Final answer:
The multiplier is used to calculate the change in autonomous expenditure needed to increase real GDP by a specified amount, taking into account the initial spending change and the multiplier effect.
Step-by-step explanation:
The multiplier is crucial because it helps us calculate the change in autonomous expenditure needed to achieve a specific economic outcome. In this case, the multiplier matters because we can use it to determine by how much we should change autonomous expenditure to increase real GDP by a given amount.
The multiplier effect reveals that an initial change in autonomous spending leads to a larger change in real GDP. This is because each round of spending generates further income and consumption. To calculate the impact of a change in autonomous spending on real GDP, one must know the marginal propensity to consume, which allows the determination of the multiplier, and the initial change in spending.
For instance, if we aim to augment aggregate demand by $100 and the multiplier is calculated to be 2.13, a government increase in spending of $100/2.13, which is approximately $47, would be necessary. This leverages the multiplier effect to ultimately generate the desired increase in real GDP.