# Overlapping generations model

{{#invoke:Hatnote|hatnote}} An overlapping generations model, abbreviated to OLG model, is a type of representative agent economic model in which agents live a finite length of time long enough to overlap with at least one period of another agent's life.

All OLG models share several key elements:

• Individuals receive an endowment of goods at birth.
• Goods cannot endure for more than one period.
• Money endures for multiple periods.
• Individual's lifetime utility is a function of consumption in all periods.

The concept of an OLG model was inspired by Irving Fisher's monograph The Theory of Interest. Notable improvements were published by Maurice Allais in 1947, Paul Samuelson in 1958, and Peter Diamond in 1965.

## Basic model

The most basic OLG model has the following characteristics:

• Individuals live for two periods; in the first period of life, they are referred to as the Young. In the second period of life, they are referred to as the Old.
• A number of individuals is born in every period.Ntt denotes individuals born in period t.
• Nt-1t denotes number of old people in period t. Since the economy begins in period 1. In period 1, there is a group of people who are already old. They are referred to as the initial old. They can be denoted as N0 .
• The size of the initial old generation is normalized to 1 i.e. N 00 = 1.
• People do not die early, N tt = N t-1t+1.
• Population grows at a constant rate n:
$N_{t}^{t}=(1+n)^{t}$ • There is only one good in this economy, and it cannot endure for more than one period.
• Each individual receives a fixed endowment of this good at birth. This endowment is denoted as y. This endowment of goods can also be thought of as an endowment of labor that the individual uses to work and create a real income equal to the value of good y produced. Under this framework, individuals only work during the young phase of their life.
• Preferences over consumption streams are given by
$u(c_{t}^{t},c_{t}^{t+1})=U(c_{t}^{t})+\beta U(c_{t}^{t+1}),$ ## Attributes

One important aspect of the OLG model is that the steady state equilibrium need not be efficient, in contrast to general equilibrium models where the First Welfare Theorem guarantees Pareto efficiency. Because there are an infinite number of agents in the economy, the total value of resources is infinite, so Pareto improvements can be made by transferring resources from each young generation to the current old generation. Not every equilibrium is inefficient; the efficiency of an equilibrium is strongly linked to the interest rate and the Cass Criterion gives necessary and sufficient conditions for when an OLG competitive equilibrium allocation is inefficient.