Question

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 where c and c2 are consumption and kı (which is given) and k2 are the stocks of capital in periods one and two. ns is work and is government expenditure in period two which is funded by a lump-sum tax in period two, T2. Production in periods one and two are (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, ci and c2, over labour, n2, capital k2, and government spending, g2. Find the optimal centrally-planned solution for c1 and c2-Hint: the government budget has to balance.] [10 points] (b) Find the private sector solutions for ci 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

Answer 1

d) The usefulness of the model derives from its close connection to important facts: economic interaction takes place between agents belonging to many di§erent age groups; agentsí working life lasts many periods; the present discounted value of expected future labor income is thus a key variable in the system; hereby the wealth e§ect of a change in the interest rate becomes important; owing to uncertainty about remaining lifetime and to retirement from the labor market at old age, a large part of saving is channelled to pension arrangements and various kinds of life-insurance; taking Önite lifetime into account, the model o§ers a more realistic approach to the study of long-run e§ects of government budget deÖcits and government debt than the Ramsey model; by including life expectancy among its parameters, the model opens up for studying e§ects of demographic changes in the industrialized countries such as increased life expectancy due to improved health conditions.