When money is spent on goods and services, those who receive the money also spend some of it. The people receiv- ing some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effecr. In a hypothetical isolated community, the local gover- ment begins the process by spending D dollars. Suppose that each recipient of spent money spends 100c% and saves 100% 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 S, be the total spending that has been generated after n transactions. Find an equation for S. (b) Show that lim-S, -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. When money is spent on goods and services, those who receive the money also spend some of it. The people receiv- ing some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effecr. In a hypothetical isolated community, the local gover- ment begins the process by spending D dollars. Suppose that each recipient of spent money spends 100c% and saves 100% 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 S, be the total spending that has been generated after n transactions. Find an equation for S. (b) Show that lim-S, -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