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Consider an economy where individuals are endowed with y units of the consumption good when young and zero units of the consumption good when old. Suppose the population is growing over time at a constant rate. In particular, assume that Nt+1 = nNt for all t ≥ 0 where n > 1. If it makes it easier, you can assume n is equal to a number larger than 1 (e.g. set n = 2).
1. Find the planner's feasible set in period t (do not assume a stationary equilibrium).
2. Assuming a stationary equilibrium, write down and explain the planner's feasible set.
3. Draw a figure depicting the Golden Rule allocation.
4. How does an increase in n affect the planner's optimal choice? That is, how do (C1*,C2*) change? Support your answer.
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