The problem is 8-43, however, the second part of the question involves the solution to 8-42. So, you will need to construct a decision tree, though I would recommend combining the EMV and utility analysis on a single tree to answer 8-43 part B. Problem 8-43 part A should be really straightforward to answer with the understanding of Utility Theory that can be gained by reading through that part of the text (Section 8.10).
1. (P8-43) Jason Scott (see Problem 8-42, below) has decided to incorporate utility theory into his decision with his mortgage application. The following table describes Jason's utility function:
|
Monetary Value
|
Utility
|
|
-$4800
|
0.00
|
|
-$2900
|
0.10
|
|
-$2400
|
0.12
|
|
-$1000
|
0.15
|
|
-$500
|
0.19
|
|
$0
|
0.21
|
|
$1900
|
0.26
|
|
$2400
|
0.30
|
|
$4800
|
1.00
|
(a) How can you best describe Jason's attitude toward risk? Justify your answer.
(b) Will the use of utilities affect Jason's original decision in Problem 8-42? How?
8-42
Jason Scott has applied for a mortgage to purchase a house, and he will go to settlement in two months. His loan can be locked in now at the current market interest rate of 7% and a cost of $1,000. He also has the option of waiting one month and locking in the rate available at that time at a cost of $500. Finally, he can choose to accept the market rate available at settlement in two months at no cost. Assume that interest rates will either increase by 0.5% (0.3 probability), remain unchanged (0.5 probability), or decrease by 0.5% (0.2 probability) at the end one month.
Rates can also increase, remain unchanged, or decrease by another 0.5% at the end on the second month. If rates increase after one month, the probability that they will increase, remain unchanged, and decrease at the end of the second month is 0.5, 0.25, and 0.25, respectively. If rates remain unchanged after one month, the probability that they will increase, remain unchanged, and decrease at the end of the second month is 0.25, 0.5, and 0.25, respectively. If rates decrease after one month, the probability that they will increase, remain unchanged, and decrease at the end of the second month is 0.25, 0.25, and 0.5, respectively.