No Such Thing as a Free Lunch: Principles of Economics (Part 110)

It should be possible to emphasize to students that the level of employment is a macroeconomic issue, depending in the short run on aggregate demand and depending in the long run on the natural rate of unemployment, with microeconomic policies like tariffs having little net effect. Trade policy should be debated in terms of its impact on efficiency, not in terms of phoney numbers about jobs created or lost.

— Paul Krugman

Aggregate Expenditure and Equilibrium Output

(Part D)

by

Charles Lamson

Equilibrium Aggregate Output (Income)

Thus far, we have described the behavior of firms and households. We now discuss the nature of equilibrium and explain how the economy achieves equilibrium.

A number of definitions of equilibrium are used in economics. They all refer to the idea that at equilibrium, there is no tendency for change. In microeconomics, equilibrium is said to exist in a particular market (e.g., the market for bananas) at the price for which the quantity demanded is equal to the quantity supplied. At this point, both suppliers and demanders are satisfied. The equilibrium price of a good is the price at which suppliers want to furnish the amount that demanders want to buy.

In macroeconomics, we define equilibrium in the goods market as that point at which planned aggregate expenditure is equal to aggregate output.

aggregate output ≡ Y

planned aggregate expenditure ≡ AE ≡ C + I

equilibrium: Y = AE, or Y = C + I

Recall that the triple equal sign means that this is an identity, or something that is always true. Then, note that the equilibrium condition is not an identity.

This definition of equilibrium can hold if, and only if, planned investment and actual investment are equal. (Remember, we are assuming there is no unplanned consumption.) To understand why, consider Y not equal to AE. First, suppose aggregate output is greater than planned aggregate expenditure:

Y > C + I

aggregate output > planned aggregate expenditure

When output is greater than planned spending, there is unplanned inventory investment. Firms planned to sell more of their goods than they sold, and the difference shows up as an unplanned increase in inventories.

Next, suppose planned aggregate expenditure is greater than aggregate output:

C + I > Y

planned aggregate expenditure > aggregate output

When planned spending exceeds output, firms have sold more than they plan to. Inventory investment is smaller than planned. Planned and actual investment are not equal. Only when output is exactly matched by planned spending will there be no unplanned inventory investment. If there is unplanned inventory investment, this will be a state of disequilibrium. The mechanism by which the economy returns to equilibrium will be discussed later.

Equilibrium in the goods market is achieved only when aggregate output (Y) and planned aggregate expenditure (C + I) are equal, or when actual (investment actually undertaken) and planned investment (the sum of everything a firm intends to invest) are equal.

Table 1 derives a planned aggregate expenditure schedule and shows the point of equilibrium for our numerical example. (Remember, from part 108, all our calculations are based on C = 100 + .75Y.) To determine planned aggregate expenditure, we add consumption spending (C) to planned investment spending (I) at every level of income. Glancing down columns 1 and 4, we see one, and only one, level at which aggregate output and planned aggregate expenditure are equal: Y = 500.

Figure 8 illustrates the same equilibrium graphically. Figure 8(a) adds planned investment, constant at $25 billion, to consumption at every level of income. Because planned investment is a constant, the planned aggregate expenditure function is simply the consumption function displaced vertically by that constant amount. Figure 8(b) plots the planned aggregate expenditure function with the 45-degree line. The 45-degree line represents all points on the graph where the variables on the horizontal and vertical axis are equal. Any point on the 45-degree line is a potential equilibrium point. The planned aggregate expenditure function crosses the 45-degree line at a single point, where Y = $500 billion. (The point at which the two lines cross is sometimes called the Keynesian cross.) At that point, Y = C + I.

Now let us look at some other levels of aggregate output (income). First, consider Y = $800 billion, planned aggregate expenditure is $725 billion. (See Table 1.) This amount is less than aggregate output, which is eight hundred billion dollars. Because output is greater than planned spending, the difference ends up in inventory as unplanned inventory investment. In this case, unplanned inventory investment is $75 billion.

Next, consider Y = $200 billion. Is this an equilibrium output? No. At Y = $200 billion dollars, planned aggregate expenditure is $275 billion. Planned spending (AE) is greater than output (Y), and there is unplanned inventory disinvestment of (the withdrawal or reduction of an investment) $75 billion.

At Y = $200 billion and Y = $800 billion, planned investment and actual investment are unequal. There is unplanned investment, and the system is out of balance. Only at Y = $500 billion, where planned aggregate expenditure and aggregate output are equal, will planned investment equal actual investment.

Finally, let us find the equilibrium level of output (income) algebraically. Recall that we know the following:

By substituting (2) and (3) into (1), we get:

There is only one value of Y for which this statement is true, and we can find it by rearranging terms:

The equilibrium level of output is 500, as seen in Table 1 and Figure 8.

The Saving/Investment Approach to Equilibrium

Because aggregate income must either be saved or spent, by definition, Y ≡ C + S, which is an identity. The equilibrium condition is Y = C + I, but this is not an identity because it does not hold when we are out of equilibrium. By substituting C + S for Y in the equilibrium condition, we can write:

This saving/investment approach to equilibrium stands to reason intuitively if we recall two things: (1) output and income are equal, and (2) saving is income that is not spent. Because it is not spent, saving is like a leakage out of the spending stream. Only if that leakage is counterbalanced by some other component of planned spending can the resulting planned aggregate expenditure equal aggregate output. This other component is planned investment (I) .

This counterbalancing effect can be seen in Figure 9. Aggregate income flows into households, and consumption and saving flow out. The diagram shows saving flowing from households into the financial market. Firms use the saving to finance investment projects. If the planned investment of firms equals the saving of households, then planned aggregate expenditure (AE ≡ C + I) equals aggregate output (income) (Y), and there is equilibrium: The leakage out of the spending stream saving is matched by an equal injection of planned investment spending into the spending stream. For this reason, the saving investment approach to equilibrium is also called the leakage/injections approach to equilibrium.

Figure 10 reproduces the saving schedule derived in Figure 6 from part 108 and the horizontal investment function from Figure 7 in part 109. Notice that S = I at one, and only one, level of aggregate output, Y = 500. At Y = 500, C = 475 and I = 25. In other words, Y = C + I, and therefore equilibrium exists. 

Adjustment to Equilibrium

We have defined equilibrium and learned how to find it, but we have said nothing about how firms might react to disequilibrium. Let us consider the actions firms might take when planned aggregate expenditure exceeds aggregate output (income).

We already know the only way firms can sell more than they produce is by selling some inventory. This means that when planned aggregate expenditure exceeds aggregate output, unplanned inventory reductions have occurred. It seems reasonable to assume firms will respond to unplanned inventory reductions by increasing output. If firms increase output, income must also increase (output and income are two ways of measuring the same thing). As GM builds more cars, it hires more workers (or pays its existing workforce for working more hours), buys more steel, uses more electricity, and so on. These purchases by GM represent income for the producers of labor, steel, electricity, and so on. If GM (and all other firms) try to keep their inventories intact by increasing production, they will generate more income in the economy as a whole. This will lead to more consumption. Remember, when income rises, consumption also rises.

The adjustment process will continue as long as output (income) is below planned aggregate expenditure. If firms react to unplanned inventory reductions by increasing output, an economy with planned spending greater than output will adjust to equilibrium, with Y higher than before. If planned spending is less than output, there will be unplanned increases in inventories. In this case, firms will respond by reducing output. As output falls, income falls, consumption falls, and so forth, until equilibrium is restored, with Y lower than before.

As Figure 8 shows, at any level of output above Y = 500, such as Y = 800, output will fall until it reaches equilibrium at Y = 500, and at any level of output below Y = 500, such as Y = 200, output will rise until it reaches equilibrium at Y = 500. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 440-445*

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