Each period there are N old people and N young people, with N= (1 +n)N.Suppose that the government establishes asocial security program in period T, which provides a social security benefit of b ( in terms of consumption goods) for each old person forever.In period T the government finances the benefits to current old by issuing debt (borrowingfromyoungpersonsinperiodT).Thisdebtisthenpaidoffinperiod T+ 1through lump-sum taxes on the young.In periods T+ 1 and later, lump-sum taxes on the young finance social security payment to the old.

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I just need help with part b and d

For reference I will give you the answers for part a and c

(a) Write down the period budget constraint and present value (life time) budget constraint for the old alive at time T with and without the social security program.

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Without Social Security

1^stperiod BC : s + c = y

2^ndperiod BC : c' = y' + (1+r)s

Present Value BC: c + (c'/(1+r)) = y + (y'/(1+r))

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With Social Security

1^st: c + s = y

2^nd: c' = y' + (1+r)s + b

Present Value BC: c + (c'/(1+r))s + b

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(c) Write down the present value budget constraint of people born in period T+ 2 and later with and without the social security program.

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Without Social Security

1^stperiod BC : c + s = y(Period T + 1)

2^ndperiod BC : c' = y' + (1+r)s(Period T + 2)

Present Value BC: c + (c'/(1+r)) = y + (y'/(1+r))

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With Social Security

1^st: c + s = y - (b/(1+n))(Period T + 2)

2^nd: c' = y' + (1+r) + b(Period T + 3)

Present Value BC: c + (c'/(1+r)) = y - (b/(1+n)) + (y'+b/(1+r))

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Part b and d is where I need help answering the question. Thank you in advance!

(b)Write down the period budget constraint and present value (life time) budget constraint for the young alive at time T with and without the social security program.Show, using diagrams,that the young alive at time T benefits from the social security program.

(d)Write down the present value budget constraint of the cohort born in period T+ 1.What is the effect of social security program on that cohort?How does this depend on the real interest rate and the population growth rate?