Consider an overlapping generations economy in which endowments increase over time. Let y t = y t-1

Consider an overlapping generations economy in which endowments increase over time. Let y_{t =} αy_t-1, where α> 1 Endowments are received by young people while old people receive no endowment. Preferences are such that a young person always wants to consume half of their endowment. The government’s only activity is to run an old-age pension plan. The government chooses a pay-as-you-go pension system in which taxes are collected from the young to pay the old-person’s pension. Assume the population is constant.
a. Write down the budget constraint for a young person.
b. Write down the budget constraint for the old person.
c. Derive the lifetime budget constraint.
d. Write down the government budget constraint. Assume the government runs a balanced budget each period.
e. Will an old person prefer a pay-as-you-go pension plan to an equilibrium in which no pension plan is operated?