An important decision that every person faces is how much income to consume today and how much to save for the future. We can me the theory of consumer choice to analyze how people make this decision and how the amount they save depends on the interest rate their savings will earn. Consider the decision facing Sam, a worker planning for retirement. To keep things simple, let’s divide Sam’s life into two periods. In the first period, Sam is young and working. In the second period, he is old and retired. When young, Sam earns $100,000. He divides this income between current consumption and saving. When he is old, Sam will consume what he has saved, including the interest that his savings have earned
Suppose that the ‘interest rate is 10 percent. Then for every dollar that Sam saves when young, he can consume $1.10 when old. We can view “consumption when young” and “consumption when old” as the two goods that Sam must choose between. The interest rate determines the relative price of these two goods Figure 15 shows Sam’s budget constraint. If he saves nothing, he consumes $100,000 when young and nothing when old. If he saves everything, he consumes nothing when young and $110,000 when old. The budget constraint shows these and all the intermediate possibilities.

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