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*<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
*Population grows at a constant rate n:
::<math> N_t^t = (1+n)^t </math>
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