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 and saves of the money that he or she receives. The values c 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 limn→∞ 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%?
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