February 21, 2017 

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A variation of the Keynesian injections-leakages model that adds the foreign sector to the three domestic sectors--the household sector, the business sector, and the government sector. This variation adds the foreign to the three domestic sectors (household, business, and government) in the three-sector model and provides an alternative to the four-sector aggregate expenditures (Keynesian cross). It provides the complete Keynesian representation of the macroeconomy, including the export-import interaction between the domestic economy and the foreign sector. Equilibrium is identified as the intersection between the S + T + M line and the I + G + X line. Two related variations are the two-sector injections-leakages model and the three-sector injections-leakages model.
The four-sector injections-leakages model provides an alternative to the more common four-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.

Four Sectors

The four sectors included in this four-sector injections-leakages model are the household sector, the business sector, the government sector, and the foreign 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.

  • Foreign Sector: The foreign sector is responsible for all economic activity beyond the political boundaries of an economy. The foreign sector includes households, businesses, and governments that reside in other countries. The domestic economy trades goods with the foreign sector through exports and imports. This foreign trade is an extension of regular market activity, except the buyers and sellers reside in different countries.

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 four-sector injections-leakages model, investment expenditures, government purchases, and exports are the three 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 four-sector injections-leakages model, saving, taxes, and imports are the three 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 four-sector injections-leakages model, equilibrium is identified as a balance or equality between the sum of saving, taxes, and imports and the sum of investment expenditures, government purchases, and exports.

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), government purchases (G), and net exports (X - M).

    AE = C + I + G + (X - M)

  • 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 + (X - M)

  • Because consumption (C) is on both sides, it cancels out.

    S + T = I + G + (X - M)

  • For reasons that will be apparent later, let's move imports (M) to the left-hand side.

    S + T + M = I + G + X

This last equation indicates that equilibrium can be achieved by equating injections I + G + X with leakages S + T + M. Most importantly, when aggregate expenditures equal aggregate production (Y = AE), then injections are necessarily equal to leakages S + T + M = I + G + X.

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 and/or exports do not equal imports) when the macroeconomy is equilibrium.

It also suggests the complex interaction that exists between financial markets (saving and investment), the budget of the government sector (government purchases and taxes), and foreign trade (exports and imports). If two are in balance then all three are in balance. If one is out of balance, then at least one of the others is also out of balance.

The Graphical Model

The Injections-Leakages Model

The exhibit to the right can be used to present the four-sector injections-leakages model. This diagram displays the three-sector injections-leakages model as a starting point. Aggregate production is measured on the horizontal axis. Leakages and injections are measured on the vertical axis. The leakage line is labeled S + T and the injection line is labeled I + G.

We now need to add the injection and leakage from the foreign sector, starting with exports. Exports, of course, are autonomous, so there's no need to worry about an induced version. Click the [Exports] button to add this injection.

The result of this button-clicking is the addition of a new horizontal line, labeled I + G + X. This line is the sum of autonomous investment, autonomous government purchases, and autonomous exports. It is derived by adding autonomous exports, X, to the injections line, I + G.

The next addition is imports, the foreign sector's leakage. For simplicity, let's also assume that imports are autonomous. Click the [Imports] button to add this leakage.

This gives us another new line, labeled S + T + M. This line is the sum of saving, taxes, and imports and is derived by adding induced imports, M, to the leakages line, S + T. The slope of the S + T + M line is parallel to the leakages line, S + T, and is equal to the marginal propensity to save. Of course, if we had used induced imports, then the slope would be greater than the marginal propensity to save.

The inclusion of exports and imports gives us the four-sector injections-leakages model. Equilibrium in this model is found in the same way as the other versions of this model, by equating injections and leakages. The only difference, once again, 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 + X line and the S + T + M 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 once again depends on the overall height of the lines, but not on the mix of injections and leakages that make up each line.

  • Second, comparable to the other models, the vertical difference between the S + T + M line and I + G + X 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.

  • Third, because equilibrium depends on total injections and leakages, there is no reason to expect that saving equals investment, taxes equal government purchases, or imports equal exports. Moreover, if any one of these pairs is out of balance, then one or more of the other pairs is also necessarily out of balance. If, for example, exports do not equal imports, then saving does not equal investment and/or taxes do not equal government purchases.
This last point serves to illustrate the interactive complexity of the macroeconomy. While people are often separately concerned about foreign trade, government spending, and private investment, this brief analysis indicates that such issues are interrelated. Promoting a positive trade balance (exports greater than imports) means that saving exceeds investment and/or taxes exceed government purchases. Solving one "problem" might very well create others.

Two Other Variations

The four-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.

  • Three-Sector Model: Another variation of the injections-leakages model adds the government sector (or public sector) to the household and business sectors contained in the two-sector model. This variation is used to analyze government stabilization policies, especially how fiscal policy changes in government purchases and taxes can be used to close recessionary gaps and inflationary gaps. Saving and taxes are the two leakages. Investment and government purchases are the two injections.


Recommended Citation:

FOUR-SECTOR INJECTIONS-LEAKAGES MODEL, AmosWEB Encyclonomic WEB*pedia,, AmosWEB LLC, 2000-2017. [Accessed: February 21, 2017].

Check Out These Related Terms...

     | two-sector injections-leakages model | three-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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     | The General Theory of Employment, Interest, and Money |

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