Problem 1 Janet Yellen has applied for a mortgage to purchase a house, and she will go to settlement in two months at which time she must have the loan secured. For a processing fee of $1,000, her loan can be locked in now at the current market interest rate of 7%. She also has the option of waiting one month and locking in the rate available at that time for a fee of $500. Finally, she can accept the rate available at settlement in two months for no fee. Janet thinks that the interest rate will either increase by 0.5%, stay the same, or decrease by 0.5% at the end of the first month. The probabilities are 30% for an increase and 20% for a decrease. Janet also thinks that interest rates could change at the end of the second month as follows: If the interest rate increases in the first month, the probability that it will increase by 0.5%, stay the same, or decrease by 0.5% in the second month is 50%, 25%, and 25%, respectively If the interest rate stays the same in the first month, the probability that it will increase by 0.5%, stay the same, or decrease by 0.5% in the second month is 25%, 50%, and 25%, respectively. If the interest rate decreases in the first month, the probability that it will increase by 0.5%, stay the same, or decrease by 0.5% in the second month is 25%, 25%, and 50%, respectively, Compared to the current rate of 7%, each 0.5% increase in the interest rate will cost Janet $2,400, and each 0.5% decrease will save her $2,400. According to Bayes' rule, what strategy should Janet adopt? Problem 2 Janet has decided to incorporate utility theory into her decision with her mortgage application. The following table describes Janet's utility function: Monetary Value Utility -$4,800 0.00 -S2,900 0.40 -$2,400 0.50 -$1.000 0.70 -S500 0.76 $0 0.78 $1,900 0.88 $2,400 0.92 $4,800 1.00 (a) How can you best describe Janet's attitude toward risk? Justify your answer. (b) How will the use of utilities affect Janet's original decision in Problem 1? Page 1 of 1