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. 1. Consider an OLG economy in which the number of initial old (at t = 0) is equal to 10,000. Let the population change according to Nt = 1.1Nt1 Agents' preferences are such that: u(c1, c2) = c 35 1 c 252 Each person is endowed with y = 20 units of the consumption good when young and nothing when old. = a) Compute the number of young people born in periods t = 1, 2, 3, 4. b) How many individuals (young and old) live in t = 3? c) Derive the equation for the feasible set line for this economy. d) Write down the planner's maximization problem and the corresponding Lagrangian. . e) Compute the stationary golden rule allocation that the planner would choose. f) Draw a graph of the planner's maximization problem and the optimal allocation. Make sure to include and label all relevant information (axis, intercepts, budget constraint, indifference curves, solution)