Editing Overlapping generations model (section)

== Pure-exchange OLG model ==

[[File:OLG model- Generation.png|thumb|Generational Shifts in OLG Models]]
The most basic OLG model has the following characteristics:<ref name="LjungqvistSargent2004">{{cite book|author1=Lars Ljungqvist|author2=Thomas J. Sargent|title=Recursive Macroeconomic Theory|date=1 September 2004|publisher=MIT Press|isbn=978-0-262-12274-0|pages = 264–267}}</ref>
*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 are born in every period. <math>N^{t}_t </math> denotes the number of individuals born in period t.
*<math>N^{t-1}_t </math> denotes the 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.'' The number of them can be denoted as <math>N_0 </math> .
*The size of the initial old generation is normalized to 1: <math>N^{0}_0 =1</math>.
*People do not die early, so <math>N^{t}_t = N^{t}_{t+1} </math>.
*Population grows at a constant rate n:
::<math> N_t^t = (1+n)^t </math>

*In the "pure exchange economy" version of the model, there is only one physical good 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''. 
*In the "production economy" version of the model (see Diamond OLG model below), the physical good can be either consumed or invested to build physical capital. Output is produced from labor and physical capital. Each household is endowed with one unit of time which is inelastically supply on the labor market.
*Preferences over consumption streams are given by
::<math> u(c_t^t,c_t^{t+1}) =  U(c_t^t) + \beta U(c_t^{t+1}),</math>
:where <math> \beta </math> is the rate of time preference.