When money is spent on goods and services, those that receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending D dollars. Suppose that each recipient of spent money spends 100c% and saves 100s% of the money that he or she receives. The values and s are called the marginal propensity to consume and the marginal propensity to save and, of course, c + s = 1.
(a) Let Sn be the total spending that has been generated after n transactions. Find an equation for Sn.
(b) Show that lim n→∞ Sn = kD, where k = 1/s. The number k is called the multiplier. What is the multiplier if the marginal propensity to consume is 80%? Note: The federal government uses this principle to justify deficit spending. Banks use this principle to justify lending a large percentage of the money that they receive in deposits.