The government injects $90 billion into the economy. Each recipient spends 90% of the
dollars received. In turn, the secondary recipients spend 90% of the dollars they receive,
etc.
Use the expansion of 1/(1-x) in powers of x to come up with a clean measurement of the total
spending that results from the $90 billion injection.

Question

The government injects $90 billion into the economy. Each recipient spends 90% of the
dollars received. In turn, the secondary recipients spend 90% of the dollars they receive,
etc.
Use the expansion of 1/(1-x) in powers of x to come up with a clean measurement of the total
spending that results from the $90 billion injection.

anonymous · Answer

$$90\times .9+90\times .9^2+90\times .9^3+...$$
$$10(1+.9+.9^2+.9^3+...$$
$$\frac{10}{1-.9}=\frac{10}{.1}=100$$

anonymous · Answer

ahh makes sense! thank you so much!

anonymous · Answer

yw
just hope it is right