5. Three decision makers have assessed utilities for the following decision problem (payoff in dollars): State of Nature Decision Alternative 55 d₁ d2 5280 $1 $2 $3 50 -20 100 -100 The indifference probabilities are as follows: Indifference Probability (p) ☐ Payoff Decision Maker A 100 1.00 80 0.95 50 0.90 20 0.70 -20 0.50 -100 0.00 Decision Maker B 1.00 0.70 0.60 0.45 0.25 0.00 a. Plot the utility function for money for each decision maker. Decision Maker C 1.00 0.90 0.75 0.60 0.40 0.00 b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral. C. For the payoff of 20, 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?

Understanding Business
12th Edition
ISBN:9781259929434
Author:William Nickels
Publisher:William Nickels
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
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5. Three decision makers have assessed utilities for the following decision problem (payoff
in dollars):
State of Nature
Decision Alternative
55
d₁
d2
5280
$1
$2
$3
50
-20
100
-100
The indifference probabilities are as follows:
Indifference Probability (p)
☐
Payoff
Decision Maker A
100
1.00
80
0.95
50
0.90
20
0.70
-20
0.50
-100
0.00
Decision Maker B
1.00
0.70
0.60
0.45
0.25
0.00
a.
Plot the utility function for money for each decision maker.
Decision Maker C
1.00
0.90
0.75
0.60
0.40
0.00
b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral.
C.
For the payoff of 20, 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?
Transcribed Image Text:5. Three decision makers have assessed utilities for the following decision problem (payoff in dollars): State of Nature Decision Alternative 55 d₁ d2 5280 $1 $2 $3 50 -20 100 -100 The indifference probabilities are as follows: Indifference Probability (p) ☐ Payoff Decision Maker A 100 1.00 80 0.95 50 0.90 20 0.70 -20 0.50 -100 0.00 Decision Maker B 1.00 0.70 0.60 0.45 0.25 0.00 a. Plot the utility function for money for each decision maker. Decision Maker C 1.00 0.90 0.75 0.60 0.40 0.00 b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral. C. For the payoff of 20, 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?
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