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

Δy is change in output (equivalent to GDP)

Δa_T is change in lump-sum tax rate

Δb_T is change in income tax rate

ΔG is change in government spending

ΔT is change in aggregate taxes

ΔI is change in investment

ΔX is change in exports

 Standard Lump-sum Tax Equation

 

Note: only Δa_T is here because if this is a change in lump-sum tax rate then Δb_T is implied to be 0.

 

 

Standard Income Tax Equation

 

Note: only Δb_T is here because if this is a change in income tax rate then Δa_T is implied to be 0.

 Standard Government Spending Equation

 

Standard Investment Equation

 

Standard Exports Equation

 

Balanced-Budget Government Spending Equation

Δy = ΔG * 1

Δy = ΔT * 1

Statistics

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.