In attempting to quantify its attitude toward risk, top management of the pharmaceutical company has reported certainty equivalent values for a variety of 50-50 risks. These are summarized in the following table.
|
Outcome of 50-50 Risk
$200 and $0
|
Certainty Equivalent
$ 50
|
|
$200 and $50
|
112
|
|
$50 and $0
|
13
|
|
$200 and $112
|
153
|
|
$112 and $50
|
70
|
|
$50 and $13
|
28
|
|
$112 and $13
|
50
|
For instance, the company's CE for a 50-50 risk between $200 million and $0 is $50 million, and so on.
a. Use these responses to determine utility values for each of the monetary values in the second column. (Hint: Set U($200) = 100 and U($0) = 0. Show that U($50) = 50, U($112) = 75, and so on.) Construct a utility graph by plotting points and drawing a smooth curve. (You may wish to check the utility values in Problem 13 against your curve.)
b. Consider the mathematical utility function U = 7.1 1y , where U is the utility value corresponding to monetary outcome y. Check that this function is an accurate description of the pharmaceutical company's attitude toward risk. Is the company very risk averse?