Encyclonomic WEB*pedia: THREE-SECTOR INJECTIONS-LEAKAGES MODEL

THREE-SECTOR INJECTIONS-LEAKAGES MODEL:
A variation of the Keynesian injections-leakages model that includes the three domestic sectors--the household sector, the business sector, and the government sector. This model provides an alternative to the three-sector aggregate expenditures (Keynesian cross) analysis of government stabilization policies, especially how fiscal policy changes in government purchases and taxes can be used to close recessionary gaps and inflationary gaps. Equilibrium is identified as the intersection between the S + T line and the I + G line. Two related variations are the two-sector injections-leakages model and the four-sector injections-leakages model.
The three-sector injections-leakages model provides an alternative to the more common three-sector Keynesian model; the Keynesian cross, aggregate expenditures-aggregate production model of the macroeconomy. Both models provide essentially the same analysis and are essentially "two sides of the same coin." The key difference between the two models is that consumption is explicitly eliminated from the injections-leakages variation. Whereas the Keynesian cross builds on the consumption function, the injections-leakages model builds on the saving function.
Three Sectors
The three sectors included in this three-sector injections-leakages model are the household sector, the business sector, and the government sector.
Household Sector: The household sector includes everyone in an economy who consumes goods and services. It is the entire population of an economy. The household sector is responsible for consumption expenditures on gross domestic product.

Business Sector: The business sector contains the private, profit-seeking firms in the economy that combine scarce resources into the production of wants-and-needs satisfying goods and services. The business sector is responsible for investment expenditures on gross domestic product.

Government Sector: The government sector, or public sector, forces involuntary resource allocation decisions on the rest of the economy through laws, rules, and regulations. The public sector enters this model in two ways--by adding government purchases to aggregate expenditures and by subtracting taxes from aggregate expenditures.
Injections and Leakages
One half of the injections-leakages model is injections, which are non-consumption expenditures on aggregate production. The three injections are investment expenditures, government purchases, and exports. These are termed injections because they are "injected" into the core circular flow of consumption, production, and income. In the three-sector injections-leakages model, investment expenditures and government purchases are the two injections included.
The other half of the injections-leakages model is leakages, which are non-consumption uses of the income generated from production. The three leakages are saving, taxes, and imports. These are termed leakages because they are "leaked" out of the core circular flow of consumption, production, and income. In the three-sector injections-leakages model, saving and taxes are the two leakages included.
Equilibrium in the injections-leakages model relies on a balance between the injections into the core circular flow and leakages out of the flow. If leakages match injections, then the volume of the core circular flow does not change. This is the same as achieving a balance between the water flowing from a faucet into a sink and that flowing out through the drain. When these two flows are equal, then the total amount of water IN the sink does not change. Equilibrium!
In the three-sector injections-leakages model, equilibrium is identified as a balance or equality between the sum of saving and taxes and the sum of investment expenditures and government purchases.
The Injections-Leakages Balance
A balance between injections and leakages generates the same equilibrium as a balance between aggregate expenditures and aggregate production. A little manipulation of the Y = AE equilibrium condition illustrates why.
Aggregate expenditures (AE) are the sum of consumption (C), investment (I), and government purchases (G).
AE = C + I + G

The income generated by aggregate production (Y) is used by the household sector for consumption (C), saving (S), and taxes (T).
Y = C + S + T

Substituting each of these equations into the Y = AE equilibrium condition gives us:
C + S + T = C + I + G

Because consumption (C) is on both sides, it cancels out.
S + T = I + G
This last equation indicates that equilibrium can be achieved by equating injections I + G with leakages S + T. Most importantly, when aggregate expenditures equal aggregate production (Y = AE), then injections are necessarily equal to leakages S + T = I + G.
This results indicates why the key classical assumption that saving is equal to investment does not necessarily hold. Saving need not equal investment (if taxes do not equal government purchases) when the macroeconomy is equilibrium.
The Graphical Model
The Injections-Leakages Model

The exhibit to the right can be used to present the three-sector injections-leakages model. This diagram displays the basic two-sector injections-leakages model. Aggregate production is measured on the horizontal axis. Leakages and injections are measured on the vertical axis. The saving line is labeled S and the investment line is labeled I.
We now need to add the government sector's injection and leakage, starting with government purchases. Like we did with investment, let's assume that government purchases are autonomous. Using induced government purchases won't really change the conclusions. Click the [Government Purchases] button to add this injection.
The result of this button-clicking is the addition of a second horizontal line, labeled I + G. This line is the sum of autonomous investment and autonomous government purchases. It is derived by adding autonomous government purchases, G, to the investment line, I.
The next addition is taxes, the government sector's leakage. For simplicity, let's also presume that taxes are autonomous. Click the [Taxes] button to add this leakage.
You should see a new line appear in this diagram, labeled S + T. This line is the sum of saving and taxes and is derived by adding autonomous taxes, T, to the saving line, S. The slope of the S + T line is parallel to the saving line, S, and is equal to the marginal propensity to save.
The inclusion of government purchases and taxes gives us the three-sector injections-leakages model. Equilibrium in this model is found in much the same way as the two-sector model, by equating injections and leakages. The only difference is the number of injections and leakages included.
More specifically, equilibrium is the level of aggregate production corresponding with the intersection of the I + G line and the S + T line. Click the [Equilibrium] button to highlight this level.
What special insight can be derived from this equilibrium?
First, the equilibrium level of aggregate production depends on the overall height of the lines, but not on the mix of injections and leakages that make up each line. If, for example, autonomous investment and government purchases total $500 billion, it doesn't matter if investment is $400 billion and government purchases are $100, or if investment is $100 billion and government purchases are $400, equilibrium is the same.

Second, fiscal policy can be seen as shifts in the I + G line and the S + T line. Expansionary fiscal policy raises the height of the I + G line and lowers the height of the S + T line. Both of these lead to a greater level of aggregate production. Contractionary fiscal policy lowers the height of the I + G line and raises the height of the S + T line. Both of these lead to a smaller level of aggregate production.

Third, comparable to the two-sector model, the vertical difference between the S + T line and I + G line is unplanned inventory changes. If leakages equal injections, then inventories don't change. If leakages exceed injections, inventories increase. If injections exceed leakages, inventories decrease.
A key conclusion from this variation of the injections-leakages model is that equilibrium depends on total injections and leakages. In particular, saving need not equal investment. In fact, saving will not equal investment if taxes do not equal government purchases. The equality of taxes and government purchases is a balanced government budget. If the budget is not in balance, then saving is not equal to investment.
Two Other Variations
The three-sector injections-leakages model is one of three variations, each based on a different combination of the four macroeconomic sectors, and thus a different number of injections and leakages.
Two-Sector Model: The simplest injections-leakages model includes the household and business sectors. Also termed the saving-investment model, this variation is often used to illustrate the basic operation of the model, including adjustment to equilibrium and the multiplier process. The two-sector model captures the role of induced activity through household saving and the role of autonomous expenditures through business investment. Saving is the only leakage and investment is the only injection.

Four-Sector Model: As the name suggests, all four macroeconomic sectors--household, business, government, and foreign--are included in the four-sector model. This model is not only used to capture the interaction between the domestic economy and the foreign sector, but also provides the foundation for detailed, empirically estimated models of the macroeconomy. Saving, taxes, and imports are the three leakages. Investment, government purchases, and exports are the three injections.
Check Out These Related Terms...
     | two-sector injections-leakages model | four-sector injections-leakages model | injections-leakages model | injections | leakages | injections line | leakages line | saving-investment model | Keynesian model |
Or For A Little Background...
     | Keynesian economics | Keynesian cross | aggregate expenditures | saving line | investment line | effective demand | induced expenditures | autonomous expenditures | macroeconomics | macroeconomic sectors | saving | investment expenditures | government purchases | taxes | imports | exports |
And For Further Study...
     | two-sector Keynesian model | three-sector Keynesian model | four-sector Keynesian model | expansionary fiscal policy | contractionary fiscal policy | automatic stabilizers | Keynesian cross and aggregate market | expenditures multiplier | accelerator principle | paradox of thrift | aggregate market analysis | business cycles |
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     THREE-SECTOR INJECTIONS-LEAKAGES MODEL, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2025. [Accessed: December 15, 2025].