2. Consider an economy that is composed of identical individuals who live for two periods. These individuals have preferences over consumption in periods 1 and 2 given by U = In (ci) + In (ci) They receive an income of $450 in period 1 and an income of $200 in period 2. They can save as much of their income as they like in bank accounts, earning an interest rate of r = 10% per period. They have no desire to bequeath anything, so they spend all their money before the end of period 2. Note that MRScic2 = 2/c, for the given utility function. Each individual's lifetime budget constraint [PDV (expenditures) = PDV(income)] is: C2 = Y 1 + = Y2 1+r $1 +r Individuals choose consumption in each period by maximizing lifetime utility subject to this lifetime budget constraint. a. What is the individual's optimal consumption in each period? How much saving does he or she do in the first period? . Suppose now the government introduces a social security program. This system will take $100 from each individual in the first (work) period, put it in the bank, and transfer it to back with interest in the second (retirement) period. i. Write out the new lifetime budget constraint. ii. How does the system affect the amount of private savings? iii. How does the system affect national savings (total savings in society)? c. Suppose instead that the government uses the $100 contribution from each individual to start paying out benefits to current retirees (who did not pay into a social security when they were working). It still promises to pay current workers their $100 (plus interest) back when they retire using contributions from future workers. Similarly, it will pay back future workers interest on their contributions using the contributions of the next generation of workers. An influential politician says: "This is a free lunch: we help out current retirees, and current and future workers will still make the same contributions and receive the same benefits, so it doesn't harm them, either." Do you buy this argument? If not, what is wrong with it