Why do we typically consider economies where the endowment when young is greater than the endowment when old? Consider a model economy as described in Module 1, but assume that workers are endowed with y units of the consumption good when old and 0 units when young. Assume the population is constant over time, i.e. Nt = Nt−1 = N for all t ≥ 0.
(a) Explain the planner’s problem in words.
(b) Derive the planner’s feasible set for a given period t and do not impose the assumption that the allocation is stationary.
(c) What is a stationary allocation? Explain.
(d) Assume the planner wants to implement a stationary allocation. Draw a figure that depicts the solution to the planner’s problem using the feasible set and sample indifference curves that satisfy the properties discussed in Module 1.
(e)Now consider a decentralized version of this economy where individuals make their own consumption and trading decisions. Do you think there is a way to sustain trade between the young and the old in this case? Explain.
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