Sunday  April 21, 2024
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 HOMOGENEOUS OF DEGREE N: A property of an equation the exists if independent variables are increased by a constant value, then the dependent variable is increased by the value raised to the power of n. The value of n can be greater than, less than, or equal to one. This property often surfaces in the analysis of production functions. If n = 1, then a doubling independent variables results in a doubling of the dependent variable and the production function has constant returns to scale. If n > 1, then a doubling independent variables results in more than a doubling of the dependent variable and the production function has increasing returns to scale. If n < 1, then a doubling independent variables results in less than a doubling of the dependent variable and the production function has decreasing returns to scale.

LEAKAGES LINE:

A graphical representation of the relation between the level of aggregate production and one or more leakages. The three leakages (non-consumption uses of the income generated from aggregate production) are saving, taxes, and imports. The leakages line sequentially adds, or layers, each of these three uses of income depending on the number of sectors used in the analysis (two, three, or four). The slope of the leakages line depends on which if any of the uses of income are induced by aggregate production. The leakages line is combined with the injections line (containing investment expenditures, government purchases, and exports) in the Keynesian injections-leakages model.
The leakages line graphically illustrates the relation between one or more of the three leakages--saving, taxes, and imports--and the level of aggregate production or income. This line is one half of the injections-leakages model used to identify and analyze the equilibrium level of aggregate production and income. The other half is the injections line that illustrates the relation between aggregate production and one or more of the three injections--investment expenditures, government purchases, and exports.

The number of leakages contained in the leakages line depends on the number of sectors included in the injections-leakages model. The leakages line used in the two-sector model contains only saving by the household sector. Taxes paid to the government sector are added to saving for the leakages line used in the three-sector analysis. And the four-sector model uses a leakages line with imports from the foreign sector added to taxes and saving.

The slope of the leakages line depends on which if any of the leakages are assumed to be induced by the level of aggregate production and income. The slope of the leakages line thus depends on the marginal propensity to save, the marginal propensity to tax (or marginal tax rate), and the marginal propensity to import.

### Building the Leakages Line

The Leakages Line

The exhibit to the right is the starting point for deriving the three alternative leakages lines. As it currently stands, this exhibit is blank, except for the horizontal axis, which measures aggregate production, and the vertical axis, which measures the assorted leakages. To move from this largely blank diagram to each of the three leakages lines, we need to sequentially add saving, taxes, and imports.
• Two-Sector Leakages Line: Let's begin with the leakages line used in the two-sector injections-leakages model. This is the simplest leakages line in that it contains only a single leakage--saving. A click of the [Saving] button displays this line. The line is positively sloped, indicating that saving is induced by income. Induced saving give the line a positive slope equal to the marginal propensity to save.

• Three-Sector Leakages Line: Next up is the leakages line used in the three-sector injections-leakages model. This leakages line contains two leakages--saving and taxes. It is derived by layering or adding taxes onto the investment line. A click of the [Taxes] button displays this new line. The line is parallel to the saving line indicating that taxes are totally autonomous. Including induced taxes would then increase the slope of the line based on the marginal propensity to tax, or marginal tax rate.

• Four-Sector Leakages Line: Last on the list is the leakages line used in the four-sector injections-leakages model. This leakages line contains all three leakages--saving, taxes, and imports. It is derived by layering or adding omports onto the three-sector leakages line. A click of the [Imports] button displays this new line. The resulting line is more steeply sloped than the three-sector line indicating that imports are induced by the level of income, the common assumption in the four-secter injections-leakages model.

### A Word About the Injections Line

The other half of the injections-leakages model is the injections line, which represents the relation between injections, the non-consumption expenditures on aggregate production--investment expenditures, government purchases, and exports, and the level of aggregate production and income. Like the leakages line, the number of injections contained in the line depends on the number of sectors included in the analysis.

The injections line used in the two-sector model contains only investment expenditures. Government purchases are added for the three-sector model and exports are added for the four-sector model. Because exports are autonomous, the slope of the injections line depends on whether or not investment expenditures and government purchases are induced.

 <= LEAKAGES LEGAL BUSINESS ORGANIZATIONS =>

Recommended Citation:

LEAKAGES LINE, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2024. [Accessed: April 21, 2024].

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