No Such Thing as a Free Lunch: Principles of Economics (Part 114)

Too often in recent history liberal governments have been wrecked on rocks of loose fiscal policy.

Franklin D. Roosevelt

The Government and Fiscal Policy

(Part C)

by

Charles Lamson

Fiscal Policy at Work: Multiplier Effects

You can see from Figure 2 (from last post and reintroduced below) that if the government were able to change the levels of either government purchases (G) or net taxes (T), it would be able to change the equilibrium level of output (income). At this point, we are assuming that the government controls G and T. In this section we will review three multipliers:

• Government spending multiplier

• Tax multiplier

• Balanced budget multiplier

The Government Spending Multiplier

Suppose you are the chief economic advisor to the president and the economy is sitting at the equilibrium output pictured in Figure 2. Output and income are being produced at a rate of $900 billion per year, and the government is currently buying $100 billion worth of goods and services each year and is financing them with $100 billion in taxes. The budget is balanced. In addition, the private sector is investing (producing capital goods) at a rate of $100 billion per year.

The president calls you into the Oval Office and says, "Unemployment is too high. We need to lower unemployment by increasing output and income." After some research, you determine that an acceptable unemployment rate could be achieved only if aggregate output increases to $1,100 billion.

You now need to determine how can the government use taxing and spending policy---fiscal policy---to increase the equilibrium level of national output? Suppose that the president has let it be known that taxes must remain at present levels---the Congress just passed a major tax reform package---so adjusting T is out of the question for several years. That leaves you with G. Your only option is to increase government spending while holding taxes constant.

To increase spending without raising taxes (which provides the government with revenue to spend), the government must borrow. When G is bigger than T, the government runs a deficit, and the difference between G and T must be borrowed. For the moment we will ignore the possible effect of the deficit and focus only on the effect of a higher G with T constant.

Meanwhile, the president is awaiting your answer. How much of an increase in spending would be required to generate a $200 billion increase in the equilibrium level of output, pushing it from $900 billion up to $1,100 billion and reducing unemployment to the president's acceptable level?

You might be tempted to say that because we need to increase income by 200 (1,100 - 900), we should increase government spending by the same amount---but what would happen? The increased government spending will throw the economy out of equilibrium. Because G is a component of aggregate spending, planned aggregate expenditure will increase by 200. Planned spending will be greater than output, inventories will be lower than planned, and firms will have an incentive to increase output. Suppose output rises by the desired 200. You might think, "We increased spending by 200 and output by 200, so equilibrium is restored."

There is more to the story than this. The moment output rises, the economy is generating more income. This was the desired effect: The creation of more employment. The newly employed workers are also consumers and some of their income gets spent. With higher consumption spending, planned spending will be greater than output, inventories will be lower than planned, and firms will raise output, and thus raise income, again. This time firms are responding to the new consumption spending. Already, total income is over 1,100.

This story should sound familiar. It is the multiplier in action. Although this time it is government spending (G) that is changed rather than planned investment (I), the effect is the same as the multiplier effect we described in part 111 of this analysis. An increase in government spending has the same impact on the equilibrium level of output and income as an increase in planned investment. A dollar of extra spending from either G or I is identical with respect to its impact on equilibrium output. The equation for the government spending multiplier is the same as the equation for the multiplier for a change in planned investment.

government spending multiplier ≡ 1/MPS

We derive the government spending multiplier algebraically in the next post.

Formally, the government spending multiplier is defined as the ratio of the change in the equilibrium level of output to a change in government spending. This is the same definition we used in the previous posts, but now the autonomous variable (assumed not to depend on the state of the economy) is government spending instead of planned investment.

Remember that we were thinking of increasing government spending (G) by 200. We can use the multiplier analysis to see what the new equilibrium level of Y would be for an increase in G of 200. The multiplier in our example is 4. [Because b---the marginal propensity to consume (MPC) is .75 (from our example originally introduced in part 108), the marginal propensity to save (MPS) must be 1 - .75 = .25, and 1/.25 = 4]. Thus, Y will increase by 800 (4 x 200). Because the initial level of Y was 900, the new equilibrium level of Y is 900 + 800 = 1700 when G is increased by 200.

The level of 1,700 is much larger than the level of 1,100 that we calculated as necessary to lower unemployment to the desired level. Let us back up, then. If we want Y to increase by 200 and if the multiplier is 4, we need G to increase by only 200/4 = 50. If G changes by 50, the equilibrium level of Y will change by 200, and the new value of Y will be 1100 (900 + 200), as desired.

Looking at Table 2 we can check our answer to be sure that it is an equilibrium. Look first at the old equilibrium of 900. When government purchases (G) were 100, aggregate output (income) was equal to planned aggregate expenditure (AE ≡ C + I + G) at Y = 900. Now G has increased to 150. At Y = 900, (C + I + G) is greater than Y, there is an unplanned fall in inventories, and output will rise, but by how much? The multiplier told us that equilibrium income would rise by four times the 50 change in G. Y should rise by 4 * 50 = 200, from 900 to 1100 before equilibrium is restored. Let us check. If Y = 1,100, then consumption is C = 100 + .75Y(1000) = 850. Because I = 100 and G now equals 100 (the original level of G) + 50 (the additional G brought about by the fiscal policy change) = 150, then C + I + G = 850 + 100 + 100 + 50 = 1,100. Y = AE, and the economy is in equilibrium.

TABLE 2 Finding Equilibrium After a $50 Billion Government Spending Increase (All

Figures in Billions of Dollars)

The graphic solution to the president's problem is presented in Figure 3. A 50 increase in G shifts the planned aggregate expenditure function up by 50. The new equilibrium income occurs where the new AE Line (AE) crosses the 45-degree line, at Y = 1,100. 

FIGURE 3 The Government Spending Multiplier

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 458-460*

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