Chapter 12.3, Problem 97AYU

Multiplier 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 $0.9(1)=\$0.90$ of it. The individual who 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:

${\mathrm{1.0.90.0.90}}^2,{0.90}^3{\mathrm{.0.90}}^4.\dots$

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?