Econ 110 / Pol Sci 135 Suggested Exercises
Set 2 Solutions
Fall 2009
Page 1 of 10
1. (a)
Jack’s expected utility is 0.5*
√
250,000 + 0.5*
√
90,000 = 400.
(b)
Since Jack’s utility is the square root of his income, to achieve a utility of 400 Jack would
need a certain income of 400
2
= $160,000.
(c) The four possible luck outcome pairs for Jack and Janet are:
(good, good)
(good, bad)
(bad, good)
(bad, bad)
Each of these outcomes happens with probability (0.5)(0.5) = 0.25.
(d)
Under the agreement, the expected utility for each participant is 0.25*
√
250,000 +
0.25*
√
170,000 + 0.25*
√
170,000 + 0.25*
√
90,000
≈
406.1552.
(e)
For either Jack or Jill to achieve a utility of 406.1552, he or she would need a certain income
of 406.1552
2
= $164,962.11.
(f)
The eight possible luck outcome triplets for Jack, Janet, and Chrissy are:
(good, good, good)
(good, good, bad)
(good, bad, good)
(bad, good, good)
(good, bad, bad)
(bad, good, bad)
(bad, bad, good)
(bad, bad, bad)
Each of these outcomes occurs with probability (0.5)(0.5)(0.5) = 0.125.
(g)
Under the agreement, the expected utility for each participant is 0.125*
√
250,000 +
3*0.125*
√
196,666.667 +3*0.125*
√
143,333.333 + 0.125*
√
90,000
≈
408.2744.
(h)
For Jack, Jill, or Chrissy to achieve a utility of 408.2744, he or she (or she) would need a
certain income of 408.2744
2
= $166,687.99.
