No Such Thing as a Free Lunch: Principles of Economics (Part 116)

Europe unified its monetary policy through the euro before it unified politically, therefore sustaining member countries' abilities to pursue the kind of independent fiscal policies that can strain a joint currency.

Amity Shlaes

The Government and Fiscal Policy

(Part D)

by

Charles Lamson

The Balanced-Budget Multiplier

We have now discussed (1) changing government spending with no change in taxes, and (2) changing taxes with no change in government spending. What if government spending and taxes are increased by the same amount? That is, what if the government decides to pay for its extra spending by increasing taxes by the same amount? The government's budget deficit would not change, because the increase in expenditures would be matched by an increase in tax income.

You might think in this case that equal increases in government spending and taxes have no effect on equilibrium income. After all, the extra government spending equals the extra amount of tax revenues collected by the government. This is not so. Take, for example, a government spending increase of $40 billion. We know from the preceding parts of this analysis that an increase in GDP of 40, with taxes (T) held constant, should increase the equilibrium level of income by 40 x the government spending multiplier. The multiplier is 1/MPS or in the case of the example we have been using, 1/.25 = 4. The equilibrium level of income should rise by 160 or (40 x 4).

Now suppose that instead of keeping tax revenues constant, we financed the 40 increase in government spending with an equal increase in taxes, so as to maintain a balanced budget. What happens to aggregate spending as a result of both the rise in G and the rise in T? There are two initial effects. First, government spending rises by 40. This effect is direct, immediate, and positive. Now the government also collects 40 more in taxes. The tax increase has a negative impact on overall spending in the economy, but it does not fully offset the increase in government spending.

The final impact of a tax increase on aggregate expenditure depends on how households respond to it. The only thing we know about household behavior so far (from the example numbers we have been using) is that households spend 75 percent of their added income and save 25 percent. We know that when disposable income falls, both consumption and saving are reduced. A tax increase of 40 reduces disposable income by 40, and that means consumption falls by 40 * MPC. Because MPC = .75, consumption falls by 30 or (40 * .75). The net result in the beginning is that government spending rises by 40 and consumption spending falls by 30. Aggregate expenditure increases by 10 right after the simultaneous balanced budget increases in G and T.

So, a balanced-budget increase in G and T will raise output, but by how much? How large is this balanced budget multiplier? The answer may surprise you:

balanced budget multiplier ≡ 1

Let us combine what we know about the tax multiplier and the government spending multiplier to explain this. To find the final effect of a simultaneous increase in government spending and increase in net taxes, we need to add the multiplier effect of the two. The government spending multiplier is 1/MPS. The tax multiplier is -MPC/MPS. Their sum is (1/MPS) + (-MPC/MPS) ≡ (1 - MPC)/MPS. Because MPC + MPS ≡ 1, then 1 - MPC is MPS. This means (1 - MPC)/MPS ≡ MPS/MPS ≡ 1. (We derive the balanced-budget multiplier in the next post.)

Back to our example, recall that by using the government spending multiplier, a 40 increase in G would raise output at equilibrium by 160 (40 * the government spending multiplier of 4). By using the tax multiplier, we know that a 40 tax hike will reduce the equilibrium level of output by 120 (40 * the tax multiplier, -3). The net effect is 160 - 120, or 40. It should be clear, then, that the effect on equilibrium Y is equal to the balanced increase in G and T. In other words, the net increase in the equilibrium level of Y resulting from the change in G and the change in T is exactly the size of the initial change in G or T itself.

If the president wanted to raise Y by 200 without increasing the deficit, a simultaneous increase in G and T of 200 would do it. To see why look at the numbers in Table 3. In Table 1 (from part 113), we saw an equilibrium level of output at 900. With both G and T up by 200, the new equilibrium is 1,100---higher by 200. At no other level of Y do we find (C + I + G) = Y.

TABLE 3

An increase in government spending has a direct initial effect on planned aggregate expenditure; a tax increase does not. The initial effect of the tax increase is that households cut consumption by the MPC times the change in taxes. This change in consumption is less than the change in taxes, because the MPC is less than 1. The positive stimulus from the government spending increase is thus greater than the negative stimulus from the tax increase. The net effect is that the balanced budget multiplier is 1.

Table 4 summarizes everything we have said about fiscal policy multipliers. If anything is still unclear, review the relevant discussions in the last several posts.

A Warning Although we have added government, the story we have told about the multiplier is still incomplete and oversimplified. For example, we have been treating net taxes (T) as a lump sum, fixed amount, whereas in practice, taxes depend on income. The next post shows that the size of the multiplier is reduced when we make the more realistic assumption that taxes depend on income. We continue to add more realism and difficulty to our analysis in the posts that follow.

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 462-463*

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