## Deriving the Government Spending Multiplier, G ^{M }:

From the equilibrium condition:

AD = AS = Y = Income = RGDP Y = C + I + G + NX (1)

Let Consumption, C, be dependent on disposable income as follows:

**C = C0 + MPCx(Y — T), (2)**

**Where:**

C0 = autonomous consumption (consumption that does not depend on income)

MPC = marginal propensity to consume

T = Taxes on personal income.

MPC is a positive number greater than 0 and less than 1, which captures the proportion (or percentage) of disposable income, (Y – T), that goes for consumption spending. The rest of income that is not consumed is saved.

Thus,

MPC + MPS = 1

Where MPS is the marginal propensity to save.

In the U.S.A, MPC has ranged from 0.7 to 0.9. Other countries, such as Italy or France, tend to have a much smaller MPC.

By plugging (2) into (1), we get:

Y = C0 + MPCx(Y — T) + I + G + NX

If we assume that T, I, G and NX do not depend on level of income, or RGDP, Y (thus are fixed terms), we can group them together with C0 under the same fixed term A, as shown below.

Y = C0 + MPCxY — MPCxT + I + G + NX = MPCxY + A

Y — MPCxY = A

(1 — MPC)xY = A

Dividing both sides by 1-MPC (or solving for Y) we get:

Y = {1÷(1—MPC)}xA

The term inside the brackets is the multiplier: **1÷(1—MPC)**

Notice that since MPC is less than 1, then 1÷(1—MPC) will be greater than 1. Also, the higher MPC, the higher the multiplier.

If G is the component of A that changes, then the government spending multiplier GM is given by the multiplier we derived above ^{(20) }:

1÷(1—MPC) = GM

## The Government Spending Multiplier and the Tax Multiplier

The following formula gives the impact on RGDP of a change in G.

Change in RGDP = 1÷(1—MPC) x (change in G)

**Implication **: Fiscal policy is more effective in countries with greater MPC (because these countries tend to have a greater G _{M }, all else equal).

**In a similar way, we can derive the Tax multiplier, T _{M }:**

Change in RGDP = —MPC÷(1—MPC) x (change in T)

**Let’s compare G _{M }with T _{M }:**

The magnitude (size) of G _{M }is greater than T _{M }.

**Implication 1**: An increase in G is more effective than the same size decrease in T. G_{M }has the opposite sign compared to T_{M }.**Implication 2**: Remember that the same directional result can be achieved if G is increased, or taxes are decreased and vice versa.**Final Implication**: If both G and T increase by same amount (thus the government is running a balanced budget), the net effect on RGDP is not zero, because of the different magnitude (size) of the G_{M }and T_{M }.^{(22)}

### Schools of Thought and Cracks in Today’s Consensus

The Keynesian view is that fiscal stimulus (expansionary fiscal policy) boosts real GDP and creates or saves jobs by increasing aggregate demand with a multiplier effect.

The mainstream view is that Keynesians over-estimate the multiplier effects of fiscal stimulus and that these effects are small, short-lived, and incapable of working fast enough to be useful.

Moreover, government stimulus “crowds out” private consumption expenditure and investment, and ultimately leads to a bigger government, lower potential GDP, a slower real GDP growth rate, and a greater burden of government debt on future generations. ^{(22)}

## Limitations of Fiscal Policy

In practice, fiscal policy is hampered by several factors:

**Law-Making Time Lag**: The law-making lag is the amount of time it takes Congress to pass the laws needed to change taxes or spending.**Estimating Potential GDP**: It is not easy to tell whether real GDP is below, above, or at potential GDP, so it is not easy tell if discretionary fiscal policy will move real GDP away from potential GDP instead of towards it. Too much fiscal stimulus can cause inflation, while too little can lead to recession.**Economic Forecasting**: Fiscal policy must target forecasts of where the economy will be in the future. Economic forecasting has improved enormously in recent years, but it remains inexact and subject to error.

### Long-Run Fiscal Policy Effects

Large budget deficits crowd out investment and slow the economic growth rate. Persistently large budget deficits that increase the debt can erode confidence in the value of money and increase inflation. These long-run effects of fiscal policy make it vital to keep government expenditures and budget deficits under control and to have a plan for restoring a balanced budget at full employment. ^{(22)}