Problem 1: As you know, utility functions incorporate a decision maker's attitude towards risk. Let's consider that the subsequent utilities were assessed for Stephanie Parker.
|
x
|
u(x)
|
|
-$400
|
0
|
|
-$365
|
10
|
|
-$320
|
20
|
|
-$270
|
30
|
|
-$200
|
40
|
|
-$110
|
50
|
|
$0
|
60
|
|
$130
|
70
|
|
$300
|
80
|
|
$600
|
90
|
|
$800
|
95
|
|
$1,100
|
100
|
Use these utilities to answer the following questions.
a) What is the monetary certainty equivalent for the following gamble: gain $130 with probability 0.4, lose $320 with probability 0.6.
b) What is the risk premium in a)? Illustrate the concept of a risk premium in addition to calculating its value for a).
c) What probability P could make Stephanie become indifferent between getting $130 for sure or taking the following gamble?