# Understanding the Multiplier Effect in Economics

## Answer the following questions about the multiplier:

**a. How much will GDP change after a $545 billion increase in government purchases, if the multiplier is 1.5?**

$817.5 billion

**b. How much will GDP change after a $400 billion decrease in government purchases, if the multiplier is 1.25?**

$500 billion

**c. If a $300 billion increase in government purchases leads to a $450 billion increase in GDP, what is the value of the multiplier?**

Multiplier: 1.5

**Final answer:** To calculate the impact on GDP, multiply the change in government purchases by the multiplier. For a $545 billion increase with a 1.5 multiplier, GDP increases by $817.5 billion. For a $400 billion decrease with a 1.25 multiplier, GDP decreases by $500 billion. The multiplier itself can be calculated as well, as shown with a $300 billion spending resulting in a $450 billion GDP increase yielding a multiplier of 1.5.

**Explanation:** To calculate the changes in GDP after a change in government purchases, we use the formula Change in GDP = Multiplier × Change in Government Spending.

a. With a multiplier of 1.5, a $545 billion increase in government purchases would change the GDP by:

1.5 × $545 billion = $817.5 billion

So, the GDP would increase by $817.5 billion.

b. With a multiplier of 1.25, a $400 billion decrease in government purchases would change the GDP by:

1.25 × -$400 billion = -$500 billion

Thus, the GDP would decrease by $500 billion.

c. If a $300 billion increase in government purchases leads to a $450 billion increase in GDP, the multiplier can be found using the formula:

Multiplier = Change in GDP / Change in Government Spending

Multiplier = $450 billion / $300 billion = 1.5

Therefore, the value of the multiplier is 1.5.

What is the formula to calculate the impact of a change in government purchases on GDP using the multiplier?

The formula to calculate the impact of a change in government purchases on GDP using the multiplier is Change in GDP = Multiplier × Change in Government Spending.