# Spending and Tax Multipliers The spending (or expenditure) multiplier is a concept that measures the change in expenditure, which causes a more-than-proportionate change in gross domestic product (GDP). The tax multiplier affects expenditures but at a lower level than spending.

The spending multiplier is one of the key concepts of Keynesian economics. The spending multiplier is the factor by which gains in total output are greater than the change in spending that caused it. The spending multiplier is a formula for determining how much an increase in government spending will affect the economy. This concept is a way to describe how government intervention impacts the overall economy by its changes in spending. A fiscal injection magnifies the initial amount spent by the government in the economy due to the multiplier effect. Thus, for each dollar the government invests, the impact on the economy is multiplied. For instance, if the government invests $1 million on an infrastructure project, it can be seen as contributing more than$1 million to the economy. This creates a domino effect because additional workers must be hired for the project, who will receive incomes. In turn, their incomes are spent elsewhere, and that money spent becomes another person's income, and so on. The benefit of that project expenditure, then, is multiplied. The use of government spending adds to output because it contributes to the workers' disposable income, and the workers can either spend it or save it. The increase in disposable income raises consumption, which increases gross domestic product (GDP). According to the spending multiplier concept, the consumption, as a result of spending, will further increase future consumption and additionally increase GDP.

The numerical value of the multiplier is dependent on marginal propensity to consume (MPC) and marginal propensity to save (MPS). The basic equation for the spending multiplier is:
$\text{Spending Multiplier}=\frac {1}{1-\text{MPC}}$
MPC is the marginal propensity to consume. If a nation, on average, receives $20 and spends$16, the MPC would be 0.8. Then, following the equation, 1 is divided by $(1 - 0.8)$, or 1 is divided by 0.2. When 1 is divided by 0.2, the multiplier is 5. In this scenario, therefore, the economy benefited five times more than the monetary amount of the spending. The multiplier concept is helpful in many stimulus scenarios and is not limited to direct cash payments. A stimulus is the use of expansionary fiscal or monetary policy to help kickstart economic growth in a sluggish or depressed economy.

The multiplier effect implies that the government should invest money in the economy during an economic downturn. From the Keynesian viewpoint, when the economy is underperforming, government intervention is crucial to its recovery. Keynes argued that if the government curbs spending in an economic depression, which might be a natural choice when revenue is smaller, the economy could weaken further. The domino effect from the spending multiplier helps support the decision for a government to spend money, even during recessionary times. The multiplier concept influenced policy-making decisions in developed countries in the 20th century and continues to influence government policy today.

The tax multiplier is the effect on the economy from changes in tax policy. This multiplier is different than spending multipliers. Its effects are much smaller than spending multipliers. This is because when the government lowers taxes, it is not actually injecting new income into the economy as new spending would because consumers can choose to either spend or save. Conversely, the spending multiplier is a direct injection of spending. The tax multiplier is calculated as the negative MPC divided by the MPS, which can also be written as 1 minus the MPC.
$\text{Tax Multiplier}=\frac{-\text{MPC}}{(1-\text{MPC})}$
For example, if the government decides to increase expenditures and spend $10 million on a project, that money is injected in the economy. With an MPC of 0.8, the spending multiplier was shown to be 5. The total impact would be$50 million in the economy with a $10 million government spending project. If the total amount of tax dollars is reduced by$10 million, only the amount ($10 million) multiplied by the tax multiplier will be spent in the economy. Because a reduction in taxes leads to an increase in income, the relationship is negative. Thus, the tax multiplier is dependent on what amount a consumer will spend or save with the tax cut. In this example where $\text{MPC} = 0.8$, the tax multiplier is calculated as $-0.8/(1-0.8)$. Multiplying the value by the$10 million spent, the total injection from a tax cut of $10 million would be$40 million.
$-\10\text{,}000\times\left(\frac{-0.8}{1-0.8}\right)=-\10\text{,}000\times-4=\40\text{,}000$