Problem 1. A life insurance rm is considering offering an annuity product to new retirees. The annuity product is designed for retirement income and pays $10,000 per year every year while the individual is alive. (In general, people may be allowed to buy multiple or even half of the annuity, but we will focus on the choice to purchase a single annuity or not). In this region, there are two types of individuals. Type 1 individuals are young and healthy, and they use a discount rate of 0.9. Type 2 individuals are older, and have experienced some health problems, and they use a discount rate of 0.8. Since the life spans of both types of individuals are uncertain, we can model them as innitely lived with the appropriate discount rates. 1. How much would Type 1 individuals pay for this annuity? 2. How much would Type 2 individuals pay for this annuity? 3. The life insurance rm has a net present cost of the annuity annuity: the ex pected amount of money they must have today in order to guarantee $10,000 a year for the rest of an individuals life. For Type 1 individuals, the net present cost is $80,000. For Type 2 individuals, the net present cost is $40,000. Sup- pose that the region is equally divided between Type 1 and Type 2 individuals. What is the break even price of the annuity assuming everyone buys? (I.e. What price will allow the rm to cover its net present costs?) 4. At this break-even price found in question 3, will everyone want to buy the annuity? If not, which types will buy? 5. What is the break-even price if only the type answered in the previous question buys? And will that group still want to buy at the breakeven price? Will anyone else want to buy? 6. What does your answers to these questions imply about annuity markets? In equilibrium, which types of individuals will have access to annuity products? 7. Would any part of this answer change if the price could depend on your health (i.e. different prices for Type 1 and Type 2)? Who would buy annuities