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Chapter 6: Problem 201

By how much must investment rise to bring about a \(\$ 300 \mathrm{M}\) change in income if \(\mathrm{MPC}=0.75\).

Short Answer

Expert verified
The investment needs to rise by \(75 \mathrm{M}\) to bring about a \(300 \mathrm{M}\) change in income with a marginal propensity to consume of 0.75.

Step by step solution

01

Calculate the multiplier effect

First, we need to calculate the multiplier effect using the given value of MPC: Multiplier = \( \frac{1}{1 - \mathrm{MPC}} \) Multiplier = \( \frac{1}{1 - 0.75} \) Multiplier = \( \frac{1}{0.25} \) Multiplier = 4
02

Rearrange the formula to solve for the change in investment (ΔI)

Now, we need to rearrange the change in income formula to solve for the change in investment (ΔI): ΔY = Multiplier × ΔI Divide both sides of the equation by the multiplier value: ΔI = \( \frac{\Delta Y}{\text{Multiplier}} \)
03

Calculate the change in investment (ΔI) required

Lastly, input the given values for the change in income (ΔY) and the calculated multiplier to compute the change in investment (ΔI): ΔI = \( \frac{\$300 \mathrm{M}}{4} \) ΔI = \( \$75 \mathrm{M} \) The investment needs to rise by \(75 \mathrm{M}\) to bring about a \(300 \mathrm{M}\) change in income with a marginal propensity to consume of 0.75.

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Most popular questions from this chapter

Show that if the multiplier is one, the slope of the savings schedule is one.

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