To understand the effects of a change in the marginal propensity to consume (MPC) on the multiplier and aggregate income, we need to look at the relationship between the MPC, the multiplier, and the total change in income.
The basic formula for the multiplier (k) is:
\[ k = \frac{1}{1 - \text{MPC}} \]
If the MPC is cut in half, let's say it changes from MPC to MPC/2, the new multiplier would be calculated as follows:
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Original multiplier with MPC: \[ k_1 = \frac{1}{1 - \text{MPC}} \]
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New multiplier with halved MPC: \[ k_2 = \frac{1}{1 - \frac{\text{MPC}}{2}} \]
To see how the multiplier changes, note that halving the MPC increases the denominator less significantly than the original MPC would, leading to a new multiplier that is not simply half of the original. Therefore, while the multiplier does decrease, it does not decrease proportionately as much as the MPC does.
Let's evaluate the answer choices given:
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Increases by 50%: This is incorrect. The multiplier will decrease, not increase.
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Decreases by less than 50%: This is a potential option, but we need to analyze further.
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Decreases by more than 50%: This is incorrect because the reduction in the MPC does not lead to a more than proportional decrease in the multiplier.
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Is also cut in half (falls by 50%): This is incorrect.
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Increases by less than 50%: This is irrelevant to the scenario.
Given that the reduction in the MPC will result in a decrease in the multiplier that is less than proportional (and less than 50%), the correct answer is:
Decreases by less than 50%.