Overlapping generations model: Difference between revisions

Revision as of 10:37, 27 November 2016

Revision as of 10:38, 27 November 2016

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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. ''N'' ^t<submath>N^{t}_t </submath> 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 ''N''<submath>''0''N_0 </submath> .

*The size of the initial old generation is normalized to 1: ''N''<supmath>N^{0}_0 0=1</supmath>₀ = 1.

*People do not die early, so ''N''<supmath>N^{t}_t t</sup><sub>t</submath> = ''N''<supmath> N^{t</sup><sub>}_{t+1} </submath>.

*Population grows at a constant rate n:

::<math> N_t^t = (1+n)^t </math>