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1 Delayed pay-as-you-go Social Security. (10 points) Modify the model of Social Security discussed in Chapter 10 to answer this question. (This is based on question 6 from chapter 10 of the textbook, but reuritten to make the assumptions more explicit.) In each time period t, there are N' = N4 young people and N = N4-1 old people, with N' = (1+n). N for every time period. (n is the exogenous population growth rate) Each generation lives for two periods (generation t are born in period t and die after period t+1), and chooses how much to save/borrow when they are young, just like in the 2-period consumer's endowment problem from chapter 9. Consumers can borrow and save at exogenous real interest rate r. (You can imagine there is some large world credit market) At time period t = 1, the government starts a new Social Security Program which will last for the rest of infinite time. There are no government expenditures; this program is the only thing the government is doing. Assume that the government's social security program doesn't change r. The benefits and payments for the social security are structured like so: In time period t = 1, the government transfers b units of consumption goods as benefits to each old person. (And so the government pays out b. No units of benefits in total.) * The government pays for these transfers by borrowing money from the young people in period 1. (generation 1, which has population Ni = (1 + n). No) * In period 2, the government pays back it's debt to generation 1 through lump-sum taxes on the new young generation (generation 2). From period t = 2 and onwards, the government continues to pay b benefits to each old person. * But now these benefits are just funded through lump-sum taxes on the current young generation (generation t). Problems: (a) The effects on the initial old generation: Write down the budget constraint(s) for generation 0. (When they are young, the program doesn't erist, and so they don't have to pay anything. But when they are old, the program begins and they receive benefits.) Argue, using diagrams or otherwise, that this generation benefits from the social security program. (b) The effects on the initial young generation: Write down the budget constraint(s) for generation 1. (When they are young, the government borrows money from them. When they are old, the government pays them back for these loans and also gives them benefits.) Argue that this generation also benefits from the social security program. (c) The effects on the second young generation: Write down the budget constraint(s) for generation 2. (When they are young, the government taxes them to pay for the benefits to generation 1, and also tazes them to pay off the government debt to generation 1. When they are old, they receive benefits.) What is the effect of social security program on this generation? Are they better or worse off? How does the answer depend on the real interest rate and the population growth rate? (d) The effects on the future generations: Write down the budget constraint(s) for generation t when t> 3. (In generation 3 and onwards, the people are taxed when they're young just to pay for the benefits of the previous generation, and then they recieve benefits when they're old. ) What is the effect of social security program on this generation? Are they better or worse off? How does the answer depend on the real interest rate and the population growth rate? 1 Delayed pay-as-you-go Social Security. (10 points) Modify the model of Social Security discussed in Chapter 10 to answer this question. (This is based on question 6 from chapter 10 of the textbook, but reuritten to make the assumptions more explicit.) In each time period t, there are N' = N4 young people and N = N4-1 old people, with N' = (1+n). N for every time period. (n is the exogenous population growth rate) Each generation lives for two periods (generation t are born in period t and die after period t+1), and chooses how much to save/borrow when they are young, just like in the 2-period consumer's endowment problem from chapter 9. Consumers can borrow and save at exogenous real interest rate r. (You can imagine there is some large world credit market) At time period t = 1, the government starts a new Social Security Program which will last for the rest of infinite time. There are no government expenditures; this program is the only thing the government is doing. Assume that the government's social security program doesn't change r. The benefits and payments for the social security are structured like so: In time period t = 1, the government transfers b units of consumption goods as benefits to each old person. (And so the government pays out b. No units of benefits in total.) * The government pays for these transfers by borrowing money from the young people in period 1. (generation 1, which has population Ni = (1 + n). No) * In period 2, the government pays back it's debt to generation 1 through lump-sum taxes on the new young generation (generation 2). From period t = 2 and onwards, the government continues to pay b benefits to each old person. * But now these benefits are just funded through lump-sum taxes on the current young generation (generation t). Problems: (a) The effects on the initial old generation: Write down the budget constraint(s) for generation 0. (When they are young, the program doesn't erist, and so they don't have to pay anything. But when they are old, the program begins and they receive benefits.) Argue, using diagrams or otherwise, that this generation benefits from the social security program. (b) The effects on the initial young generation: Write down the budget constraint(s) for generation 1. (When they are young, the government borrows money from them. When they are old, the government pays them back for these loans and also gives them benefits.) Argue that this generation also benefits from the social security program. (c) The effects on the second young generation: Write down the budget constraint(s) for generation 2. (When they are young, the government taxes them to pay for the benefits to generation 1, and also tazes them to pay off the government debt to generation 1. When they are old, they receive benefits.) What is the effect of social security program on this generation? Are they better or worse off? How does the answer depend on the real interest rate and the population growth rate? (d) The effects on the future generations: Write down the budget constraint(s) for generation t when t> 3. (In generation 3 and onwards, the people are taxed when they're young just to pay for the benefits of the previous generation, and then they recieve benefits when they're old. ) What is the effect of social security program on this generation? Are they better or worse off? How does the answer depend on the real interest rate and the population growth rate

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