Thursday  August 18, 2022
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 YIELD TO MATURITY: The annual rate of return on a financial asset that is held until maturity. Yield to maturity depends on both the coupon rate and the face or par value paid at maturity. If the selling price of a financial asset is equal to its par value, then the yield to maturity is equal to the current yield and the coupon rate. However, if the asset is selling at a discount, then the yield to maturity exceeds the current yield, which is greater than the coupon rate. And if the asset is selling at a premium, then the yield to maturity is less than the current yield, which is below than the coupon rate.

MULTIPLIER, SLOPE OF AGGREGATE EXPENDITURES LINE:

The slope of the aggregate expenditures line determines the magnitude of the multiplier process and the numerical value of the multiplier. In particular, the expenditures multiplier is the inverse of one minus the slope of the aggregate expenditures line. This slope is largely based on the marginal propensity to consume, but also depends on other induced activities. A steeper slope generates a larger multiplier and a flatter slope leads to a smaller multiplier.
The standard Keynesian expenditures multiplier is the inverse of one minus the slope of the aggregate expenditures line. The slope of the aggregate expenditures line captures the extent to which consumption expenditures, investment expenditures, government purchases, and other macroeconomic activities are induced by aggregate production and income. If the slope is steeper and aggregate expenditures are induced more by aggregate production, then the multiplier is greater.

### The Multiplier Formula

The total change in aggregate production caused by an autonomous expenditure change depends on the extent to which consumption and other expenditures are induced by income.

Consider if you will the simple formula for the multiplier m stated in terms of the marginal propensity to consume and the marginal propensity to save.

 m = 1marginal propensity to save = 1(1 - marginal propensity to consume)
For example, if 75 percent of the income received by the household sector is used for consumption (a marginal propensity to consume of 0.75) then the multiplier is 4. A larger marginal propensity to consume means a larger multiplier. A smaller marginal propensity to consume means a smaller multiplier. If the marginal propensity to consume is 0.9, then the multiplier is 10. If the marginal propensity to consume is 0.6, then the multiplier is 2.5.

If consumption is the only induced expenditure, then the marginal propensity to consume is the slope of the aggregate expenditures line. However, in more complex models, the slope of the aggregate expenditures line depends on other induced factors, which also affects the value of the multiplier.

As such, a more general formula for the multiplier m is stated as the slope of the aggregate expenditures line.

 m = 1(1 - slope of aggregate expenditures line)
With this specification, the connection between the multiplier and the slope of the aggregate expenditures line, and induced activity that affects this slope, is explicitly stated. If the slope is greater, the denominator of the equation is smaller (because the slope is subtracted from 1), and hence the multiplier is larger.

### Changing Slopes

Changing Slopes

For a bit of graphical insight into the connection between slope and multiplier, consider the Keynesian aggregate expenditures model presented in the exhibit to the right.
• This diagram displays an initial equilibrium of \$12 trillion found at the intersection of the aggregate expenditures line and the 45-degree line. The slope of the aggregate expenditures line is equal to 0.75, which is the marginal propensity to consume in this simple example but it could be based on any number of induced activities.

• An investment injection of \$1 trillion shifts the aggregate expenditures line higher, triggering the multiplier process and a generating a new equilibrium at \$16 trillion. Click the [Inject Investment] button to illustrate this.

• The \$4 trillion change in aggregate production is four times the initial change in investment. The multiplier has a value of 4 because the slope of the aggregate expenditures line is 0.75.
The change in aggregate expenditures and the multiplier depend on the slope of the aggregate expenditures line. What might happen if the slope of the aggregate expenditures line decreases to 0.5.
• Click the [Flatter Line] to display this new aggregate expenditures line. Note that this new line intersects the 45-degree line at the initial \$12 trillion equilibrium level of production. This makes it possible to compare the two aggregate expenditures lines.

• Now consider the multiplier process triggered by a \$1 trillion injection with this steeper aggregate expenditures line. Click the [Inject Again] button. You should now see that the new flatter aggregate expenditures line shifts vertically by the same amount as the original, flatter line.

• However, the resulting equilibrium level is different. The intersection between the new aggregate expenditures line and the 45-degree line results in an equilibrium level of aggregate production of \$14 trillion rather than \$16 trillion.

• The change in aggregate production is now \$2 trillion, half as much as the original multiplier change of \$4 trillion. This change in production is two times the initial change in investment, giving a multiplier of 2. This multiplier value can also be found by plugging 0.5 into the formula presented above.
The key conclusion is that the slope of the aggregate expenditures line determines the size of the multiplier. A flatter slope means a smaller multiplier. A steeper slope means a larger multiplier. However, the slope of the aggregate expenditures line is based on all induced factors. If investment and government purchases are induced in addition to consumption, then the slope is steeper and the multiplier is bigger. If taxes and imports are also induced, then the slope is flatter and the multiplier is smaller.

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Recommended Citation:

MULTIPLIER, SLOPE OF AGGREGATE EXPENDITURES LINE, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2022. [Accessed: August 18, 2022].

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