We now go beyond our numerical example and give a more general analysis of how an individual’s lifetime consumption choices are influenced by Social Security. We first consider the budget constraints faced by an individual or household (remember that we are using the two terms interchangeably). There are two household budget constraints. The first applies in any given period: ultimately, you must either spend the income you receive or save it; there are no other choices. For example, disposable income = consumption + household savings. Households also face a lifetime budget constraint. They can save in some periods of their life and borrow/dissave in other periods, but over the course of any household’s lifetime, income and spending must balance. The simplest case is when real interest rates equal zero, which means that it is legitimate simply to add together income and consumption in different years. In this case the lifetime budget constraint says that total lifetime consumption = total lifetime income. If real interest rates are not zero, then the budget constraint must be expressed in terms of discounted present values. The household’s lifetime budget constraint is then discounted present value of lifetime consumption = discounted present value of lifetime income. If the household begins its life with some assets (say a bequest), we count this as part of income. If the household leaves a bequest, we count this as part of consumption. As in our earlier numerical example, we can think about the lifetime budget constraint in terms of the household’s assets. Over the course of a lifetime, the household can save and build up its assets or dissave and run down its assets. It can even have negative assets because of borrowing. But the lifetime budget constraint says that the household’s consumption and saving must result in the household having zero assets at the end of its life.
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