1. The Aggregate Expenditures Model11
The Aggregate Expenditures Model
The chapter begins with the simple version of the AE model, that of a closed, private economy. Equilibrium GDP is determined and multiplier effects are briefly reviewed. The simplified “closed” economy is then “opened” to show how it would be affected by exports and imports. Government spending and taxes are brought into the model to include the “public” aspects of the system. The price level is assumed constant in this chapter unless stated otherwise, so the focus is on real GDP.
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Assumptions and Simplifications
Not at full-employment
Prices are fixed
GDP = DI
Begin with private, closed economy
No government
No trade
Keynes developed this model during the depression of the 1930s and the model can help explain how modern economies adjust to economic shocks. This is used today to provide insight regarding current economic conditions. Government is ignored, so the economy just consists of the private sector; households and businesses. Assume a “closed economy”, one with no international trade. Although both households and businesses save, we assume here that all saving is personal. With no government or foreign trade, GDP, national income (NI), personal income (PI), and disposable income (DI) are all the same.
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3. Assumptions and Simplifications
Private, Closed Economy
The two components of aggregate expenditures are consumption (C) and gross investment (Ig)
GDP, NI, PI, and DI are same
Keynes developed this model during the depression of the 1930s and the model can help explain how modern economies adjust to economic shocks. This is used today to provide insight regarding current economic conditions. Government is ignored, so the economy just consists of the private sector; households and businesses. Assume a “closed economy”, one with no international trade. Although both households and businesses save, we assume here that all saving is personal. With no government or foreign trade, GDP, national income (NI), personal income (PI), and disposable income (DI) are all the same.
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4. Income, Consumption, and Saving
Figure 27.1 shows the consumption and disposable income for the U.S. for 1987–2009. Each dot in this figure shows consumption and disposable income in a specific year. The line, C, which generalizes the relationship between consumption and disposable income, indicates a direct relationship and shows that households consume most of their after-tax incomes.
This figure represents graphically the recent historical relationship between disposable income (DI), consumption (C), and saving (S) in the United States.
A 45-degree line represents all points where consumer spending is equal to disposable income; other points represent actual C, DI relationships for each year.
If the actual graph of the relationship between consumption and income is below the 45-degree line, then the difference must represent the amount of income that is saved. Notice that consumption can exceed disposable income and personal saving can be negative.
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5. Investment Schedule (Ig)
Shows the amount that businesses plan to invest at different levels of GDP
Assume investment (Ig) is independent of GDP
Investment is constant at all GDP levels
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6. Consumption and Investment
Investment Demand Curve
Investment Schedule
Investment
demand
curve
Investment
schedule 20 Ig
r and i (percent)
Investment (billions of dollars) 8 20 20 ID
This figure reflects (a) the investment demand curve and (b) the investment schedule. (a) The level of investment spending (here, $20 billion) is determined by the real interest rate (here, 8 percent) together with the investment demand curve, ID. (b) The investment schedule, Ig, relates the amount of investment ($20 billion) determined in (a) to the various levels of GDP. 20
Investment
(billions of dollars)
(a)
Investment demand curve
Real domestic product, GDP
(billions of dollars)
(b)
Investment schedule
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7. GDP, output, income are the same
Leakages/Injections
Leakages – Income not used to buy domestically produced goods and services
Injections – Spending in addition to consumption expenditures on domestically produced goods and services
GDP, output, income are the same
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8. Aggregate Expenditures
The amount of goods and services produced and the level of employment depend directly on the level of aggregate expenditures
C + Ig
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9. Equilibrium GDP (C + Ig = GDP)
Table 28.2 shows equilibrium GDP using the expenditures-output approach for a private, closed economy. Table 28.2 combines consumption and savings data from Tables 27.1 and the investment schedule 28.1.
Real domestic output in column 2 shows ten possible levels that producers are willing to offer, assuming their sales would meet the output planned. In other words, they will produce $370 billion of output if they expect to receive $370 billion in revenue.
Ten levels of aggregate expenditures are shown in column 6. The column shows the amount of consumption and planned gross investment spending (C + Ig) at each output level. Recall that the consumption level is directly related to the level of income and that here income is equal to output. Investment is independent of income and is planned or intended regardless of the current income situation.
Equilibrium GDP is the level of output whose production will create total spending just sufficient to purchase that output. Otherwise there will be a disequilibrium situation. In Table 28.2, equilibrium occurs only at $470 billion. At $410 billion GDP level, total expenditures (C + Ig) would be $425 = $405(C) + $20 (Ig) and businesses will adjust to this excess demand (revealed by the declining inventories) by stepping up production. They will expand production at any level of GDP less than the $470 billion equilibrium. At levels of GDP above $470 billion, such as $510 billion, aggregate expenditures will be less than GDP. At $510 billion level, C + Ig = $500 billion. Businesses will have unsold, unplanned inventory investment and will cut back on the rate of production. As GDP declines, the number of jobs and total income will also decline, but eventually the GDP and aggregate spending will be in equilibrium at $470 billion. No level of GDP other than the equilibrium level of GDP can be sustained.
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10. Equilibrium GDP
TABLE 28.2 Determination of the Equilibrium Levels of Employment, Output, and Income: A Private Closed Economy
(1)
Possible Levels of Employment, Millions
(2)
Real Domestic Output (and Income) (GDP = DI),*Billions
(3)
Consumption (C),
Billions
(4)
Saving (S),
(5)
Investment (Ig),
(6)
Aggregate Expenditure (C+Ig),
(7)
Unplanned Changes in Inventories, (+ or -)
(8)
Tendency of Employment, Output, and Income
(1) 40
$370
$375
$-5
$20
$395
$-25
Increase
(2) 45
390 20
410
-20
(3) 50
405 5
425
-15
(4) 55
430
420 10
440
-10
(5) 60
450
435 15
455 -5
(6) 65
470
Equilibrium
(7) 70
490
465 25
485 +5
Decrease
(8) 75
510
480 30
500
+10
(9) 80
530
495 35
515
+15
(10) 85
550 40
+20
* If depreciation and net foreign factor income are zero, government is ignored and it is assumed that all saving occurs in the household sector of the economy, then GDP as a measure of domestic output is equal to NI,PI, and DI. Household income = GDP
Table 28.2 shows equilibrium GDP using the expenditures-output approach for a private, closed economy. Table 28.2 combines consumption and savings data from Tables 27.1 and the investment schedule 28.1.
Real domestic output in column 2 shows ten possible levels that producers are willing to offer, assuming their sales would meet the output planned. In other words, they will produce $370 billion of output if they expect to receive $370 billion in revenue.
Ten levels of aggregate expenditures are shown in column 6. The column shows the amount of consumption and planned gross investment spending (C + Ig) at each output level. Recall that the consumption level is directly related to the level of income and that here income is equal to output. Investment is independent of income and is planned or intended regardless of the current income situation.
Equilibrium GDP is the level of output whose production will create total spending just sufficient to purchase that output. Otherwise there will be a disequilibrium situation. In Table 28.2, equilibrium occurs only at $470 billion. At $410 billion GDP level, total expenditures (C + Ig) would be $425 = $405(C) + $20 (Ig) and businesses will adjust to this excess demand (revealed by the declining inventories) by stepping up production. They will expand production at any level of GDP less than the $470 billion equilibrium. At levels of GDP above $470 billion, such as $510 billion, aggregate expenditures will be less than GDP. At $510 billion level, C + Ig = $500 billion. Businesses will have unsold, unplanned inventory investment and will cut back on the rate of production. As GDP declines, the number of jobs and total income will also decline, but eventually the GDP and aggregate spending will be in equilibrium at $470 billion. No level of GDP other than the equilibrium level of GDP can be sustained.
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11. Equilibrium GDP (C + Ig = GDP) Equilibrium point Aggregate
530
510
490
470
450
430
410
390
370
45°
Real domestic product, GDP (billions of dollars)
Aggregate expenditures, C + Ig (billions of dollars)
C + Ig
(C + Ig = GDP) C
Equilibrium
point
Aggregate
expenditures
Ig = $20 billion
This figure graphically illustrates equilibrium GDP in a private closed economy. The aggregate expenditures schedule, C + Ig, is determined by adding the investment schedule, Ig, to the upsloping consumption schedule, C. Since investment is assumed to be the same at each level of GDP, the vertical distances between C and C + Ig do not change. Equilibrium GDP is determined where the aggregate expenditures schedule intersects the 45 degree line, in this case at $470 billion.
C = $450 billion
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12. Other Features of Equilibrium GDP
Saving equals planned investment
Saving is a leakage of spending
Investment is an injection of spending
No unplanned changes in inventories
Firms do not change production
Savings and planned investment are equal at equilibrium GDP. It is important to note that in our analysis above we spoke of “planned” investment. Saving represents a “leakage” from the spending stream and causes C to be less than GDP. Some of the output is planned for business investment and not consumption, so this investment spending can replace the leakage due to saving.
If aggregate spending is less than equilibrium GDP, then businesses will find themselves with unplanned inventory investment on top of what was already planned. This unplanned portion is reflected as a business expenditure, even though the business may not have desired it, because the total output has a value that belongs to someone—either as a planned purchase or as unplanned inventory.
If aggregate expenditures exceed GDP, then there will be less inventory investment than businesses planned as businesses sell more than they expected. This is reflected as a negative amount of unplanned investment in inventory.
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13. Planned vs. Actual Investment
Actual investment includes planned investment (Ig) and unplanned changes in inventories.
As a result, actual investment equals savings at all GDP levels.
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14. An initial change in spending can cause a greater change in real GDP
Multiplier Effect
An initial change in spending can cause a greater change in real GDP
Multiplier =
change in real GDP
initial change in spending
Changes in spending ripple through the economy to generate event larger changes in real GDP. This is called the multiplier effect.
Multiplier = change in real GDP / initial change in spending. Alternatively, it can be rearranged to read change in real GDP = initial change in spending x multiplier.
Points to remember about the multiplier:
The initial change in spending is usually associated with investment because it is so volatile, but changes in consumption (unrelated to income), net exports, and government purchases also are subject to the multiplier effect.
The initial change refers to an up-shift or down-shift in the aggregate expenditures schedule due to a change in one of its components, like investment.
The multiplier works in both directions (up or down).
It occurs because of the interconnectedness of the economy.
Change in GDP = multiplier x initial change in spending
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15. Multiplier & Marginal Propensities
Multiplier and MPC directly related
Multiplier and MPS inversely related
Multiplier = 1
1- MPC
Multiplier = 1
MPS
The significance of the multiplier is that a small change in investment plans or consumption-saving plans can trigger a much larger change in the equilibrium level of GDP. The magnitude of the change in GDP is dependent on the size of the MPC and MPS.
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16. Adding International Trade
Include net exports spending in aggregate expenditures
Private, open economy
Xn can be positive or negative
Net exports are independent of GDP => net exports are constant at all GDP levels
Net exports (exports minus imports) affect aggregate expenditures in an open economy. Exports (X) create domestic production, income, and employment due to foreign spending on U.S. produced goods and services. Imports (M) reduce the sum of consumption and investment expenditures by the amount expended on imported goods, so this figure must be subtracted so as not to overstate aggregate expenditures on U.S. produced goods and services. Positive net exports increase aggregate expenditures beyond what they would be in a closed economy and thus have an expansionary effect. Negative net exports decrease aggregate expenditures beyond what they would be in a closed economy and thus have a contractionary effect.
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17. Adding the Public Sector
Simplifying assumptions are helpful for clarity when we include the government sector in our analysis. We simplified investment and net export schedules that are used by assuming that they are independent of the level of current GDP. We assume government purchases do not impact private spending schedules. We assume that net tax revenues are derived entirely from personal taxes so that GDP, NI, and PI remain equal. DI is PI minus net personal taxes. We assume tax collections are a constant amount and independent of the GDP level (a lump-sum tax). An increase in taxes has an indirect effect on aggregate expenditures because taxes reduce disposable incomes first, and then C falls by the amount of the tax times the MPC. With the addition of government to aggregate expenditures, the economy is now a mixed, open economy.
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18. Assumptions and Simplifications
Government purchases do not impact private spending schedules (C+Ig+Xn)
Net tax revenues derived from personal taxes
GDP, NI, & PI remain equal
DI = PI – Net Personal Taxes
Fixed amount of taxes collected regardless of GDP (Lump sum tax)
Simplifying assumptions are helpful for clarity when we include the government sector in our analysis. We simplified investment and net export schedules that are used by assuming that they are independent of the level of current GDP. We assume government purchases do not impact private spending schedules. We assume that net tax revenues are derived entirely from personal taxes so that GDP, NI, and PI remain equal. DI is PI minus net personal taxes. We assume tax collections are a constant amount and independent of the GDP level (a lump-sum tax). An increase in taxes has an indirect effect on aggregate expenditures because taxes reduce disposable incomes first, and then C falls by the amount of the tax times the MPC. With the addition of government to aggregate expenditures, the economy is now a mixed, open economy.
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19. Adding the Public Sector
Addition of government purchases to aggregate expenditures (C+Ig+G+Xn) = mixed open economy
Higher level of aggregate expenditures
Simplifying assumptions are helpful for clarity when we include the government sector in our analysis. We simplified investment and net export schedules that are used by assuming that they are independent of the level of current GDP. We assume government purchases do not impact private spending schedules. We assume that net tax revenues are derived entirely from personal taxes so that GDP, NI, and PI remain equal. DI is PI minus net personal taxes. We assume tax collections are a constant amount and independent of the GDP level (a lump-sum tax). An increase in taxes has an indirect effect on aggregate expenditures because taxes reduce disposable incomes first, and then C falls by the amount of the tax times the MPC. With the addition of government to aggregate expenditures, the economy is now a mixed, open economy.
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20. Government Purchases and Eq. GDP
TABLE 28.4 The Impact of Government Purchases on Equilibrium GDP
(1)
Real Domestic Output and Income
(GDP=DI), Billions
(2)
Consumption (C),
Billions
(3)
Saving (S),
(4)
Investment (Ig),
(5)
Net Exports
(Xn), Billions
(6)
Government Purchases
(G), Billions
(7)
Aggregate Expenditures (C+Ig+Xn+G),
(2)+(4)+(5)+(6)
Exports
(X)
Imports
(M)
(1) $370
$375
$-5
$20
$10
$415
(2) 390
390 20 10
430
(3) 410
405 5
445
(4) 430
420
460
(5) 450
435 15
475
(6) 470
450
490
(7) 490
465 25
505
(8) 510
480 30
520
(9) 530
495 35
535
(10) 550
510 40
550
TABLE 28.4 shows the impact of government purchases on equilibrium GDP. Before adding government purchases, equilibrium GDP had been at $470. Now with government purchases equilibrium GDP rises to $550, implying a multiplier effect since the rise in GDP is greater than the $20 billion in additional aggregate expenditures.
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21. Government Purchases and Eq. GDP
45°
Real domestic product, GDP (billions of dollars)
Aggregate expenditures (billions of dollars)
C + Ig + Xn + G
C + Ig + Xn C
Government spending
of $20 billion
This figure illustrates the impact of government spending on equilibrium GDP. The addition of government expenditures, G, to our analysis raises the aggregate expenditures (C + Ig + Xn + G) schedule and increases the equilibrium level of GDP, as would an increase in C, Ig, or Xn. The multiplier is again 4 (80 divided by 20).
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22. Taxation and Equilibrium GDP
TABLE 28.5 Determination of the Equilibrium Levels of Employment, Output, and Income: Private and Public Sectors
(1)
Real Domestic Output and Income
(GDP), Billions
(2)
Taxes
(T),
Billions
(3)
Disposable Income (DI), Billions, (1)-(2)
(4)
Consump-tion (Ca),
(5)
Saving (Sa),
(6)
Invest-ment (Ig),
(7)
Net Exports
(Xn), Billions
(8)
Govern-ment Pur-chases
(G), Billions
(9)
Aggregate Expendi-tures (Ca +Ig+Xn
+G),
(4)+(6)+(7)+(8)
Exports
(X)
Imports
(M)
(1) $370
$20
$350
$360
$-10
$10
$400
(2) 390 20
370
375 -5 10
415
(3) 410
390
430
(4) 430
410
405 5
445
(5) 450
420
460
(6) 470
450
435 15
475
(7) 490
470
490
(8) 510
465 25
505
(9) 530
510
480 30
520
(10) 550
530
495 35
535
Table 28.5 shows the determination of the equilibrium levels of employment, output, and income with the private sector and taxes. With taxes of $20 billion at all levels of GDP, equilibrium GDP falls from $550 to $490. Again, we can see that there is a multiplier effect. The multiplier = 60/15 = 4.
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23. Taxation and Equilibrium GDP
45°
Real domestic product, GDP (billions of dollars)
Aggregate expenditures (billions of dollars)
C + Ig + Xn + G
Ca + Ig + Xn + G
$15 billion
decrease in
consumption
from a
$20 billion
increase
in taxes
This figure reflects the impact of taxes on equilibrium GDP. If the MPC is .75, the $20 billion of taxes will lower the consumption schedule by $15 (20 x .75) billion and cause a $60 billion decline in the equilibrium GDP. In the open economy with government, equilibrium GDP occurs where Ca (after-tax income) + Ig + Xn + G = GDP. Here, that equilibrium is $490 billion.
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