No Such Thing as a Free Lunch: Principles of Economics (Part 115)

The fact that we are here today to debate raising America's debt limit is a sign of leadership failure... It is a sign that we now depend on ongoing financial assistance from foreign countries to finance our Government's reckless fiscal policies.

Barack Obama

The Government and Fiscal Policy

(Part D)

by

Charles Lamson

The Tax Multiplier

Remember that fiscal policy comprises policies concerning government spending and policies concerning taxation. To see what effect a change in tax policy has on the economy, imagine the following. Just like in the last post, you are still chief economic advisor to the president, but now you are instructed to devise a plan to reduce unemployment to an acceptable level without increasing the level of government spending. In your plan, instead of increasing government spending (G), you decide to cut taxes and maintain the current level of spending. A tax cut increases disposable income, which is likely to lead to added consumption spending. (Remember our general rule that increased income leads to increased consumption.) Would the decrease in taxes affect aggregate output (income) the same as an increase in G?

A decrease in taxes would increase income. The government spends no less than it did before the tax cut, and households find they have a larger after-tax, or disposable, income than they had before. This leads to an increase in consumption. Planned aggregate expenditure will increase, which will lead to inventories being lower than planned, which will lead to a rise in output. When output rises, more workers will be employed and more income will be generated, causing a second-round increase in consumption, and so on. Thus, income will increase by a multitude of the decrease in taxes, but there is a "wrinkle."

Why does the tax multiplier---the ratio of change in the equilibrium level of output to a change in taxes---differ from the spending multiplier? To answer this, we need to compare the ways in which a tax cut and a spending increase work their way through the economy.

Look at Figure 1. When the government increases spending, there is an immediate and direct impact on the economy's total spending. Because G is a component of planned aggregate expenditure, an increase in G leads to a dollar-for-dollar increase in planned aggregate expenditure. When taxes are cut, there is no direct impact on spending. Taxes enter the picture only because they have an effect on the household's disposable income, which influences our household consumption (which is part of total spending). As Figure 1 shows, the tax cut flows through households before affecting aggregate expenditure.

Let us assume the government decides to cut taxes buy $1. By how much would spending increase? We already know the answer. The marginal propensity to consume (MPC) tells us how much consumption spending changes when disposable income changes. In the example running through the last several posts, the marginal propensity to consume out of disposable income is .75. This means that if households after-tax incomes rise by $1, they will increase consumption not by the full $1, but by only $0.75.

In summary, When government spending increases by $1, planned aggregate expenditure increases initially by the full amount of the rise in G, or $1. When taxes are cut, however, the initial increase in planned aggregate expenditure is only the MPC times the change in taxes. Because the initial increase in planned aggregate expenditure is smaller for a tax cut than for our government spending increase, the final effect on the equilibrium level of income will be smaller.

We figure the size of the tax multiplier in the same way we derived the multiplier for an increase in investment and an increase in government purchases. The final change in the equilibrium level of output (income) (Y) is:

△Y = (initial increase in aggregate expenditure) x (1/MPS)

Because the initial change in aggregate expenditure caused by a tax change of △T is (-△T * MPC), we can solve for the tax multiplier by substitution:

△Y = (△T * MPC) * (1/MPS) = -△T x (MPC/MPS)

Because a tax cut will cause an increase in consumption expenditures and output and a tax increase will cause a reduction in consumption expenditures and output, the tax multiplier is a negative multiplier:

tax multiplier ≡ -(MPC/MPS)

Again, note that the triple equal sign means this is an identity, or something that is always true.

We derive the tax multiplier algebraically not in the next post, which will cover the balanced-budget multiplier, but in the post after that.

If the MPC is .75, as in our example, the multiplier is .75/.25 = -3. A tax cut of 100 will increase the equilibrium level of output by -100 x -3 = 300. This is very different than the effect of our government spending multiplier of 4. Under these same conditions, a 100 increase in G will increase the equilibrium level of output by 400 or (100 x 4).

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 461-462*

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