2. Refer to Chapter Nine's Exhibit 4, on page 194. The consumption function shows the relationship between consumption expenditure and disposable income. Because consumption rises with disposable income, the consumption function has a positive slope. The slope of the consumption function is the marginal propensity to consume from disposable income, or the MPC. The reason is that the MPC is the ratio of additional consumption to additional disposable income. The saving function is similar, showing the relationship between disposable income and saving. Saving rises with income, so the saving function has a positive slope. The slope of the saving function is the marginal propensity to save from disposable income, or the MPS.

The saving and consumption functions are closely related because saving equals disposable income minus consumption. Consider Exhibit 3 on page 193. Add a 45° line. Saving equals the vertical difference between the 45° line and the consumption function. When the consumption function is below the 45° line, saving is positive; when the consumption function is above the 45° line, saving is negative. Any time the consumption function shifts, the saving function shifts by an equal but opposite amount. Moreover, the marginal propensity to consume plus the marginal propensity to save equals 1; that is, MPC + MPS = 1.0 and if C=a + b(Y-NT), then S=-a + (1-b)(Y-NT), where a=autonomous consumption, b=MPC and (1-b)=MPS.

3. The marginal propensity to consume, MPC, measures the fraction of an additional dollar of disposable income spent on consumption. Because the MPC measures the fraction consumed, the MPC can range only between 1.00 — all of the dollar is spent on consumption — to 0.0 — none of the dollar is spent on consumption. Empirically, the estimated MPC is close to 0.80.

4. The MPC + MPS = 1.0. Why? The MPC measures the fraction of an additional dollar of disposable income spent on consumption and the MPS measures the fraction of the extra dollar of disposable income saved. Because there are only two uses for an extra dollar of income — part or all must be consumed and the remainder must be saved — it must be that MPC + MPS = 1.0.

5. The marginal propensity to consume equals the slope of the consumption function. Thus the slope is determined by how much of an additional dollar of disposable income is spent on additional consumption.

6. The import function shows the relationship between expenditures on imports and real GDP. An increase in real GDP increases expenditures on imports. The marginal propensity to import is defined as or the fraction of a change in real GDP spent on imports. In recent years in the United States, the marginal propensity to import is approximately 0.2.

7. The aggregate expenditure schedule lists aggregate planned expenditure generated at each level of real GDP. The aggregate expenditure curve is a plot of aggregate planned expenditure against real GDP. For an example, refer to Exhibit 1 on page 213.

8. Induced expenditure is expenditure that depends on real GDP. For instance, as GDP increases, consumption expenditure and import expenditure both rise. The increase in these categories of expenditure that are the result of the increase in real GDP are "induced expenditure." Autonomous expenditure does not depend on real GDP. In other words, autonomous expenditure — such as investment and government expenditure — is independent of real GDP.

9. As illustrated in Exhibit 1 on page 213, equilibrium expenditure occurs where the aggregate expenditure curve crosses the 45° line because that is where aggregate planned expenditure equals real GDP. If aggregate planned expenditure is larger than real GDP, which is the case at less than $14 trillion in the figure, firms find their inventories are reduced in an unwanted manner. Hence they increase production and GDP by hiring more workers. These actions raise workers’ disposable incomes and their consumption expenditures. Planned expenditure rises but not by as much as GDP. Thus real GDP increases by more than aggregate planned expenditure, so this process restores the equilibrium with equality between aggregate planned expenditure and GDP.

10. When aggregate planned expenditure exceeds real GDP, firms find that their inventories are being depleted in an unwanted manner. In response, firms hire more workers to produce more output. These actions in turn raise workers’ consumption expenditures, and the economy moves toward a higher equilibrium level of expenditure. An expansion occurs.

11. An increase in autonomous expenditure refers to an increase in investment, government purchases, exports, or an autonomous part of consumption expenditure or, possibly, a decrease in an autonomous part of import expenditure. All of these are represented by the intercept of the aggregate expenditure curve. Whenever autonomous expenditure increases, the aggregate expenditure curve, which equals the sum of consumption plus investment plus government plus net exports, shifts upward to reflect that increase.

12. The multiplier is the amount by which a change in autonomous expenditure is multiplied to determine the change in equilibrium expenditure.

13. The multiplier occurs because a change in autonomous expenditure causes an additional change in induced expenditure. The multiplier equals the change in equilibrium expenditure divided by the change in autonomous expenditure. Ignoring income taxes and imports, the multiplier equals If induced taxes, induced transfers, and imports are included, the multiplier becomes Without induced taxes, induced transfers, and imports, the slope of the AE curve equals the MPC. Hence in this case both formulas for the multiplier are the same. Then, because induced taxes, induced transfers, and imports all decrease the slope of the AE curve, all three operate to decrease the magnitude of the multiplier.

14. Some may respond that the multiplier exceeds 1.00 because it equals Because the MPC is less than 1.00, the fraction must exceed 1.00. Others may present essentially the same answer, using the more general equation for the multiplier, that the multiplier equals Then, with the slope of the AE curve less than 1.00, again the fraction must exceed 1.00 in value. In other words, the denominator of the multiplier is less than 1.00, so the entire fraction must exceed 1.00. While this is certainly correct, it falls short of a complete explanation. A more complete answer is that an increase in autonomous expenditure induces additional expenditure. An increase in, say, investment, raises aggregate expenditure directly on a one-to-one basis. But the increase in aggregate expenditure also boosts people’s incomes, which in turn induces a further increase in their consumption demand. This process continues through many rounds, but each time time AE rises by a fraction (g) of the increase in real GDP. Thus the total increase in aggregate expenditure exceeds the initial increase in investment.

15. Without income taxes or imports, the autonomous-expenditure multiplier equals An increase in the MPC increases the multiplier. This result makes sense: The multiplier exists because an increase in autonomous expenditure increases aggregate disposable income, and part of the increase in disposable income is spent on additional consumption. Thus the increase in disposable income induces additional consumption expenditure, which in turn boosts disposable income still more and induces even more consumption expenditure. The larger the MPC, the more consumption expenditure increases from an increase in disposable income and hence the larger is the multiplier.

Induced (income) taxes reduce the size of the multiplier. With these taxes, an increase in aggregate income translates into a smaller increase in disposable income. And the smaller increase in disposable income means that the (induced) consumption expenditure will not increase by as much, so the multiplier is smaller.

Imports also reduce the size of the multiplier. If some of the induced consumption expenditure goes to imports, total aggregate expenditure for domestic goods and services drops. Thus the added increase in aggregate income is less, the amount of (induced) consumption is less, and the multiplier is smaller.

16. The aggregate demand curve is derived from the aggregate expenditure curve. The aggregate expenditure (AE ) curve shows how aggregate expenditures vary with disposable income, and the aggregate demand (AD) curve shows how the equilibrium level of aggregate expenditure depends on the price level. A change in the price level causes the aggregate expenditure curve to shift and results in a new equilibrium level of expenditure. The change in the price level causes a movement along the aggregate demand curve to the new price level and new level of equilibrium expenditure.

17. The aggregate expenditure curve shifts downward when the price level rises because the higher price level decreases aggregate expenditures. A higher price level lowers aggregate expenditure for two reasons: the wealth effect, and the substitution effects. The wealth effect indicates that a higher price level decreases the purchasing power of people’s wealth (net assets), which decreases their consumption expenditures. There are two substitution effects: Intertemporal substitution and international substitution. The intertemporal substitution effect indicates that a higher current price level makes the current purchase of goods and services more expensive than their purchase in the future. As a result, current purchases are delayed, and aggregate expenditure decreases. Finally, the international substitution effect indicates that a higher U.S. price level increases the price of U.S. goods and services relative to foreign goods and services. People substitute foreign goods and services for U.S. goods and services, thereby decreasing aggregate expenditure on goods and services produced in America.

18. When the price level changes, the aggregate expenditure (AE) curve shifts. When the price level changes, there is a movement along the aggregate demand (AD) curve.

19. Aggregate demand shows how total (equilibrium) expenditure is related to the price level. An increase in autonomous expenditure raises total (equilibrium) expenditure at the current price level and hence increases aggregate demand (shifts AD to the right). The change in autonomous expenditure times the multiplier equals the change in equilibrium expenditure. The latter is the increase in AD. See above for further discussion of the process.

20. The multiplier essentially shows how aggregate demand changes when autonomous expenditure changes. In the very short run, firms do not raise prices and are willing to produce the quantity that is demanded. Hence an increase in demand is met completely, first by selling inventories, then by increasing the amount produced. However, as more time passes, firms start to raise prices. As the prices of goods and services rise, the quantity demanded falls. Alternatively, as the price level rises, the equilibrium level of expenditure falls. (The AE curve shifts downward when the price level rises.) Hence the increases in both output and the multiplier become smaller as time passes.

21. In the long run, the economy produces the potential level of real GDP. In the long run, changes in aggregate demand have no impact on the equilibrium level of real GDP: It returns to its potential level. Thus the multiplier, which shows how much real GDP changes, is zero.

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