Overlapping generations model: Difference between revisions

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*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</sub><sub>,</sub><sub>t</sub> income. They earn no income in the second period of their life (Y<sub>2</sub><sub>,</sub><sub>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><sub>,</sub>a<sub>1</sub><sub>,</sub><sub>t</sub> where a<sub>1</sub><sub>,</sub><sub>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><sub>,</sub>a<sub>1</sub><sub>,</sub><sub>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).