Chapter 12.3, Problem 98AYU

Multiplier Refer to Problem 97. Suppose that the marginal propensity to consume throughout the U.S. economy is $$0.95$$. What is the multiplier for the U.S. economy?

To determine

To calculate: The value of multiplier if individual spend $0.95$ of every additional dollar that they earn.

Answer to Problem 98AYU

Multiplier value $=20$.

Explanation of Solution

Given:

It is given that throughout the U.S. economy, individuals spend $0.95$ of every additional dollar that they earn.

It is also given that the process of spending continues and results in an infinite geometric series as follows:

$1,0.95,{0.95}^2,{0.95}^3,{0.95}^4,\cdots$

First term $a_1=1$ and the common ratio $r=\frac{a^n}{a^{n-1}}=0.95$.

Formula used:

Convergence of an infinite geometric series theorem states that ‘If $\left|r\right|<1$ converges. Its sum is ${\displaystyle \sum }_{k=1}^{\infty }{a}_1{r}^{k-1}=\frac{a_1}{1-r}$’.

Calculation:

Multiplier if individual $=\frac{1}{1-0.9}=\frac{1}{0.05}=20$.