Economic growth leads to higher income for everyone – at least in theory. This isn’t a surprising fact. What may be surprising, though, is that adding $500 to the economy can actually increase economic growth by more than $500. This is possible because of a phenomenon known in economics as the multiplier effect; let’s take a look at what the multiplier effect is and how it works.

Put simply, the multiplier effect is the macroeconomic phenomenon that causes the economy to grow (or shrink) by more than the amount of money that has been introduced into or taken away from it. This is possible because of a chain reaction caused by the fact that money can be used many times.

The effect in action

Let’s begin with an economic growth example, where the effect has a positive impact on the economy. Suppose that someone experiences an exogenous increase in wealth of $500, meaning that this $500 magically appears in the economy and is granted to one randomly-chosen person – let’s call him Frank. When Frank receives this magically generated $500, the total amount of money in the economy grows by $500 immediately. Thus, GDP (defined by the income method) has also grown by $500.

But Frank hasn’t even done anything with the money yet! Let’s say he chooses to save $200 of it, and he spends the other $300 on a pair of limited-edition Air Jordan shoes from Nike. Now, although the amount of money in the economy hasn’t changed, the economy itself has actually grown by $800 (in total)! That’s because the $300 that Frank spent on Nike shoes just became new income for the owner of the Nike store.

Now, suppose that the owner of the Nike store chooses to save $200 of Frank’s extra spending, and chooses to use the remaining $100 to have the store cleaned by Silva’s cleaning service. The $100 becomes income for Mr. Silva, the owner of the cleaning service. Now, the economy has grown by a total of 500 + 300 + 100 = $900, all from Frank’s magical $500. This process will continue, increasing GDP by much more than the original $500 that Frank acquired.

Readers may wonder how this makes sense. Hasn’t the money just moved around, and Frank has become poorer? After all, once Frank spends $300, he only has $200 left.

This question seems logical but is missing a key fact. Frank isn't poorer. Rather, he's just traded $300 in cash for $300 worth of goods (the Air Jordans), which theoretically increased his utility by at least $300 (since we assume he’s behaving rationally to maximize utility). Then, his $300 became income for another person, and the cycle continued. If the money changes hands faster, the economy grows faster; this is measured by the velocity of circulation.

Mathematically-minded readers might realize at this point that there is technically no end to this ripple effect – just like an infinite series in math, the money will perpetually continue to circulate through and stimulate the economy. Of course, in economic terms, eventually the amount of money received is so negligible (fractions of cents) that we can ignore it.

While most economics courses won’t test your calculus knowledge by asking you to solve a limit problem, it’s important to understand this concept as it filters through many layers of macroeconomic policy. Government spending, fractional reserve banking requirements, changes in national income, changes in consumer sentiment, and more can have massive ripple effects on the economy thanks to the multiplier effect.

Multiplier Math

From our example with Frank above, it’s clear that there are two factors controlling the size of the multiplier effect: the speed in which the money changes hands, and the amount of money that is saved by each person in this chain reaction. The former effect is determined by the velocity of circulation, and the latter by the marginal propensity to consume (MPC).

The formula for the multiplier m is:

m = 1 / (1 – MPC)

where MPC is the marginal propensity to consume. To recap, the MPC is a proportion that determines how much money individuals will spend when they receive an amount of money. A high MPC means that there’s a lot of spending, but little saving. A high MPC also means that the multiplier m is high as well.

The closer the MPC is to 1, the higher the multiplier m becomes. In other words, as people save less and less money, the multiplier effect causes the economy to grow more and more from an influx of new (exogenous) income. This is clear when considering our story with Frank earlier.

The formula above accounts for the MPC, but we also mentioned that the velocity of money plays an important role. Although it doesn’t appear formally in the above equation, the velocity of money is partly determined by the MPC, and is proportional to m itself; when the velocity is high, m is high and MPC is also high. For a formal treatment on the derivation of the multiplier effect that also covers its mathematical relationship with velocity, see the Further Reading section.

Implications for recessions and government spending

The multiplier effect may also be referred to as the fiscal multiplier or the Keynesian Multiplier. The reason for this is simple: the multiplier effect was proposed by John Maynard Keynes, and is implied by his theories.

In classical economics, individuals perfectly anticipate that an increase in government spending must be funded by taxes taken from them, and when they adjust their behavior to account for that, the economy is unaffected. For the rest of this section, we ignore the classical model and assume that the Keynesian model is correct.

Recessions are one of the unfortunate realities of economic life. When a recession hits, people tend to cut back on their consumption spending (especially on things like luxury goods) and attempt to save as they seek to weather the economic storm. Unfortunately, this behavior can make recessions worse – and the multiplier effect shows how.

Consider the case where Frank lost $500 instead of gaining it, perhaps because he had a $500 bill, but it was burned up on accident and ruined. This would reduce the money supply, and the future transactions with the Nike store and the cleaning company wouldn’t happen. In fact, because Frank is poorer now than he was before, Frank would cut back on his spending such that even fewer transactions happen in the economy than before he lost the money.

This gives us a template for how recessions can occur and linger in the economy. An exogenous negative shock to the economy causes a reduction in income. Then, people tend to cut back on their spending, and because of the multiplier effect, even more people cut back on even more spending. The result is that the economy shrinks by much more than the original amount that was lost.

Enter Keynesian economics. One of the tenets of Keynesian theory is that an increase in government spending (G in the aggregate demand formulation) can offset the downturn, and help the economy recover.

The initial spending increase by the government first improves the economy by itself. Then, those who receive this spending as income will in turn save some and spend some – according to their marginal propensity to consume – and the multiplier effect will get to work, bolstering the economy by more than the initial amount of government spending.

Good to Know

Throughout this article, we have assumed that everyone has the same marginal propensity to consume. But, in the real world, people’s MPC varies greatly depending on many factors, like personality and how well-off they are.

People with more money tend to have lower marginal propensities to consume. That’s partly because the proportion of money they need to spend on necessary items (like food and heating) is very low. Naturally, this also means that people with larger amounts of wealth tend to save more.

This fact is one potential argument in favor of focusing government stimulus efforts – like giving out cash during a pandemic, or tax cuts – to poorer people rather than richer people. The former group is not only much more likely to spend their money in the local economy, but they also have higher marginal propensities to consume, bolstering the multiplier effect compared to a very wealthy person who would save more of that money.

Further Reading

For a formal derivation of the multiplier effect, along with an examination of its relationship with the velocity of circulation through the quantity theory of money equation (MV = PY), be sure to read Wang, Xu, and Liu’s “Keynesian multiplier versus velocity of money”, published in Physics Procedia, Volume 3, Issue 5 in 2010: https://doi.org/10.1016/j.phpro.2010.07.009.