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 Certainty Equivalent

$200 and $0 ............$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. (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, 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?