Lifetime Consumption and Saving

For his 45 working years, Carlo saves $3,000 a year. For his 15 retirement years, Carlo dissaves at a rate of $9,000 a year. We have discovered a rather remarkable conclusion: the change in the government’s Social Security scheme has no effect on Carlo’s lifetime resources or lifetime consumption. From Carlo’s point of view, the change means that the government is saving more on Carlo’s behalf, and therefore he does not need to save so much for himself. Carlo’s saving declines by exactly the same amount as the increase in Social Security taxes ($1,000) per year; likewise, his dissaving declines by exactly the same amount as the increase in Social Security payments. Another example is even more striking. Suppose there were no Social Security system at all. Then Carlo would receive $40,000 a year for 45 years but nothing at all in his retirement years. His lifetime resources would equal lifetime income = $40,000 × 45 = $1,800,000, which is again the same as before. To enjoy lifetime consumption of $30,000 a year, Carlo would save $10,000 in every working year and dissave $30,000 in every retirement year. These numerical examples suggest an extraordinary conclusion: Social Security seems to be completely irrelevant for Carlo. No matter what the scheme looks like, Carlo has the same lifetime resources and same lifetime consumption. This is an amazing and perhaps even shocking finding. We have used some economics to analyze one of the most important government programs, one that is a source of constant scrutiny and debate (and, not incidentally, requires substantial resources for its administration). Not only have we found no reason to expect a crisis in Social Security, we have found that it is irrelevant. Should we now pack up and go home, saying that “economists have analyzed Social Security and it is actually a nonissue”? We hope it is obvious that the answer is no. After all, all we have done so far is present a numerical example. The example suggests that Social Security might be irrelevant under certain circumstances, but it certainly does not prove that it is irrelevant in general. This is how economists very often work. A simple numerical example can help us understand the operation of a complicated system like Social Security and can lead to some suggestive conclusions. Our next task is to determine whether the conclusion from our example holds more generally. We will first see that the result does not depend only on the particular numbers that we chose. We will then try to understand exactly where the conclusion comes from.