= Consider an Overlapping generations economy in which Nt young individuals are born each period. Individuals...

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= Consider an Overlapping generations economy in which Nt young individuals are born each period. Individuals are endowed with y 15 units of the consumption good when young and nothing when old. The utility function of one typical agent is a typical time-separable CRRA: u(c₁, c₂) = + ²₂. ß € (0, 1] is the time discount factor and σ > 0 is the 1-o -σ 1-o inverse of the elasticity of intertemporal substitution. Population of the future generations are determined by Nt+1 = n.Nt for all t > 1. 1. What is the equation for the feasible set of this economy? 2. Portray the feasible set on a graph. 3. Let's solve the Planner's Problem. (i) State the Planner's problem as a constrained maximization problem. (ii) Write down the Lagrangean for this problem. (iii) What are the FOCs? (iv) Assuming a stationary equilibrium, find the optimal allocations as a function of 3 and o only. 4. How does consumption when young respond to changes in 3? What about o? And n? 5. Now, B = 0.5 and 2. Substitute and find c₁ and C2. = Consider an Overlapping generations economy in which Nt young individuals are born each period. Individuals are endowed with y 15 units of the consumption good when young and nothing when old. The utility function of one typical agent is a typical time-separable CRRA: u(c₁, c₂) = + ²₂. ß € (0, 1] is the time discount factor and σ > 0 is the 1-o -σ 1-o inverse of the elasticity of intertemporal substitution. Population of the future generations are determined by Nt+1 = n.Nt for all t > 1. 1. What is the equation for the feasible set of this economy? 2. Portray the feasible set on a graph. 3. Let's solve the Planner's Problem. (i) State the Planner's problem as a constrained maximization problem. (ii) Write down the Lagrangean for this problem. (iii) What are the FOCs? (iv) Assuming a stationary equilibrium, find the optimal allocations as a function of 3 and o only. 4. How does consumption when young respond to changes in 3? What about o? And n? 5. Now, B = 0.5 and 2. Substitute and find c₁ and C2.

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