Chapter 11.4, Problem 55PPS

To determine

Find the amount of money is generated for the economy for every $500 that government provides.

Answer to Problem 55PPS

$2500 is generated for the economy for every $500 that government provides.

Explanation of Solution

Given:

A state government decides to stimulate its economy by giving $500 to every adult. The government assumes that everyone who receives the money will spend 80% on consumer goods and that the producers of these goods will in turn spend 80% on consumer goods. How much money is generated for the economy for every $500 that government provides?

Concept Used:

This is a geometric series. $a_1=500\text{and}r=80\%=0.80$

The total number of revolutions done by the tire before it stops spinning is the sum of the series. Because $\left|r\right|=0.80<1$ , we use the formula: $\text{S}=\frac{a_1}{1-r}$

Calculation:

This is a geometric series. $a_1=500\text{and}r=80\%=0.80$

The total number of revolutions done by the tire before it stops spinning is the sum of the series. Because $\left|r\right|=0.80<1$ , we use the formula: $\text{S}=\frac{a_1}{1-r}$

  $\begin{array}{l}{a}_1=500;r=0.80;\text{find}\text{S}\\ \text{S}=\frac{a_1}{1-r}=\frac{500}{1-0.80}=\frac{500}{0.20}=2500\end{array}$

$2500 is generated for the economy for every $500 that government provides.

Thus, $2500 is generated for the economy for every $500 that government provides.