Money Multiplier vs Spending Multiplier
Money Multiplier and Spending Multiplier are related concepts in AP Economics that students often mix up. The money multiplier is the maximum amount the money supply can increase for each dollar of new bank reserves. The spending multiplier measures how much real GDP changes for each dollar change in autonomous spending. Here is how they compare side by side.
It equals the reciprocal of the required reserve ratio, assuming banks lend all excess reserves and the public holds no extra cash. A lower reserve ratio gives a larger multiplier. Real-world leakages make the actual multiplier smaller.
A higher marginal propensity to consume produces a larger multiplier because more of each dollar is re-spent. It is used to estimate the GDP impact of fiscal policy. It assumes spare capacity and ignores crowding out.
Money Multiplier vs Spending Multiplier: What Each One Actually Multiplies
| Money Multiplier | Spending Multiplier | |
|---|---|---|
| What goes in | A dollar of new bank reserves, usually from a central bank purchase of bonds. | A dollar of new autonomous spending, such as government purchases or investment. |
| What comes out | A larger money supply, a stock measured in dollars at a point in time. | A larger real GDP, a flow measured in dollars per period. |
| The formula | 1 divided by the required reserve ratio. | 1 divided by (1 minus MPC), which is the same as 1 divided by MPS. |
| What the denominator represents | The leak into required reserves that each bank must hold back from lending. | The leak into saving at each round of re-spending. |
| Where it is used | The banking system and the money market diagram. | The expenditure model and shifts of aggregate demand. |
| What shrinks it in practice | Banks holding excess reserves and households holding currency instead of deposits. | Income taxes, spending on imports, and crowding out. |
| Typical prompt wording | 'The maximum possible change in the money supply is...' | 'Real GDP will change by...' |
Both multipliers can equal 5 and still describe unrelated things
Set the required reserve ratio at 0.20 and the marginal propensity to consume at 0.80. The money multiplier is 1 divided by 0.20, which is 5. The spending multiplier is also 1 divided by 0.20, since MPS is 0.20, so it is 5 as well. Now apply each to a 50 billion dollar injection. A 50 billion dollar open market purchase can expand the money supply by as much as 250 billion dollars. A 50 billion dollar increase in government purchases raises real GDP by 250 billion dollars. Identical arithmetic, identical number, completely different claims. The first is a stock of deposits and currency created as banks lend and borrowers redeposit. The second is output produced and income earned over a period, created as households re-spend what they receive. A student who reports 250 billion dollars of extra GDP from the bond purchase has run the right formula on the wrong variable.
They chain in one direction only, and the interest rate is the hinge
A bond purchase does eventually change GDP, but not through the money multiplier alone. The route runs through the money market. Continue the numbers above. A 50 billion dollar open market purchase with a reserve ratio of 0.20 raises the money supply by up to 250 billion dollars. That shift moves the money market to a lower nominal rate, say from 6 percent down to 4 percent. Read the investment demand curve at 4 percent instead of 6 percent and suppose planned investment rises by 30 billion dollars. Only now does the spending multiplier apply, and it applies only to that 30 billion dollars. With MPC at 0.80 the multiplier is 5, so real GDP rises by 150 billion dollars. Notice that the final answer, 150 billion dollars, matches neither the 50 billion dollars injected nor the 250 billion dollars of new money. Skipping the interest rate step is the single most common way this calculation goes wrong.
The word maximum in a money multiplier question is doing real work
The money multiplier gives a ceiling, not a forecast. Every step of the deposit expansion assumes banks lend out all excess reserves immediately and that borrowers redeposit everything rather than holding currency. Break either assumption and the actual expansion falls short. If banks in the example above hold an extra 5 percent of deposits voluntarily, the effective reserve ratio becomes 0.25, the multiplier drops from 5 to 4, and the same 50 billion dollar purchase creates 200 billion dollars of money rather than 250 billion dollars. The spending multiplier leaks too, but its leaks get written into the formula instead of being left as caveats. Let 10 cents of each new dollar leave the country for imports while MPC stays at 0.80, and the leak per round climbs from 0.20 to 0.30, dragging the multiplier from 5 down to about 3.3. The asymmetry is worth remembering. A money multiplier answer that ignores excess reserves is still the answer the exam wants when the prompt says maximum, while a spending multiplier answer has to use whichever leaks the prompt actually handed you.
Frequently asked questions
Can the money multiplier and the spending multiplier both apply to the same policy?
Both multipliers can appear in one chain, but never applied to the same dollars. An open market purchase is multiplied by the money multiplier to get the change in the money supply. That larger money supply lowers the nominal interest rate, which raises planned investment by an amount read off the investment demand curve. Only that change in investment is multiplied by the spending multiplier to get the change in real GDP. Multiplying the original bond purchase by both figures double counts and produces a number with no meaning.
Why does one formula use the reserve ratio and the other use MPS?
Each denominator measures the share that leaks out at every round. In the banking system, the leak is the fraction of each new deposit a bank must hold as reserves rather than lend, so the reserve ratio sits in the denominator. In the expenditure model, the leak is the fraction of each new dollar of income that households save rather than spend, so MPS sits there instead. Same geometric series, different leak. Recognizing that both formulas are 1 divided by the leakage rate makes them easier to keep straight than memorizing them separately.
Which multiplier applies to a tax cut?
A tax cut uses the spending multiplier family, not the money multiplier, but with an adjustment. Households save part of any tax cut, so only the consumed portion enters the spending stream. The tax multiplier is MPC divided by (1 minus MPC), which with an MPC of 0.80 gives 4 rather than 5. A 50 billion dollar tax cut therefore raises real GDP by 200 billion dollars, against 250 billion dollars from 50 billion dollars of direct government purchases. The money multiplier never enters, because no new bank reserves were created.
Live Money Market graph. Drag the curves, or open the full version.
Live Fiscal Policy graph. Drag the curves, or open the full version.
Related comparisons
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