing to accept _______ risk than a risk-neutral person.
a.The same
b.More
c.Less
6-For John, what certain amount would give him satisfaction equal to this lottery? Express your answer to nearest whole $.
a.$50
b.$51
c.$52
d.$53
e.$54
Explanation / Answer
1) U(x) = (40/100)^2 = 0.16
2) In the long term,his average utility will be equal to [u(80)*0.40 + u(10)*0.60] =0.8*0.8*0.4+ 0.6* 0.1*0.1 = 0.256+0.006=0.262
In this case, long term utility is equal to 0.262
3) Utility function is related to x^2 and is thus,concave
4) It shows that incremental satistfaction increases with increasing x as in a concave function
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