Imagine that the government of a small community decides to give a total of $W, distributed equally, to all its citizens. Suppose that each month each citizen saves a fraction p of his or her new wealth and spends the remaining 1 - p in the community. Assume no money leaves or enters the community, and all the spent money is redistributed throughout the community. 

a. If this cycle of saving and spending continues for many months, how much money is ultimately spent? Specifically, by what factor is the initial investment of $W increased (in terms of p)? Economists refer to this increase in the investment as the multiplier effect. 

b. Evaluate the limits p→0 and p→1, and interpret their meanings.