6. certainty equivalents Ralph is anxious to display understanding of the mechanics of risk aversion. For this purpose, five distinct choices are available, with probabilities given in the table below. #4, for example, will result in 2, 000 with a probability of .60 and 3, 000 with a probability of .40.

For convenience, Ralph’s utility measure is given by U(w) = √w, with zero initial wealth. Determine the certainty equivalent for each of the possible choices.

1,000 2,000 3,000 4,000

#1 .25 .25 .25 .25

#2 .50 .50

#3 .40 .60

#4 .60 .40

#5 .40 .60