Definitions

# Spending multiplier

In economics, the multiplier effect refers to the idea that an initial spending rise can lead to an even greater increase in national income. In other words, an initial change in aggregate demand can cause a further change in aggregate output for the economy.

The multiplier effect is a tool used by governments to restimulate aggregate demand. This can be done in a period of recession or economic uncertainty. The money invested by a government creates more jobs, which in turn will mean more spending and so on.

For example: a company spends \$1 million to build a factory. The money does not disappear, but rather becomes wages to builders, revenue to suppliers etc. The builders will have higher disposable income as a result, so consumption, hence aggregate demand will rise as well. Say that all of these workers combined spend \$2 million dollars in total, since there was an initial \$1 million input which created a \$2 million output, the multiplier is 2.

Another example is when a tourist visits somewhere they need to buy the plane ticket, catch a taxi from the airport to the hotel, book in at the hotel, eat at the restaurant and go to the movies or tourist destination. The taxi driver needs petrol (gasoline) for his cab, the hotel needs to hire the staff, the restaurant needs attendants and chefs, and the movies and tourist destinations need staff and cleaners.

It must be noted that the extent of the multiplier effect is dependent upon the marginal propensity to consume and marginal propensity to import. Also that the multiplier can work in reverse as well, so an initial fall in spending can trigger further falls in aggregate output.

The basic formula for the economic multiplier, in macroeconomics, is $Delta Y over Delta I$, or the change in equilibrium GDP divided by the change in investment (i.e. the initial increase in spending).

It is particularly associated with Keynesian economics; some other schools of economic thought reject, or downplay the importance of multiplier effects, particularly in the long run. The multiplier has been used as an argument for government spending or taxation relief to stimulate aggregate demand.

The concept of the economic multiplier on a macroeconomic scale can be extended to any economic region. For example, building a new factory may lead to new employment for locals, which may have knock-on economic effects for the city or region.

## Various Multipliers

Note: In the following examples the multiplier is the right-hand-side equation without the first component.

• y is original output (GDP)
• $b_C$ is marginal propensity of consumption (MPC)
• $b_T$ is original income tax rate
• $b_M$ is marginal propensity to import
• $Delta y$ is change in output (equivalent to GDP)
• $Delta a_T$ is change in lump-sum tax rate
• $Delta b_T$ is change in income tax rate
• $Delta G$ is change in government spending
• $Delta T$ is change in aggregate taxes
• $Delta I$ is change in investment
• $Delta X$ is change in exports

### Standard Lump-sum Tax Equation

$Delta y = Delta a_T * frac\left\{- b_C\right\}\left\{1 - b_C\left(1 - b_T\right) + b_M\right\}$

Note: only $Delta a_T$ is here because if this is a change in lump-sum tax rate then $Delta b_T$ is implied to be 0.

### Standard Income Tax Equation

$Delta y = Delta b_T * frac\left\{- b_C * y\right\}\left\{1 - b_C\left(1 - b_T\right) + b_M\right\}$

Note: only $Delta b_T$ is here because if this is a change in income tax rate then $Delta a_T$ is implied to be 0.

### Standard Government Spending Equation

$Delta y = Delta G * frac\left\{1\right\}\left\{1 - b_C\left(1 - b_T\right) + b_M\right\}$

### Standard Investment Equation

$Delta y = Delta I * frac\left\{1\right\}\left\{1 - b_C\left(1 - b_T\right) + b_M\right\}$

### Standard Exports Equation

$Delta y = Delta X * frac\left\{1\right\}\left\{1 - b_C\left(1 - b_T\right) + b_M\right\}$

### Balanced-Budget Government Spending Equation

$Delta y = Delta G * 1$

$Delta y = Delta T * 1$

## Statistics

### United States of America

Estimation has found "textbook" values of multipliers such as the value in the above example are overstated. The following tables has assumptions about monetary policy along the left hand side. Along the top is whether the multiplier value is for a change in government spending (ΔG) or a tax cut (-ΔT).
Monetary Policy Assumption ΔY/ΔG ΔY/(-ΔT)
Interest Rate Constant 1.93 1.19
Money Supply Constant 0.6 0.26
The above table is for the fourth quarter under which a permanent change in policy is in force.