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.

Answer 1

w+w(1-p)+w(1-p)^2…
a/1-r
w/(1-1-p)

Answer 2

@asnaseer

Answer 3

@.Sam.

Answer 4

@sirm3d @chihiroasleaf

Answer 5

what i did at the start was the start of the problem having trouble with the rest.

Answer 6

@agent0smith

Answer 7

Gotta go to sleep, may have a look at this tomorrow.

Answer 8

don't bother i'll have done by then.

Answer 9

thanks anyways.

Answer 10

let's see...

Answer 11

does it give an interest rate at which the money is saved?

Answer 12

does the government give each citizen w each month? or only once?

Answer 13

once, and interest rate.

Answer 14

no interest rate.

Answer 15

is provided.

Answer 16

p.s. i'm ridiculously tired so please excuse my mistakes and otherwise terrible answers.

Answer 17

so... the citizens get one amount of money, w

Answer 18

yeps.

Answer 19

and they spend a fraction p of it every time

Answer 20

yeps, pretty much.

Answer 21

so then the amount of money they have left would be\[$=(1-p)^t\]
where t is time in months

Answer 22

if it goes on forever, they spend all the money

Answer 23

w is not increased

Answer 24

so the question doesn't really make sense

Answer 25

unless p is such that they don't spend any money

Answer 26

you forgot something... w(n+1)=wn(1-p)^t

Answer 27

() denote subscripts

Answer 28

that's about what I said with the equation $=
just more accurate.

unless the government is giving more money out after the start