13.2 The Aggregate Expenditures Model

The Aggregate Expenditures Model: A Simplified View

To develop a simple model, we assume that there are only two components of aggregate expenditures: consumption and investment. In the chapter on measuring total output and income, we learned that real gross domestic product and real gross domestic income are the same thing. With no government or foreign sector, gross domestic income in this economy and disposable personal income would be nearly the same. To simplify further, we will assume that depreciation and undistributed corporate profits (retained earnings) are zero. Thus, for this example, we assume that disposable personal income and real GDP are identical.

Finally, we shall also assume that the only component of aggregate expenditures that may not be at the planned level is investment. Firms determine a level of investment they intend to make in each period. The level of investment firms intend to make in a period is called planned investment. Some investment is unplanned. Suppose, for example, that firms produce and expect to sell more goods during a period than they actually sell. The unsold goods will be added to the firms’ inventories, and they will thus be counted as part of investment. Unplanned investment is investment during a period that firms did not intend to make. It is also possible that firms may sell more than they had expected. In this case, inventories will fall below what firms expected, in which case, unplanned investment would be negative. Investment during a period equals the sum of planned investment (I_P) and unplanned investment (I_U).

We shall find that planned and unplanned investment play key roles in the aggregate expenditures model.

We can omit the subscript on disposable personal income because of the simplifications we have made in this section, and the symbol Y can be thought of as representing both disposable personal income and GDP. Because we assume that the price level in the aggregate expenditures model is constant, GDP equals real GDP. At every level of real GDP, consumption includes $300 billion in autonomous aggregate expenditures. It will also contain expenditures “induced” by the level of real GDP. At a level of real GDP of $2,000 billion, for example, consumption equals $1,900 billion: $300 billion in autonomous aggregate expenditures and $1,600 billion in consumption induced by the $2,000 billion level of real GDP.

Figure 13.6 “Autonomous and Induced Consumption” illustrates these two components of consumption. Autonomous consumption, C_a, which is always $300 billion, is shown in Panel (a); its equation is

Induced consumption C_i is shown in Panel (b); its equation is

The consumption function is given by the sum of Equation 13.7 and Equation 13.8; it is shown in Panel (c) of Figure 13.6 “Autonomous and Induced Consumption”. It is the same as the equation C = $300 billion + 0.8Y_d, since in this simple example, Y and Y_d are the same.

Plotting the Aggregate Expenditures Curve

In this simplified economy, investment is the only other component of aggregate expenditures. We shall assume that investment is autonomous and that firms plan to invest $1,100 billion per year.

The level of planned investment is unaffected by the level of real GDP.

Aggregate expenditures equal the sum of consumption C and planned investment I_P. The aggregate expenditures function is the relationship of aggregate expenditures to the value of real GDP. It can be represented with an equation, as a table, or as a curve.

We begin with the definition of aggregate expenditures AE when there is no government or foreign sector:

Substituting the information from above on consumption and planned investment yields (throughout this discussion all values are in billions of base-year dollars)

[latex]AE = \$ 300 + 0.8Y + \$ 1,100[/latex]

The Slope of the Aggregate Expenditures Curve

The slope of the aggregate expenditures curve, given by the change in aggregate expenditures divided by the change in real GDP between any two points, measures the additional expenditures induced by increases in real GDP. The slope for the aggregate expenditures curve in Figure 13.7 “Plotting the Aggregate Expenditures Curve” is shown for points B and C: it is 0.8.

In Figure 13.7 “Plotting the Aggregate Expenditures Curve”, the slope of the aggregate expenditures curve equals the marginal propensity to consume. This is because we have assumed that the only other expenditure, planned investment, is autonomous and that real GDP and disposable personal income are identical. Changes in real GDP thus affect only consumption in this simplified economy.

Equilibrium in the Aggregate Expenditures Model

Real GDP is a measure of the total output of firms. Aggregate expenditures equal total planned spending on that output. Equilibrium in the model occurs where aggregate expenditures in some period equal real GDP in that period. One way to think about equilibrium is to recognize that firms, except for some inventory that they plan to hold, produce goods and services with the intention of selling them. Aggregate expenditures consist of what people, firms, and government agencies plan to spend. If the economy is at its equilibrium real GDP, then firms are selling what they plan to sell (that is, there are no unplanned changes in inventories).

Figure 13.8 “Determining Equilibrium in the Aggregate Expenditures Model” illustrates the concept of equilibrium in the aggregate expenditures model. A 45-degree line connects all the points at which the values on the two axes, representing aggregate expenditures and real GDP, are equal. Equilibrium must occur at some point along this 45-degree line. The point at which the aggregate expenditures curve crosses the 45-degree line is the equilibrium real GDP, here achieved at a real GDP of $7,000 billion.

Equation 13.11 tells us that at a real GDP of $7,000 billion, the sum of consumption and planned investment is $7,000 billion—precisely the level of output firms produced. At that level of output, firms sell what they planned to sell and keep inventories that they planned to keep. A real GDP of $7,000 billion represents equilibrium in the sense that it generates an equal level of aggregate expenditures.

If firms were to produce a real GDP greater than $7,000 billion per year, aggregate expenditures would fall short of real GDP. At a level of real GDP of $9,000 billion per year, for example, aggregate expenditures equal $8,600 billion. Firms would be left with $400 billion worth of goods they intended to sell but did not. Their actual level of investment would be $400 billion greater than their planned level of investment. With those unsold goods on hand (that is, with an unplanned increase in inventories), firms would be likely to cut their output, moving the economy toward its equilibrium GDP of $7,000 billion. If firms were to produce $5,000 billion, aggregate expenditures would be $5,400 billion. Consumers and firms would demand more than was produced; firms would respond by reducing their inventories below the planned level (that is, there would be an unplanned decrease in inventories) and increasing their output in subsequent periods, again moving the economy toward its equilibrium real GDP of $7,000 billion. Figure 13.9 “Adjusting to Equilibrium Real GDP” shows possible levels of real GDP in the economy for the aggregate expenditures function illustrated in Figure 13.8 “Determining Equilibrium in the Aggregate Expenditures Model”. It shows the level of aggregate expenditures at various levels of real GDP and the direction in which real GDP will change whenever AE does not equal real GDP. At any level of real GDP other than the equilibrium level, there is unplanned investment.

Changes in Aggregate Expenditures: The Multiplier

In the aggregate expenditures model, equilibrium is found at the level of real GDP at which the aggregate expenditures curve crosses the 45-degree line. It follows that a shift in the curve will change equilibrium real GDP. Here we will examine the magnitude of such changes.

Figure 13.10 “A Change in Autonomous Aggregate Expenditures Changes Equilibrium Real GDP” begins with the aggregate expenditures curve shown in Figure 13.8 “Determining Equilibrium in the Aggregate Expenditures Model”. Now suppose that planned investment increases from the original value of $1,100 billion to a new value of $1,400 billion—an increase of $300 billion. This increase in planned investment shifts the aggregate expenditures curve upward by $300 billion, all other things unchanged. Notice, however, that the new aggregate expenditures curve intersects the 45-degree line at a real GDP of $8,500 billion. The $300 billion increase in planned investment has produced an increase in equilibrium real GDP of $1,500 billion.

How could an increase in aggregate expenditures of $300 billion produce an increase in equilibrium real GDP of $1,500 billion? The answer lies in the operation of the multiplier. Because firms have increased their demand for investment goods (that is, for capital) by $300 billion, the firms that produce those goods will have $300 billion in additional orders. They will produce $300 billion in additional real GDP and, given our simplifying assumption, $300 billion in additional disposable personal income. But in this economy, each $1 of additional real GDP induces $0.80 in additional consumption. The $300 billion increase in autonomous aggregate expenditures initially induces $240 billion (= 0.8 × $300 billion) in additional consumption.

The $240 billion in additional consumption boosts production, creating another $240 billion in real GDP. But that second round of increase in real GDP induces $192 billion (= 0.8 × $240) in additional consumption, creating still more production, still more income, and still more consumption. Eventually (after many additional rounds of increases in induced consumption), the $300 billion increase in aggregate expenditures will result in a $1,500 billion increase in equilibrium real GDP. Table 13.1 “The Multiplied Effect of an Increase in Autonomous Aggregate Expenditures” shows the multiplied effect of a $300 billion increase in autonomous aggregate expenditures, assuming each $1 of additional real GDP induces $0.80 in additional consumption.

The size of the additional rounds of expenditure is based on the slope of the aggregate expenditures function, which in this example is simply the marginal propensity to consume. Had the slope been flatter (if the marginal propensity to consume were smaller), the additional rounds of spending would have been smaller. A steeper slope would mean that the additional rounds of spending would have been larger.

This process could also work in reverse. That is, a decrease in planned investment would lead to a multiplied decrease in real GDP. A reduction in planned investment would reduce the incomes of some households. They would reduce their consumption by the MPC times the reduction in their income. That, in turn, would reduce incomes for households that would have received the spending by the first group of households. The process continues, thus multiplying the impact of the reduction in aggregate expenditures resulting from the reduction in planned investment.

Factor out the ΔY_eq term on the left:

[latex]\Delta Y_{eq} (1 - MPC) = \Delta A^-[/latex]

The Aggregate Expenditures Model in a More Realistic Economy

Four conclusions emerge from our application of the aggregate expenditures model to the simplified economy presented so far. These conclusions can be applied to a more realistic view of the economy.

1. The aggregate expenditures function relates aggregate expenditures to real GDP. The intercept of the aggregate expenditures curve shows the level of autonomous aggregate expenditures. The slope of the aggregate expenditures curve shows how much increases in real GDP induce additional aggregate expenditures.
2. Equilibrium real GDP occurs where aggregate expenditures equal real GDP.
3. A change in autonomous aggregate expenditures changes equilibrium real GDP by a multiple of the change in autonomous aggregate expenditures.
4. The size of the multiplier depends on the slope of the aggregate expenditures curve. The steeper the aggregate expenditures curve, the larger the multiplier; the flatter the aggregate expenditures curve, the smaller the multiplier.

These four points still hold as we add the two other components of aggregate expenditures—government purchases and net exports—and recognize that government not only spends but also collects taxes. We look first at the effect of adding taxes to the aggregate expenditures model and then at the effect of adding government purchases and net exports.

The Addition of Government Purchases and Net Exports

Suppose that government purchases and net exports are autonomous. If so, they enter the aggregate expenditures function in the same way that investment did. Compared to the simplified aggregate expenditures model, the aggregate expenditures curve shifts up by the amount of government purchases and net exports.^[1]

Figure 13.11 “The Aggregate Expenditures Function: Comparison of a Simplified Economy and a More Realistic Economy” shows the difference between the aggregate expenditures model of the simplified economy in Figure 13.8 “Determining Equilibrium in the Aggregate Expenditures Model” and a more realistic view of the economy. Panel (a) shows an AE curve for an economy with only consumption and investment expenditures. In Panel (b), the AE curve includes all four components of aggregate expenditures.

Figure 13.11 The Aggregate Expenditures Function: Comparison of a Simplified Economy and a More Realistic Economy

Panel (a) shows an aggregate expenditures curve for a simplified view of the economy; Panel (b) shows an aggregate expenditures curve for a more realistic model. The AE curve in Panel (b) has a higher intercept than the AE curve in Panel (a) because of the additional components of autonomous aggregate expenditures in a more realistic view of the economy. The slope of the AE curve in Panel (b) is flatter than the slope of the AE curve in Panel (a). In a simplified economy, the slope of the AE curve is the marginal propensity to consume (MPC). In a more realistic view of the economy, it is less than the MPC because of the difference between real GDP and disposable personal income.

There are two major differences between the aggregate expenditures curves shown in the two panels. Notice first that the intercept of the AE curve in Panel (b) is higher than that of the AE curve in Panel (a). The reason is that, in addition to the autonomous part of consumption and planned investment, there are two other components of aggregate expenditures—government purchases and net exports—that we have also assumed are autonomous. Thus, the intercept of the aggregate expenditures curve in Panel (b) is the sum of the four autonomous aggregate expenditures components: consumption (C_a), planned investment (I_P), government purchases (G), and net exports (X_n). In Panel (a), the intercept includes only the first two components.

Second, notice that the slope of the aggregate expenditures curve is flatter for the more realistic economy in Panel (b) than it is for the simplified economy in Panel (a). This can be seen by comparing the slope of the aggregate expenditures curve between points A and B in Panel (a) to the slope of the aggregate expenditures curve between points A′ and B′ in Panel (b). Between both sets of points, real GDP changes by the same amount, $1,000 billion. In Panel (a), consumption rises by $800 billion, whereas in Panel (b) consumption rises by only $600 billion. This difference occurs because, in the more realistic view of the economy, households have only a fraction of real GDP available as disposable personal income. Thus, for a given change in real GDP, consumption rises by a smaller amount.

Let us examine what happens to equilibrium real GDP in each case if there is a shift in autonomous aggregate expenditures, such as an increase in planned investment, as shown in Figure 13.12 “A Change in Autonomous Aggregate Expenditures: Comparison of a Simplified Economy and a More Realistic Economy”. In both panels, the initial level of equilibrium real GDP is the same, Y₁. Equilibrium real GDP occurs where the given aggregate expenditures curve intersects the 45-degree line. The aggregate expenditures curve shifts up by the same amount—ΔA is the same in both panels. The new level of equilibrium real GDP occurs where the new AE curve intersects the 45-degree line. In Panel (a), we see that the new level of equilibrium real GDP rises to Y₂, but in Panel (b) it rises only to Y₃. Since the same change in autonomous aggregate expenditures led to a greater increase in equilibrium real GDP in Panel (a) than in Panel (b), the multiplier for the more realistic model of the economy must be smaller. The multiplier is smaller, of course, because the slope of the aggregate expenditures curve is flatter.

Figure 13.12 A Change in Autonomous Aggregate Expenditures: Comparison of a Simplified Economy and a More Realistic Economy

In Panels (a) and (b), equilibrium real GDP is initially Y₁. Then autonomous aggregate expenditures rise by the same amount, ΔI_P. In Panel (a), the upward shift in the AE curve leads to a new level of equilibrium real GDP of Y₂; in Panel (b) equilibrium real GDP rises to Y₃. Because equilibrium real GDP rises by more in Panel (a) than in Panel (b), the multiplier in the simplified economy is greater than in the more realistic one.

Key Takeaways

• The aggregate expenditures model relates aggregate expenditures to real GDP. Equilibrium in the model occurs where aggregate expenditures equal real GDP and is found graphically at the intersection of the aggregate expenditures curve and the 45-degree line.
• Economists distinguish between autonomous and induced aggregate expenditures. The former do not vary with GDP; the latter do.
• Equilibrium in the aggregate expenditures model implies that unintended investment equals zero.
• A change in autonomous aggregate expenditures leads to a change in equilibrium real GDP, which is a multiple of the change in autonomous aggregate expenditures.
• The size of the multiplier depends on the slope of the aggregate expenditures curve. In general, the steeper the aggregate expenditures curve, the greater the multiplier. The flatter the aggregate expenditures curve, the smaller the multiplier.
• Income taxes tend to flatten the aggregate expenditures curve.

Try It!

Suppose you are given the following data for an economy. All data are in billions of dollars. Y is actual real GDP, and C, I_P, G, and X_n are the consumption, planned investment, government purchases, and net exports components of aggregate expenditures, respectively.

Y	C	Ip	G	Xn
$0	$800	$1,000	$1,400	−$200
2,500	2,300	1,000	1,400	−200
5,000	3,800	1,000	1,400	−200
7,500	5,300	1,000	1,400	−200
10,000	6,800	1,000	1,400	−200

1. Plot the corresponding aggregate expenditures curve and draw in the 45-degree line.
2. What is the intercept of the AE curve? What is its slope?
3. Determine the equilibrium level of real GDP.
4. Now suppose that net exports fall by $1,000 billion and that this is the only change in autonomous aggregate expenditures. Plot the new aggregate expenditures curve. What is the new equilibrium level of real GDP?
5. What is the value of the multiplier?

Case in Point: Fiscal Policy in the Kennedy Administration

401(K) 2012 – Tax – CC BY-SA 2.0.

It was the first time expansionary fiscal policy had ever been proposed. The economy had slipped into a recession in 1960. Presidential candidate John Kennedy received proposals from several economists that year for a tax cut aimed at stimulating the economy. As a candidate, he was unconvinced. But, as president he proposed the tax cut in 1962. His chief economic adviser, Walter Heller, defended the tax cut idea before Congress and introduced what was politically a novel concept: the multiplier.

In testimony to the Senate Subcommittee on Employment and Manpower, Mr. Heller predicted that a $10 billion cut in personal income taxes would boost consumption “by over $9 billion.”

To assess the ultimate impact of the tax cut, Mr. Heller applied the aggregate expenditures model. He rounded the increased consumption off to $9 billion and explained,

“This is far from the end of the matter. The higher production of consumer goods to meet this extra spending would mean extra employment, higher payrolls, higher profits, and higher farm and professional and service incomes. This added purchasing power would generate still further increases in spending and incomes. … The initial rise of $9 billion, plus this extra consumption spending and extra output of consumer goods, would add over $18 billion to our annual GDP.”

We can summarize this continuing process by saying that a “multiplier” of approximately 2 has been applied to the direct increment of consumption spending.

Mr. Heller also predicted that proposed cuts in corporate income tax rates would increase investment by about $6 billion. The total change in autonomous aggregate expenditures would thus be $15 billion: $9 billion in consumption and $6 billion in investment. He predicted that the total increase in equilibrium GDP would be $30 billion, the amount the Council of Economic Advisers had estimated would be necessary to reach full employment.

In the end, the tax cut was not passed until 1964, after President Kennedy’s assassination in 1963. While the Council of Economic Advisers concluded that the tax cut had worked as advertised, it came long after the economy had recovered and tended to push the economy into an inflationary gap. As we will see in later chapters, the tax cut helped push the economy into a period of rising inflation.

Source: Economic Report of the President 1964 (Washington, DC: U.S. Government Printing Office, 1964), 172–73.

Answers to Try It! Problems

1. The aggregate expenditures curve is plotted in the accompanying chart as AE₁.

2. The intercept of the AE₁ curve is $3,000. It is the amount of aggregate expenditures (C + I_P + G + X_n) when real GDP is zero. The slope of the AE₁ curve is 0.6. It can be found by determining the amount of aggregate expenditures for any two levels of real GDP and then by dividing the change in aggregate expenditures by the change in real GDP over the interval. For example, between real GDP of $2,500 and $5,000, aggregate expenditures go from $4,500 to $6,000. Thus,

   
   [latex]\frac{ \Delta AE_{1}}{ \Delta Y} = \frac{ \$ 6,000 - \$ 4,500}{ \$ 5,000 - \$ 2,500} = \frac{ \$ 1,500}{ \$ 2,500} = 0.6[/latex]

The equilibrium level of real GDP is $7,500. It can be found by determining the intersection of AE₁ and the 45-degree line. At Y = $7,500, AE₁ = $5,300 + 1,000 + 1,400 − 200 = $7,500.
A reduction of net exports of $1,000 shifts the aggregate expenditures curve down by $1,000 to AE₂. The equilibrium real GDP falls from $7,500 to $5,000. The new aggregate expenditures curve, AE₂, intersects the 45-degree line at real GDP of $5,000.
The multiplier is 2.5 [= (−$2,500)/(−$1,000)].