Longer retirements. People are living longer than ever before. However, the retirement age in most countries remains mostly unchanged. Consider the consequences of this change in the following OLG economy where people live three periods. Assume that people work in the first period and earn labour income At wt and live off of their savings plus interest income in periods two and three. The household utility maximization problem is given by Max U = InC1,t + BlnC2,t+1+B² In C3,t+2 s. t. C₁,t + St= Atwt, C2₁t+1+St+1 = (1 + rt+1) St, C3,t+2 = (1 + rt+2) St- A. Write out the lifetime budget constraint of the household.

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Longer retirements. People are living longer than ever before. However, the
retirement age in most countries remains mostly unchanged. Consider the
consequences of this change in the following OLG economy where people live three
periods. Assume that people work in the first period and earn labour income At wt
and live off of their savings plus interest income in periods two and three. The
household utility maximization problem is given by
Max U = InC1,t + BlnC2,t+1+B² InC3,t+2
s.t. C₁,t + St Atwt, C2₁t+1+St+1 = (1 + rt+1) St, C3,t+2 = (1 + rt+2) St-
=
A. Write out the lifetime budget constraint of the household.
B. Write out the Lagrangian for the household utility maximization problem.
Transcribed Image Text:Longer retirements. People are living longer than ever before. However, the retirement age in most countries remains mostly unchanged. Consider the consequences of this change in the following OLG economy where people live three periods. Assume that people work in the first period and earn labour income At wt and live off of their savings plus interest income in periods two and three. The household utility maximization problem is given by Max U = InC1,t + BlnC2,t+1+B² InC3,t+2 s.t. C₁,t + St Atwt, C2₁t+1+St+1 = (1 + rt+1) St, C3,t+2 = (1 + rt+2) St- = A. Write out the lifetime budget constraint of the household. B. Write out the Lagrangian for the household utility maximization problem.
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