2. Consider an overlapping generations model with a pay-as-you-go pension system. The government collects the contributions from young generation and transfers them to old generation. d is the contribution from a young person to the pension system. b is the benefit received by old person. (a) Derive the following intertemporal budget constraint, b 1 + rt+1 C₁t + C2t+1 1 + rt+1 = W₂ - d + (b) Derive the following saving function, 1 St= -(wt - d) — 2+p 1+p (2 + p)(1 + rt+1) ·bl

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2. Consider an overlapping generations model with a pay-as-you-go pension system.
The government collects the contributions from young generation and transfers
them to old generation. d is the contribution from a young person to the pension
system. b is the benefit received by old person.
(a) Derive the following intertemporal budget constraint,
b
1 + rt+1
C₁t +
St
C2t+1
1 + rt+1
(b) Derive the following saving function,
1
·(wt – d)
2+p
=
= Wt
d +
1+p
(2 + p)(1+rt+1)
- bl.
Transcribed Image Text:2. Consider an overlapping generations model with a pay-as-you-go pension system. The government collects the contributions from young generation and transfers them to old generation. d is the contribution from a young person to the pension system. b is the benefit received by old person. (a) Derive the following intertemporal budget constraint, b 1 + rt+1 C₁t + St C2t+1 1 + rt+1 (b) Derive the following saving function, 1 ·(wt – d) 2+p = = Wt d + 1+p (2 + p)(1+rt+1) - bl.
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