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.
Step-by-step 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.