Please solve all bits

2. Parvati is 24 years old and just got her rst job after college. Because she is a nancially responsible young adult, she is considering how much she should save for retirement. Parvati expects to live to 90 with 50% probability and expects to live to 80 with 50% probability. Suppose that these are the only two options and that she will retire at 60 years old. a. If Parvati needs $30,000 to live off of each year that she is retired, what is the expected value of her total required income in retirement? b. If Parvati is offered an annuity that pays out $30,000 per year in her retirement, and I charge her $600,000 for it, should she take it? c. What is risk aversion? If Parvati is risk averse, could this change your answer to part b? d. What market failure prevents the market for private annuities from functioning properly? How specically does it work in this case? Explain thoroughly. e. Suppose that Parvati decides not to purchase a private annuity, and instead saves her money in a bank (i.e. forget the numbers mentioned before). Suppose, for simplicity, that her total income in her working years is $1000, and her total (expected) income in her retired years is $100. Her retirement income is coming from her sale of Survivor memorabilia, not from social security. Use the life-cycle mode to draw Parvati's intertemporal budget constraint, assuming that the interest rate is 4%. Label the axes, her endowment and the slope