Household incomes tend to vary quite a lot, but households like their consumption to be approximately constant over time. Households therefore use their savings to smooth out the variations in their income.  For the purposes of understanding Social Security—both its problems and its reforms—we need to examine this idea of consumption smoothing more rigorously. Because Social Security is a program to provide for consumption in retirement, we must carefully lay out the decisions of a household over the entire lifetime of its members. By so doing, we can determine the likely effect of a promise of a transfer in the future on behavior today. Bear in mind that these transfers may be far in the future: for a 25-year-old worker, we are thinking about money that won’t be received for another 40 years or so. As is often the case in economics, we start by looking at the simplest setup we can imagine. We do this not because we think we can answer every question with a simple model, but because we must make sure we understand the fundamentals of Social Security before we worry about the complexities. So, to keep things simple, we examine the life of a single individual—that is, think of the household as containing just one person. Hence we do not have to worry about multiple wage earners (who might be of different ages), and we do not have to worry about how to incorporate children (who grow up and leave the household) into our story. In this chapter, we use the terms individual and household interchangeably. We call our individual Carlo. Carlo thinks about his income and consumption over his entire lifetime. Because he has the possibility of saving and borrowing, his income and consumption need not be equal in any given year. Carlo faces a lifetime budget constraint, however; in the end, his lifetime spending is limited by his lifetime income. The life- cycle model of consumption examines Carlo’s decisions about how much to consume each year, given this budget constraint. We begin with a simple numerical example. Suppose Carlo is 20 years old and very well informed about his future. He knows that he is going to work for 45 years—that is, up to age 65. He knows that, every year, he will receive income of $40,000, excluding Social Security contributions. He has to pay Social Security contributions on this income at a rate of 15 percent. Thus he knows he will pay $6,000 each year to Social Security, and his after-tax income is $40,000 − $6,000 = $34,000. After he retires at age 65, he knows he will receive a Social Security payment of $18,000 each year until he dies, 15 years later, on his 80th birthday (of heart failure, brought on by the exertion of blowing out all those candles). To decide on his lifetime consumption and saving patterns, Carlo needs to know what his lifetime resources are. We know that, in general, a dollar today is not worth the same amount as a dollar next year—or 60 years from now—because of interest rates and inflation. We sidestep that problem for the moment by imagining that the real interest rate is zero. In this case, it is legitimate to add together dollars from different time periods. So Carlo earns $34,000 per year for each of his 45 working years and obtains $18,000 per year for his 15 retired years. His total lifetime resources are as follows: lifetime income = income during working years + income during retirement years = ($34,000 × 45) + ($18,000 × 15) = $1,530,000 + $270,000 = $1,800,000. Over his life, therefore, he has $1.8 million to spend. Figure 13.1 “Lifetime Income”shows his lifetime income. His total lifetime resources are obtained by adding together the two rectangles labeled “Lifetime Income from Working” and “Lifetime Social Security Income.” The height of each rectangle gives his income, and the width of each rectangle gives the number of years for which he earns that income.
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