Third Fiscal Model and Equilibrium Level of Income/Output

The third fiscal model assumes that taxes are related to the income level of individuals and households. It assumes that government follows a proportional income tax system based on the income level of the people. Tax is considered as income induced variable. Symbolically, it can be expressed as

T= T0 + tY


T= Gross tax;

T0= Autonomous component of tax [tax at theoretical zero level of income];

Y= National output/income;

t= Marginal propensity to tax (MPT)

Marginal propensity to tax (MPT) is the change that occurs in tax revenue as a result of a unit of change in the income level. It is also defined as the income tax rate. Generally ‘t’ is expressed as (0 < t < 1) because generally, tax is never zero and individuals do not have to pay taxes more than their level of income.

The figure below shows the tax function which is positively related to income level. The increase in national output/income will automatically increase the tax revenue of the government.

When transfer payments are introduced, net tax function shifts downwards since transfer payments are deducted from taxes to determine the total government revenue used for the purchase of goods and services.

Figure: Gross and Net Tax Functions

The three fiscal model also considers all the fiscal policies to be autonomous, that is, it assumes that government purchases (G = G0), and transfer payments are autonomous (R=R0). Similarly, it assumes business investment expenditures are autonomous (I= I0) as well, so interest rates have no effect on the business investment demand.  

Equilibrium Level of Income/Output: Equations

The equilibrium level of income/output for the three fiscal policy can be determined after considering all the assumptions and basing it on aggregate expenditure and actual output/income. We have,


Substituting components of AE,

Y= C + I + G

Or, Y= Ca + λYD + Ia + Ga

Or, Y= Ca + λ (Y – Tn) + Ia + Ga

Or, Y= Ca + λ [Y – (T – R) + Ia + Ga]      {Net tax= gross tax – transfer payments)

Or, Y = Ca + λ [Y – (Ta + tY – Ra)] + Ia + Ga

Or, Y = Ca + λY – λTa - λtY + λRa + Ia + Ga

Or, Y – λY + λtY = Ca – λTa + λRa + Ia + Ga

Or, Y (1 – λ + λt) = Ca – λTa + λRa + Ia + Ga

Thus, the final equilibrium income is determined as

The equation shows that government transfer payments have a positive effect on the equilibrium income through its positive relation with marginal propensity to consume. Taxes imposed on income reduces disposable income of the households and negatively affects marginal propensity to consume.

When income tax is included in the equation without considering autonomous tax, the equilibrium level of income/output is