Which of the following must be true to have a closed economy with no government, and yet the value of the investmet multiplier still increase?

Analyze the question

The question asks what must be true for the investment multiplier to rise in a closed economy with no government (no taxes, no imports).

Concept

In a simple two-sector economy (households and firms only):

• Investment multiplier, k = 1 / (1 − MPC)
• Since MPC + MPS = 1, then 1 − MPC = MPS
• So k = 1 / MPS

The multiplier depends only on the marginal propensity to save (or equivalently, the marginal propensity to consume). It does not depend on the actual level of investment, actual saving, or the average propensity to invest.

Solution

For k to increase, 1/MPS must increase, which means MPS must fall.

Example:

• If MPS = 0.4, then k = 1/0.4 = 2.5
• If MPS falls to 0.2, then k = 1/0.2 = 5

The multiplier rose because MPS fell (equivalently, MPC rose).

Checking the other options:

• B. Actual investment had fallen: this is the size of the injection and has no effect on the multiplier's value.
• C. Average propensity to invest has fallen: this is not a component of the multiplier formula.
• D. Actual saving has fallen: this is a level of saving, not the rate (MPS). A change in the amount saved can happen without any change in MPS.

Answer

The correct option is A.

Tip

In a closed economy with no government, remember k = 1/MPS. Any multiplier question comes down to the marginal propensities. Ignore "actual" or "average" values, because they are distractors. Lower MPS means a higher multiplier.