Overlapping Generations Model - Basic OLG Model

Basic OLG 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.Nt_t denotes individuals born in period t.
• Nt-1_t 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 t_t = N t_t+1.
• Population grows at a constant rate n:

• 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