# Tax Multiplier

Tax multiplier represents the multiple by which gross domestic product (GDP) increases (decreases) in response to a decrease (increase) in taxes. There are two versions of the tax multiplier: the simple tax multiplier and the complex tax multiplier, depending on whether the change in taxes affects only the consumption component of GDP or it affects all the components of GDP.

Let us assume that the government engages in expansionary fiscal policy by decreasing tax rates by 5% which is expected to reduce total tax volume by \$300 billion. This increases disposable income by \$300 billion. Assume further than the marginal propensity to consume is 0.8. Households will spend \$240 billion of the increase in disposal income (= 0.8 × \$300 billion). The first-round of increase in consumption of \$240 billion will trigger second round of increase in disposable income of the same amount, which in turn will trigger second-round of consumption increase of \$192 billion (= 0.8 × 0.8 × \$300 billion), and so on. The final outcome is that the GDP increases by a multiple of initial decrease in taxes. This multiple is the tax multiplier and the effect that it has is called multiplier effect. On the other hand, an increase in taxes decreases GDP by a multiple in the same fashion.

## Formula

In the simple version of tax multiplier, it is assumed that any increase or decrease in tax affects consumption only (and has no effect on investment, government expenditures etc.)

 TMS = MPC = MPC MPS 1 − MPC

Where,
TMS is the simple tax multiplier;
MPS stands for marginal propensity to save (MPS); and
MPC is marginal propensity to consume.

MPS equals 1 − MPC

Given the same value of marginal propensity to consume, simple tax multiplier will be lower than the spending multiplier. This is because in the first round of increase in government expenditures, consumption increases by 100%, while in case of a decrease in taxes of the same amount, consumption increase by a factor of MPC.

In case of complex tax multiplier it is assumed that any change in tax affects all components of the GDP.

 TMC = MPC 1 − (MPC × (1 − MPT) + MPI + MPG + MPM)

Where,
TMC is the complex tax multiplier;
MPC is marginal propensity to consume;
MPT is marginal propensity to tax;
MPI is marginal propensity to invest;
MPG is marginal propensity of government expenditures; and
MPM is marginal propensity to import.

## Example

Anshula Venkataraman is working as chief economist at the congressional budget office of Herzoslovakia. The country is falling behind on its growth target and the finance minister, Corentin Denis, is sure he has to convince the congress to provide the required stimulus to the economy. Corentin met with Anshula and told her that according to his estimates the GDP must grow by at least \$40 billion in order to achieve the target growth rate. The country is already running a budget deficit and Corentin has requested Anshula's opinion on whether to decrease taxes or increase government expenditures in order to achieve the target with least increase in budget deficit.

An assistant of Anshula has estimated that the country has a marginal propensity to save of 0.25. Draft a response to Corentin's request on behalf of Anshula.

### Solution

Increasing government expenditures and investment is more effective than decreasing taxes in increasing the GDP because it requires lower increase in budget deficit. The target increase in GDP of \$40 billion can be achieved by increasing government expenditures and investment by \$10 billion. \$13.3B of tax reduction would be needed if the country decides to achieve the target growth in GDP by decreasing taxes. This is because spending multiplier is higher than the tax multiplier. Relevant calculations are shown below.

Spending multiplier in Herzoslovakia = 1/MPS = 1/0.25 = 4

Tax multiplier in Herzoslovakia = MPC/(1 − MPC) = 0.75/0.25 = 3

Increase in government expenditures needed = target change in GDP/spending multiplier = \$40B/4 = \$10B

Decrease in taxes needed = target change in GDP/tax multiplier = \$40B/3 = \$13.3B