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.