2 Housing Finance Suppose you work at a local housing finance agency. Your agency's mission is to provide interest-free mortgages so families can buy a home. The agency derives utility from the number of families who live in a house they helped them buy. However, borrowers must still meet minimum income requirements in order to qualify. In good times, the agency can lend to 350 families, but only 300 in a recession. Suppose the federal government is offering a block grant so agencies can lower their lending standards and offer mortgages to families with less in- come. In good times, this allows the agency to lend to 600 families, and 375 in bad. Assume recessions occur 10 percent of the time. For simplicity, assume that the agency values each family served at $1 1. Set up a contingency table for this problem. (see slides) 2. Calculate the surplus for the agency in good and bad times. What is the expected surplus? 3. Calculate the variance of benefits to the agency with and without the program. Is this a risk-reducing or risk-increasing policy? 4. Assume U(x) = loga where a is the benefits accruing to the agency. Calculate expected utility with and without the program. Derive an ex- pression for the expected utility when paying option price z for the block grant. 5. Calculate the option price, and compare to expected surplus. (Hint: You will need to use Wolfram Alpha.) 6. Suppose the opportunity cost is $225, and assume the agency is the only beneficiary. Would a standard CBA recommend this project? Would you recommend this project? 7. Bonus: Suppose utility were linear - U(x) = r. What would the option price be