A Surprising Example

Suppose the government keeps a balanced budget, increasing both spending and taxes by B (for Balanced Budget). Common sense probably suggests that this would leave everything else unchanged -- that the increase in taxes would just offset the increase in government purchases. But it doesn't work out that way.

Suppose, for example, that we start off with no government purchases nor taxation, and both taxation and spending are increased to 500. That is, B goes from zero to 500. As usual, our numerical example will use the consumption function

C = 500 +0.7*(Y - T)

and we will assume that I is 1000. With B = G = T = 0, we have autonomous spending of 1500 and a multiplier of 3.333, equilibrium income is

3.333*(1500)=5000,

as we have seen in earlier examples.

Now both government purchases, G, and taxes, T, increase to 500. To get the equilibrium income, we will have to use both the autonomous spending multiplier, 3.333, and the tax multiplier, 2.333 in this example. Autonomous spending is

500 + 1000 + 500 = 2000,

equilibrium income is computed as

Y = 3.333*2000 - 2.333*500 = 5500.

We see that after government purchases and taxes are introduced -- even though the budget is balanced -- equilibrium income is increased, and it is increased by exactly the amount of the balanced budget.

What has happened here? The increase in spending increases equilibrium income by

*B,

*B.

( - )* B

But it turns out that

( - )

is one -- so the difference, the net increase in equilibrium income, is exactly B.

Another way of putting this is to say that, in the simple Keynesian model, the balanced budget multiplier is one.

Mathematics versus Common Sense