IN EARLIER CHAPTERS we used the overlapping generations model as a model of money. People needed money, whether fiat, commodity, or inside money, to acquire a market good for which they must pay with a form of money. We did not interpret this good literally as consumption in old age because money balances are a trivial source of savings for retirement. We used the overlapping generations structure as a simple way to model exchange without taking the age of the model's people very seriously.

Now we will take the age structure of the overlapping generations model more seriously as we turn to the subject of the determinants of aggregate saving and investment. Our attitude changes because government bonds and capital, the focuses of our inquiry, are important parts of people's lifetime savings.

The Savings Decisions

Let us now look at how individuals choose their level of savings. We will do this in the context of the overlapping generations model of two-period-lived people who must choose how much to consume when young and when old. Let us generalize the model by assuming that people have endowments of y1 goods when young and y2 goods when old. We may think of the endowments as labor income. We will assume that young people face a gross real interest rate, r, and choose accordingly the number of goods they wish to save, st.

We can now describe the budget of someone born at t. When young, this person has y1 goods from her labor, which she can either consume or save.