3 Exercise 3 - Basic OLG model Consider the following two-period OLG model. People consume in...

 

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3 Exercise 3 - Basic OLG model Consider the following two-period OLG model. People consume in both periods but work only in period two. The inter-temporal utility of the representative individual in the first period is U = In c +3[ln c +aln(1-) + y ln g2] where c and are consumption and k (which is given) and k2 are the stocks of capital in periods one and two, n is work and g2 is government expenditure in period two which is funded by a lump-sum tax in period two, T. Production in periods one and two are y = Rk = C +k 32 = Rk + n = 0 +92 (a) In class we discussed that a benevolent social planner would internalise the decisions of each agent in the economy, solving the model from a central point of view. In this context a social planner would decide over both periods consumption, c and c2, over labour, n2, capital k, and government spending, 92. Find the optimal centrally-planned solution for c and . [Hint: the government budget has to balance.] [10 points] (b) Find the private sector solutions for c and c2, taking government expenditures as given. [10 points] (c) Compare the two solutions. [5 points] (d) Assess the main assumptions of OLG models and explain which type of economic questions can be answered in this framework and not in a standard representative agent model. [15 points] 3 Exercise 3 - Basic OLG model Consider the following two-period OLG model. People consume in both periods but work only in period two. The inter-temporal utility of the representative individual in the first period is U = In c +3[ln c +aln(1-) + y ln g2] where c and are consumption and k (which is given) and k2 are the stocks of capital in periods one and two, n is work and g2 is government expenditure in period two which is funded by a lump-sum tax in period two, T. Production in periods one and two are y = Rk = C +k 32 = Rk + n = 0 +92 (a) In class we discussed that a benevolent social planner would internalise the decisions of each agent in the economy, solving the model from a central point of view. In this context a social planner would decide over both periods consumption, c and c2, over labour, n2, capital k, and government spending, 92. Find the optimal centrally-planned solution for c and . [Hint: the government budget has to balance.] [10 points] (b) Find the private sector solutions for c and c2, taking government expenditures as given. [10 points] (c) Compare the two solutions. [5 points] (d) Assess the main assumptions of OLG models and explain which type of economic questions can be answered in this framework and not in a standard representative agent model. [15 points]

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a The social planner maximizes intertemporal utility subject to the resource constraints Max U lnc1 ... View the full answer