Three decision makers have assessed payoffs for the following decision problem (payoff in dollars).
?
Decision Alternative
State of Nature
s1
s2
s3
d1
15
40
-20
d2
60
80
-80
?
?
The indifference probabilities are as follows:
?
Indifference Probability (p)
Payoff
Decision Maker A
Decision Maker B
Decision Maker C
80
Does not apply
Does not apply
Does not apply
60
0.70
0.95
0.87
40
0.50
0.90
0.74
15
0.30
0.80
0.59
-20
0.15
0.60
0.37
-80
Does not apply
Does not apply
Does not apply
?
a. Plot the utility function for money for each decision maker.
b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral.c. For the payoff of 40, what is the premium that the risk avoider will pay to avoid risk? What is the premium that the risk taker will pay to have the opportunity of the high payoff?
What will be an ideal response?
a.
b. A - Risk taker
B - Risk avoider
C - Risk neutral
c. For risk avoider B: at $40, indifference probability p = 0.9
Thus, EV(Lottery) = 0.9(80) + 0.1(-80) = $64. Therefore, B will pay $64 - $40 = $24.
For risk taker A: at $40, indifference probability p = 0.5
Thus, EV(Lottery) = 0.5(80) + 0.5(-80) = $0. Therefore, A will pay $40 - $0 = $40.
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