Q2 (b)
every person faces is how much income to consume today and how much to save for the future. We
can use 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 Saul, a worker planning for retirement. To keep things simple, let’s
divide Saul’s life into two periods. In the first period, Saul is young and working. In the second
period, he is old and retired. When young, Saul earns $100,000. He divides this income between
current consumption and saving. When he is old, Saul will consume what he has saved, including the
interest that his savings have earned. Suppose the interest rate is 10 percent. Then for every dollar
that Saul 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 Saul must choose between.
Now consider what happens when the interest rate increases from 10 percent to 20 percent. Figure
16 shows two possible outcomes. In both cases, the budget constraint shifts outward and becomes
steeper. At the new, higher interest rate, Saul gets more consumption when old for every dollar of
consumption that he gives up when young. The two panels show the results given different
preferences by Saul. In both cases, consumption when old rises. Yet the response of consumption
when young to the change in the interest rate is different in the two cases. In panel (a), Saul
responds to the higher interest rate by consuming less when young. In panel (b), Saul responds by
consuming more when young. Saul’s saving is his income when young minus the amount he
consumes when young. In panel (a), an increase in the interest rate reduces consumption when
young, so saving must rise. In panel (b), an increase in the interest rate induces Saul to consume
more when young, so saving must fall.
The case shown in panel (b) might at first seem odd: Saul responds to an increase in the return to
saving by saving less. Yet this behavior is not as peculiar as it might seem. We can understand it by
considering the income and substitution effects of a higher interest rate. Consider first the
substitution effect. When the interest rate rises, consumption when old becomes less costly relative
to consumption when young. Therefore, the substitution effect induces Saul to consume more when
old and less when young. In other words, the substitution effect induces Saul to save more. Now
consider the income effect. When the interest rate rises, Saul moves to a higher indifference curve.
He is now better off than he was. As long as consumption in both periods consists of normal goods,
he tends to want to use this increase in well-being to enjoy higher consumption in both periods. In
other words, the income effect induces him to save less. The result depends on both the income and
substitution effects. If the substi tution effect of a higher interest rate is greater than the income
effect, Saul saves more. If the income effect is greater than the substitution effect, Saul saves less.
Thus, the theory of consumer choice says that an increase in the interest rate could either encourage
or discourage saving.
