18. dominance Ralph is contemplating various lotteries. The possible prizes are 100, 200, 300 or 400 dollars. Assume in what follows that more is strictly preferred to less dollars. Below are some representative lotteries (For example, lottery c yields 100 with probability .2 and 300 with probability

.8.

100 200 300 400 a .1 .9 b .2 .8 c .2 .8 d .25 .25 .25 .25 e .15 .35 .25 .25 f .24 .21 .25 .30

(a) Consider lotteries

a, b, and c.Which choice from among the three is best? Try an expected utility analysis with several different U(w) functions. Why does lottery a always turn out to be best?

(b) Do the same thing for lotteries d and f.

(c) Now consider lotteries e and

f. Exhibit one U(w) function such that e is preferred to f and another such that the opposite holds.

What is the explanation?