Open-market purchase of bonds by Fed â†' bank reserves and interest rate:
The multiplier is 5 when the marginal propensity to consume is 0.8.
The multiplier effect is calculated using the formula \( \text{Multiplier} = \frac{1}{1 - \text{MPC}} \). With a marginal propensity to consume (MPC) of 0.8, the multiplier becomes \( \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5 \).
A multiplier of 2 would imply an MPC of 0.5, as calculated by \( \text{Multiplier} = \frac{1}{1 - \text{MPC}} \), leading to \( 2 = \frac{1}{1 - \text{MPC}} \) which simplifies to an MPC of 0.5. This does not align with the stated MPC of 0.8.
A multiplier of 4 suggests an MPC of 0.75, derived from the same formula. The calculation \( 4 = \frac{1}{1 - \text{MPC}} \) yields an MPC of 0.75, which is less than the given MPC of 0.8, hence it cannot be the correct answer.
This is the correct choice, as calculated above. The multiplier is determined by the formula \( \text{Multiplier} = \frac{1}{1 - 0.8} \), leading to a result of 5, which accurately reflects the relationship between the MPC and the multiplier.
A multiplier of 8 would indicate an MPC of 0.875, obtained from the formula \( 8 = \frac{1}{1 - \text{MPC}} \). This suggests an MPC higher than 0.8, which does not correspond to the given information.
The marginal propensity to consume of 0.8 leads to a multiplier of 5, demonstrating the significant impact consumption has on overall economic activity. Recognizing how the MPC influences the multiplier is crucial for understanding fiscal policy and its effects on the economy. The incorrect choices reflect different MPC values, emphasizing the precise relationship necessary to derive the correct multiplier outcome.
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