Chapter 13.3, Problem 17E

Redo Example 9 if the marginal propensity to consume is 95%.

Example 9 The Multiplier

Suppose that Americans spend 90% of every additional dollar they earn. Economists would say that an individual’s marginal propensity to consume is 0.90. For example, if Roberta earns a dollar, she will spend 0.9($1) = $0,90 of it and save $0.10. Whoever earns $0.90 (from Roberta) will spend 90% of it, or 0.9($0.90) = $0.81. This process of spending continues and results in geometric series as follows:

$\$1+\$0.90+\$0.81+\$0.729+\cdots$

The sum of this geometric series is called the multiplier. The multiplier is used to determine the total impact of spending on the U.S. economy. Suppose the government gives a child-tax rebate of $500 to Roberta. Determine the impact of the rebate on the U.S. economy if Americans spend 90% of every dollar they earn.