The Multiplier, Growth and Money and Banking: Question 10

Worked solution

Step 1: Recall what the multiplier formula assumes

The formula $k=\dfrac{1}{MPS+MRT+MPM}$ treats the marginal propensities to save, tax and import as fixed numbers, so that a single value of $k$ can be applied to any injection. In reality, these marginal propensities are estimated from past data over a particular period, and there is no guarantee they stay constant. Households may save a larger share of extra income as their income rises (a higher marginal propensity to save at higher income levels), the marginal rate of tax may change if the government alters tax bands, and the marginal propensity to import may shift with the exchange rate or import prices. If the true marginal propensities differ from the ones used to calculate $k$, the actual change in national income following a change in government spending will differ from the prediction.

Step 2: Check option A

Option A directly identifies this instability of the underlying marginal propensities as the reason a single, constant multiplier value may not reliably predict the real-world effect of a change in government spending. This is the most significant, general limitation of the constant-multiplier approach.

Step 3: Rule out options B, C and D

• Option B: false. The formula $k=\dfrac{1}{MPS+MRT+MPM}$ is precisely the version of the multiplier that already includes a government sector (via $MRT$) and an open economy (via $MPM$); it is the simple closed-economy formula, $k=\dfrac{1}{MPS}$, that assumes no government or trade sector, not this one.
• Option C: false. The size of the multiplier depends only on the marginal propensities to withdraw, and says nothing by itself about whether the economy’s actual output is currently above or below its potential output (the output gap); a large multiplier in a deeply depressed economy does not mean real GDP is growing faster than potential.
• Option D: false. The multiplier process is triggered by a change in any injection or autonomous component of aggregate demand (investment, exports, government spending or autonomous consumption), not government spending alone.

Final answer

Option A, because the marginal propensities to save, tax and import are unlikely to remain constant across income levels or over time, a single, constant multiplier value is only ever an approximation, and the actual change in national income following a change in government spending can differ from the value it predicts.