Editing Overlapping generations model (section)

=== Basic one-sector OLG model ===
The pure-exchange OLG model was augmented with the introduction of an aggregate neoclassical production by [[Peter Diamond]].<ref name="Diamond65" />  In contrast, to Ramsey–Cass–Koopmans neoclassical growth model in which individuals are infinitely-lived and the economy is characterized by a unique steady-state equilibrium, as was established by Oded Galor and Harl Ryder,<ref>{{cite journal|last1=Galor|first1=Oded|author-link=Oded Galor|last2=Ryder|first2=Harl E.|year=1989|title=Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital|journal=[[Journal of Economic Theory]]|volume=49|issue=2|pages=360–375|doi=10.1016/0022-0531(89)90088-4}}</ref> the OLG economy may be characterized by multiple steady-state equilibria, and initial conditions may therefore affect the long-run evolution of the long-run level of income per capita. 

Since initial conditions in the OLG model may affect economic growth in long-run, the model was useful for the exploration of the [[convergence hypothesis]].<ref>{{Cite journal|last=Galor|first=Oded|date=1996|title=Convergence? Inferences from theoretical models|url=https://www.brown.edu/academics/economics/sites/brown.edu.academics.economics/files/uploads/1996-3.pdf|journal=The Economic Journal|volume=106|issue=437|pages=1056–1069|doi=10.2307/2235378|jstor=2235378}}</ref>[[File:OLG Model - Diamond.png|thumb|Convergence of OLG Economy to Steady State]]
The economy has the following characteristics:<ref>{{cite book|title=OLG Model|last=Carrol|first=Christopher}}</ref>

*Two generations are alive at any point in time, the young (age 1) and old (age 2).
*The size of the young generation in period t is given by N<sub>t</sub> =  N<sub>0</sub> E<sup>t</sup>.
*Households work only in the first period of their life and earn Y<sub>1,t</sub> income. They earn no income in the second period of their life (Y<sub>2,t+1</sub> =  0).
*They consume part of their first period income and save the rest to finance their consumption when old.
*At the end of period t, the assets of the young are the source of the capital used for aggregate production in period t+1.So K<sub>t+1</sub> = N<sub>t,</sub>a<sub>1,t</sub> where a<sub>1,t</sub> is the assets per young household after their consumption in period 1. In addition to this there is no depreciation.
*The old in period t own the entire capital stock and consume it entirely, so dissaving by the old in period t is given by N<sub>t-1,</sub>a<sub>1,t-1</sub> = K<sub>t</sub>.
*Labor and capital markets are perfectly competitive and the aggregate production technology is CRS, Y = F(K,L).