What Is the Multiplier Effect? Formula and Example

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The multiplier effect is the process by which an initial change in spending produces a larger total change in national income or output. When a government, business or household spends money, that spending becomes someone else’s income. Part of that income is spent again, which creates more income, and the cycle repeats in shrinking rounds. The multiplier is the number that measures the result: the total change in income divided by the initial change in spending. A multiplier of 3 means each $1 of new spending eventually raises income by $3.

Key takeaways

• The multiplier effect describes how one round of spending sets off further rounds, so total income rises by more than the original amount.
• The basic spending multiplier is 1 / (1 − MPC), which equals 1 / MPS, where MPS is the marginal propensity to save.
• Saving, taxes and imports are “leakages” that shrink each round and lower the multiplier.
• The money multiplier (1 / RRR) describes bank deposit creation, a separate mechanism from the Keynesian spending multiplier, and should not be confused with the equity multiplier or the earnings multiple.
• Real-world multipliers depend on spare capacity, interest rates, monetary policy and tax expectations, and can be smaller than the formula suggests.

How the Multiplier Effect Works

Picture a city that pays a construction firm to repair a bridge. The firm uses the payment for wages, materials and equipment, so the government’s spending becomes income for the firm, its workers and its suppliers. That is the first round. The workers spend some of their pay on groceries, rent, car repairs and restaurant meals and save the rest. That spending is new income for the grocer, landlord, mechanic and restaurant, the second round, and their own spending starts a third round, and so on.

Each round is smaller than the one before because some money leaks out of the spending stream:

• Saving: income that households put aside rather than spend.
• Taxes: income that goes to the government instead of being spent on goods and services.
• Imports: spending on goods produced abroad, which becomes income in another country.

If the leakages are small, each round stays large and the total effect is big. If they are large, the rounds die out quickly and the multiplier stays close to 1.

The process also runs in reverse. A cut in spending lowers someone’s income, which leads them to cut their own spending, and the decline spreads through the economy in the same shrinking rounds. Economists sometimes call this a negative multiplier effect.

The Multiplier Formula

The Basic Definition

In its most general form, the multiplier is a ratio:

Multiplier = Change in income / Change in spending

At the level of a national economy, “income” is usually measured as real GDP. The “spending” in the denominator can be government purchases, business investment, exports or a change in consumer spending caused by something outside the model, such as a tax rebate.

The Simple Spending Multiplier: 1 / (1 − MPC)

The marginal propensity to consume is the share of each extra dollar of income that people spend. The marginal propensity to save is the share they save. In a simple economy with no taxes or trade, the two add up to 1:

MPC + MPS = 1

If the first round of new spending is ΔG, the rounds of income look like this:

ΔG + (MPC × ΔG) + (MPC² × ΔG) + (MPC³ × ΔG) + …

This is a geometric series. As long as MPC is between 0 and 1, it sums to:

Total change in income = ΔG × 1 / (1 − MPC)

So the spending multiplier, often called the expenditure multiplier or Keynesian multiplier, is:

k = 1 / (1 − MPC) = 1 / MPS

A few hypothetical values, not estimates of any real economy, show how sensitive the result is to MPC:

Adding Taxes and Imports

Real economies have income taxes and foreign trade. With a proportional income tax rate t, households spend only out of after-tax income, so each round is multiplied by MPC × (1 − t) rather than MPC alone:

k = 1 / [1 − MPC × (1 − t)]

Adding a marginal propensity to import (MPM), the share of extra income spent on foreign goods, gives an open-economy version:

k = 1 / [1 − MPC × (1 − t) + MPM]

Each extra term in the denominator makes the multiplier smaller. As a hypothetical example, with an MPC of 0.8 and no taxes, the multiplier is 5. Add a 25% tax rate and it falls to 1 / (1 − 0.8 × 0.75) = 1 / 0.4 = 2.5. Add an MPM of 0.1 and it falls again to 1 / 0.5 = 2.

Tax Multipliers and the Balanced Budget Multiplier

A tax cut works through the same rounds, but it starts one step later. When the government buys $1 of goods, the full dollar is spent in the first round. When it cuts taxes by $1, households save part of it first, so only MPC × $1 enters the spending stream. In the simple model the tax multiplier is:

Tax multiplier = −MPC / (1 − MPC)

The sign is negative because a tax increase lowers income. With an MPC of 0.8, the spending multiplier is 5 and the tax multiplier is −4.

That gap leads to the balanced budget multiplier. If the government raises spending and taxes by the same amount, the spending multiplier (5) and the tax multiplier (−4) net to 1, so income rises by exactly the amount of the spending increase. The result depends on the model’s assumptions, but it shows why economists distinguish spending-based from tax-based stimulus.

Example of the Multiplier Effect

Hypothetical example. A national government launches a $1 billion infrastructure program. Assume the economy has idle workers and equipment, prices stay stable, there are no taxes or imports, and households have an MPC of 0.75.

The contractors and workers who receive the first $1 billion spend 75% of it ($750 million) and save $250 million. The next recipients spend 75% again, and the rounds keep shrinking.

Using the formula, the multiplier is 1 / (1 − 0.75) = 4, so total income rises by $1 billion × 4 = $4 billion. Notice what happens to saving along the way: by the time the rounds die out, households have saved a total of $1 billion, exactly the amount of the original injection. In the simple model, income keeps rising until the new saving it generates equals the new spending that started the process.

Change one assumption and the answer changes. If a 20% income tax applies, each round is multiplied by 0.75 × 0.8 = 0.6, the multiplier drops to 1 / 0.4 = 2.5, and the same $1 billion raises income by $2.5 billion instead of $4 billion.

The term is also used loosely for a single business: a firm whose $100,000 equipment purchase later raises its income by $200,000 might call that a multiplier of 2. That is a return on investment, not a macroeconomic multiplier, because it does not trace spending through the rest of the economy.

Where the Idea Comes From

British economist Richard Kahn set out the mathematics of the employment multiplier in a 1931 paper, showing how public works spending could create jobs beyond those directly hired. John Maynard Keynes made the idea central to his 1936 book The General Theory of Employment, Interest and Money, using the marginal propensities to consume and save to link a change in investment to the eventual change in income. The multiplier became a core argument for countercyclical fiscal policy: when private spending falls and resources sit idle, government spending can fill the gap with an effect on output larger than the dollars spent. The same logic explains why a collapse in investment can produce a much larger drop in income.

How the Multiplier Is Used

Fiscal policy. The fiscal multiplier is the change in GDP divided by the change in government spending or taxes that caused it. Legislators and budget offices use multiplier estimates to judge how much a stimulus package or a spending cut might change output and employment. Estimates differ by type of spending, by country and by the state of the economy, so forecasts of the same policy can disagree.

Investment analysis. The investment multiplier applies the same logic to new public or private investment, such as a factory or a highway, to capture effects beyond the investment’s immediate output.

Regional and local impact studies. When a city studies the effect of a new stadium or a plant closure, analysts often break the multiplier into three layers:

1. Direct impact: the spending or jobs at the project itself, such as construction contracts or the plant’s own payroll.
2. Indirect impact: extra activity at suppliers, such as the concrete supplier, the trucking firm and the parts manufacturer.
3. Induced impact: extra household spending by everyone whose income rose in the first two layers, at shops, restaurants and service businesses.

Geographers use the same breakdown when a new industry attracts related businesses and population to a region. Because a small area imports much of what it consumes, regional multipliers are usually smaller than national ones.

The Money Multiplier

The money multiplier describes a different process: how banks can expand the money supply in a fractional reserve system. It deals with deposits and lending, not with rounds of spending on goods and services.

The Money Multiplier Formula

Under a reserve requirement, a bank must hold a fraction of its deposits as reserves and may lend out the rest. When a loan is spent and the recipient deposits the money at another bank, that bank can lend out its own non-reserved share, and the process repeats. The simple money multiplier is:

Money multiplier = 1 / Reserve requirement ratio (RRR)

Hypothetical example. Assume a 10% reserve requirement, that banks lend every dollar beyond required reserves, and that every borrower redeposits the full loan in the banking system.

• A customer deposits $1,000. The bank holds $100 in reserves and lends $900.
• The $900 is deposited at a second bank, which holds $90 and lends $810.
• The $810 is deposited at a third bank, which holds $81 and lends $729.

The deposits form a geometric series that sums to $1,000 × (1 / 0.10) = $10,000: the original $1,000, which the depositor still owns, plus $9,000 of new money created through loans made against it.

A lower reserve requirement raises the multiplier, and a higher one lowers it. At a 25% requirement the multiplier is 4; at 10% it is 10.

Deposit Multiplier vs. Money Multiplier

The two terms are often treated as synonyms, but they differ. The deposit multiplier (1 / RRR) is the maximum amount of deposit creation possible if banks lend out everything beyond required reserves and every dollar lent is redeposited. The money multiplier, in its broader sense, is the actual ratio between the money supply and the monetary base.

The actual figure is lower than the maximum because of leakages similar to those in the spending multiplier:

• People hold some money as cash instead of depositing it (a “currency drain”).
• Banks may hold excess reserves above the requirement.
• Banks may not find enough creditworthy borrowers, or may choose to lend less.

The Money Multiplier in Practice

The textbook model treats reserves as the constraint on lending. In practice, banks generally make loans based on demand and their capital position, and the central bank supplies reserves as needed to keep its interest rate target. That makes the simple 1 / RRR formula a teaching device rather than a reliable forecast of money supply growth.

The United States illustrates the point. Before 2020, the Federal Reserve required institutions with more than $127.5 million in certain deposits to hold reserves of 10% against them. On March 26, 2020, the Fed reduced reserve requirement ratios to 0%. With a zero requirement, the formula 1 / RRR has no finite value, yet the money supply did not become infinite, because the reserve requirement was no longer the binding limit on bank lending.

Limitations of the Multiplier Effect

The simple formula rests on assumptions that often do not hold. With MPC between 0 and 1, the simple model’s multiplier is always at least 1, but each of the following can make the real multiplier smaller, and some can push it below 1, so that each dollar of government spending raises GDP by less than a dollar.

Full employment and inflation. The multiplier assumes there are idle workers and machines to put back to work. Near capacity, extra spending mainly bids up prices: the nominal increase in income may look large, but rising prices reduce the purchasing power of each round, so the real increase is small.

Crowding out. When the government borrows to spend, it may push up interest rates, which can discourage private investment and interest-sensitive purchases such as homes and cars. The private spending that is displaced offsets part of the public spending.

Monetary offset. If a central bank raises interest rates to counter the inflationary effect of fiscal stimulus, it can cancel part of the multiplier. When interest rates are near zero and the central bank is not raising them, this offset is weaker, which is why economists often argue multipliers are larger in deep recessions.

Expectations about future taxes. Under the idea known as Ricardian equivalence, households that expect higher future taxes to repay government debt may save a tax cut or stimulus payment instead of spending it. The more people behave this way, the lower the effective MPC and the smaller the multiplier.

Time lags. The rounds of spending do not happen instantly. Approving, contracting and building a project can take years, and by then the economic conditions that justified it may have changed.

MPC is not fixed. Different groups spend different shares of extra income, and the same household may behave differently in a boom than in a recession, so the multiplier is an estimate with a wide range, not a constant.

The quality of spending. The multiplier counts how much spending flows through the economy, not whether the spending is useful. A project that raises GDP in the short run might still be a poor use of resources compared with the alternatives, which is the logic of opportunity cost.

Multiplier Effect vs. Related Concepts

Several terms sound similar but measure different relationships.

• Keynesian (spending) multiplier vs. money multiplier: the first traces rounds of spending on goods and services through income; the second traces rounds of deposits and loans through the banking system.
• Multiplier vs. accelerator: the multiplier says a change in investment changes income by a larger amount; the accelerator says a change in income or output growth leads firms to change investment. Combined, they form the multiplier-accelerator model, which explains how the two can reinforce each other and produce business cycles.
• Multiplier vs. velocity of money: velocity is GDP divided by the money supply, how many times a unit of money is used over a period. It describes how actively money circulates, not the effect of a specific change in spending.
• Equity multiplier: total assets divided by total shareholders’ equity, a corporate measure of financial leverage, not economic growth.
• Earnings multiplier (earnings multiple): share price divided by earnings per share, better known as the price-to-earnings ratio.

FAQs

The Bottom Line

The multiplier matters most to anyone judging stimulus plans, spending cuts or local projects such as stadiums and plant closures. The formula shows why one dollar of spending can raise income by several dollars, but real results depend on spare capacity, interest rates, central bank responses and how households expect taxes to change. Treat any multiplier as an estimate with a wide range, and expect smaller effects near full employment and in small regional economies.