Question

Suppose that, throughout the U.S. economy,

individuals spend 90% of every additional dollar that they earn. Economists would say that an individual’s marginal propensity to consume is 0.90. For example, if Jane earns an additional dollar, she will spend 0.9112 = \(0.90 of it. The individual that earns \)0.90 (from Jane) will spend 90% of it or $0.81. This process of spending continues and results in an infinite geometric series as follows: $1,0.9,0.9^2,0.9^3,.....$

The sum of this infinite geometric series is called the

multiplier. What is the multiplier if individuals spend 90%

of every additional dollar that they earn?

Short answer

The multiplier is 10.

Step-by-step solution

Given information

We are given$a=1,r=0.9.a_n=r{a}_{n-1}$

Calculate

We use the formula $S=\frac{a_1}{1-r}$

We have,

$$\begin{gathered} S=\frac{1}{1-0.9} \\ S=10 \end{gathered}$$

The multiplier is 10.