When money is spent on goods and services, those who 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 c and s are called the marginal propensity to consume and the marginal propensity to save and, of course, c+s=1.

Show that

lim Sn=kD, where k = 1/s.
n→[infinity]

The number k is called the multiplier. What is the multiplier if the marginal propensity to consume is 80%?