Overlapping generations model

As Overlapping - Generations Models ( OLG models ) is called in economics a certain class of theoretical models that describe the long-term development of an economy. OLG models are characterized in that individuals are grouped into generations, always lives over an infinite time horizon across each generation for some (finite) time and each stages of life (such as " young" and " old " ) passes; name-giving is the fact that there is always at least two generations at the same time (each in different stages of life ) alive, which equates to an " overlap " between the generations.

Basic model in a pure exchange economy ( Samuelson model )

Samuelson (1958 ) is based on a simple scenario, in which individuals have a certain initial endowment of an estate that they can not take over in the next by a period; in other words, is the durability of the equipment exactly one period or, in Samuelson's formulation, the interest rate is -1. The time is assumed to be discrete and infinite; the observed periods are given by. Suppose now, as usual, that an individual lives two periods long. Each generation consists of individuals and the inter-temporal features vector of each individual of generation t is given by, where for the equipment in the first period of life ( "young" ) and for those in the second period of life ( " old " ) is; defined analogous to the intertemporal consumption vector of each individual of generation t. The intertemporal utility function is noisy and, according to common assumptions, strictly increasing, strictly concave and twice continuously differentiable (in each case in both arguments ). The thus described OLG economy is subject in period t of the ( aggregate ) budget constraint

Which can be understood as follows: The consumption of all "old " from the previous generation, plus the consumption of all the " boys " from the current generation ( consequently therefore the entire consumption of all living individuals ) just need the current facilities of all living individuals meet.

If you compare the equation with the aid of the growth rate of the population, in order, we have the following equivalent, a meaningful graphical representation but more accessible form:

It illustrates the intergenerational interdependence that makes up the OLG model: maintains all consumption of the old population that exceeds their own equipment, is financed in full by the complete saving of the younger population. Figure 2 illustrates this. If every living generation consumed in t exactly in proportion to their amenities, you are in the so-called endowment point. An exogenously induced redistribution of per capita consumption of the young generation to a unit in favor of the older generation ( moving to the left above), to impose on this a per capita consumption increase with it. Changes in the population growth lead to a rotation of the budget line.