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 money is redistributed throughout the community.
a. if this cycle is continued for many months, how much money is ultimately spent? specifically by what factor is the initial investment of w increased.
b. evaluate the limits p--0 and p--1 and interpret their meanings.

Question

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 money is redistributed throughout the community.
a. if this cycle is continued for many months, how much money is ultimately spent? specifically by what factor is the initial investment of w increased.
b. evaluate the limits p-->0 and p-->1 and interpret their meanings.