Question
Background information for the Question: Each period there are N old people and N young people, with N= (1 +n)N.Suppose that the government establishes asocial
Background information for the Question:
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.
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.
Without Social Security
1stperiod BC : s + c = y
2ndperiod BC : c' = y' + (1+r)s
Present Value BC: c + (c'/(1+r)) = y + (y'/(1+r))
With Social Security
1st: c + s = y
2nd: c' = y' + (1+r)s + b
Present Value BC: c + (c'/(1+r))s + b
(c) Write down the present value budget constraint of people born in period T+ 2 and later with and without the social security program.
Without Social Security
1stperiod BC : c + s = y(Period T + 1)
2ndperiod BC : c' = y' + (1+r)s(Period T + 2)
Present Value BC: c + (c'/(1+r)) = y + (y'/(1+r))
With Social Security
1st: c + s = y - (b/(1+n))(Period T + 2)
2nd: c' = y' + (1+r) + b(Period T + 3)
Present Value BC: c + (c'/(1+r)) = y - (b/(1+n)) + (y'+b/(1+r))
These are the part that I am stuck on. 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?
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