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.(a) Let Sn be the total spending that has been generated after n transactions. Find an equation for Sn in terms of D and c. Sn = (b) Show thatlim n → [infinity] Sn = kD, wherek = 1/s