Problem 2: Unfunded Social Security. Consider a model in which everyone lives for three periods. In the first two periods of life, everyone works and earns $30,000 in each of those two periods. In the third/last period of life, everyone is retired and does not work. There is no wage growth and no population growth. Generation 1 works in t = 1, 2 and is retired in t = 3. Generation 2 works in t = 2, 3 and is retired in t = 4 ... Generation 6 works in t = 6, 7 and is retired in t = 8. Consider an unfunded Social Security program that starts at the beginning of period t = 3 and ends after period t = 6. Every worker is taxed at a rate of 5% while Social Security is in place, and all tax revenue is used to fund the current retiree benefits. a) Calculate the rate of return on Social Security for each Generation (1 through 6). Explain your answers. (Hint: For each generation, think about total taxes paid per person T and total benefits received per person B.) b) Suppose there is an alternative to Social Security: Everyone can make a positive 6% rate of return on a private investment. In any given period, three consecutive genera- tions (of equal size) vote "Yes" or "No" on the unfunded Social Security system. Before the Social Security system is in place, will three consecutive generations vote in a majority to immediately begin the Social Security system? (Hint: To deter