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10Expenditure Multipliers* Chapter EXPENDITURE 10 MULTIPLIERS* Key Concepts FIGURE 10.1 The Consumption Function Fixed Prices and Expenditure Plans1 5 In the very short run, firms do not change their prices and they sell the amount that is demanded. As a result: 4 ♦ The price level is fixed. ♦ GDP is determined by aggregate demand. 3 Aggregate planned expenditure is the sum of planned consumption expenditure, planned investment, planned Consumption 2 function government purchases, and planned exports minus planned imports. GDP and aggregate planned expenditures have a two- 1 way link: An increase in real GDP increases aggregate planned expenditures, and an increase in aggregate expenditures increases real GDP. 123 45 Consumption expenditure (trillions of 1996 dollars) Consumption expenditure, C, and saving, S, depend on Disposable income (trillions of 1996 dollars) disposable income (disposable income, YD, is income minus taxes plus transfer payments), the real interest ♦ The slope of the consumption function equals the rate, wealth, and expected future income. MPC. The slope of the U.S. consumption function The consumption function is the relationship between is about 0.9. consumption expenditure and disposable income. Fig- ♦ Changes in the real interest rate, wealth, or expected ure 10.1 illustrates a consumption function. future income shift the consumption function. ♦ The amount of consumption when disposable in- Consumption varies when real GDP changes because come is zero ($1 trillion in Figure 10.1) is called changes in real GDP change disposable income. autonomous consumption. Consumption above this The saving function is the relationship between saving amount is called induced consumption. and disposable income. The marginal propensity to ♦ The marginal propensity to consume,,, MPC,,, is save, MPS,,, is the fraction of a change in disposable the fraction of a change in disposable income that is ∆S income that is saved, or MPS = . ∆C ∆YD consumed, or MPC = , where ∆ means ∆YD The sum of the MPC plus MPS equals 1. “change in.” Domestic imports are determined in the short run mainly by U.S. GDP. The marginal propensity to import is the fraction of an increase in real GDP spent on imports. 1* This is Chapter 25 in Economics. 149 150 CHAPTER 10 (25) Real GDP with a Fixed Price Level equilibrium expenditure and real GDP. The multiplier is larger than 1.0 because a change in autonomous ex- FIGURE 10.2 penditure also changes induced expenditure. Aggregate Expenditure ♦ With no income taxes or imports, the multiplier 12 1 1 equals , or, equivalently, . 0 ()1 − MPC MPS 45 line AE 11 ♦ Income taxes and imports shrink the multiplier. ♦ Imports and income taxes reduce the slope of the 10 AE curve. With them the multiplier equals 1 . (trillions of 1996 dollars) (1− slope of the AE curve) 9 Aggregate planned expenditure ♦ A business cycle expansion occurs when autono- mous expenditure increases and the multiplier ef- 8 fect increases equilibrium expenditure; a business cycle recession occurs when autonomous expendi- ture decreases. 8 9 10 11 12 Real GDP (trillions of 1996 dollars) The Multiplier and the Price Level The aggregate planned expenditure schedule shows The aggregate expenditure curve (AE ) shows the rela- how aggregate expenditure depends on real GDP. The tionship between aggregate planned expenditure and aggregate expenditure curve plots the aggregate planned disposable income; the aggregate demand curve (AD) expenditure schedule. Figure 10.2 illustrates an aggre- shows the relationship between the aggregate quantity gate expenditure curve, AE = C + I + G + NX, where of goods demanded and the price level. The AD curve NX is exports minus imports. is derived from the AE curve. ♦ ♦ Induced expenditure is the sum of the compo- An increase in the price level shifts the AE curve nents of aggregate expenditure that change with downward and equilibrium expenditure decreases. GDP. FIGURE 10.3 ♦ Autonomous expenditure is the sum of the com- Increase in the Price Level and the AE Curve ponents of aggregate expenditure that do not change when real GDP changes. In Figure 10.2 12 autonomous expenditure is $8 trillion. 0 45 line AE0 Equilibrium expenditure is the level of aggregate ex- 11 penditure that occurs when aggregate planned expen- AE1 diture equals real GDP. In Figure 10.2 the equilibrium 10 expenditure is the point at which the 45° line crosses the AE line, or $10 trillion. (trillions of 1996 dollars) ♦ If real GDP exceeds equilibrium expenditure, un- 9 planned inventories accumulate; if real GDP is less Aggregate planned expenditure than equilibrium expenditure, inventories are 8 drawn down in an unplanned manner. The Multiplier 8 9 10 11 12 A change in autonomous expenditure creates an addi- Real GDP (trillions of 1996 dollars) tional change in induced expenditure. The multiplier is the amount by which a change in autonomous ex- ♦ Figure 10.3 illustrates this effect: When the price penditure is multiplied to determine the change in level rises from 130 to 170, the AE curve shifts EXPENDITURE MULTIPLIERS 151 from AE0 to AE1 and equilibrium expenditure de- FIGURE 10.5 creases from $10 to $8 trillion. Increase in Aggregate Demand ♦ Figure 10.3 shows that, when the price level is 130, 190 the aggregate quantity demanded is $10 trillion and, when the price level is 170, the aggregate SAS quantity demanded is $8 trillion. These are two 170 points on the AD curve in Figure 10.4. 150 FIGURE 10.4 Increase in the Price Level and the AD Curve 130 190 AD1 170 b 110 Price level (GDP deflator, 1996 = 100) AD0 150 8 9 101112 Real GDP (trillions of 1996 dollars) 130 a ♦ In the long run, real GDP returns to potential real 110 GDP and does not change as a result of a change in Price level (GDP deflator, 1996 = 100) aggregate demand. In the long run, the multiplier is AD zero. 8 9 10 11 12 Real GDP (trillions of 1996 dollars) Helpful Hints ♦ An increase in the price level leads to a movement 1. AUTONOMOUS AND INDUCED EXPENDITURE : along the aggregate demand curve. Figure 10.4 Autonomous expenditure is independent of changes shows how an increase in the price level from 130 in real GDP, whereas induced expenditure varies as to 170 lead to a movement along the AD curve real GDP changes. In general, a change in autono- from point a to point b. The AD curve does not mous expenditure creates a change in real GDP, shift in response to a change in the price level. which in turn creates a change in induced expen- ♦ The AD curve shifts when autonomous expenditure diture. The induced changes are at the heart of the changes for any reason other than a change in the multiplier effect. price level. For instance, a change in investment or 2. THE INTUITION OF THE MULTIPLIER : The con- government purchases shifts the AD curve. cept of the multiplier is very important. An initial ♦ The size of the shift in the AD curve equals the increase in autonomous expenditure, such as invest- multiplier times the change in autonomous expen- ment, increases real GDP directly, but that is not diture. Figure 10.5 shows this result, where the AD the end of the story. The initial increase in real curve shifts rightward and the multiplied change in GDP generates an increase in induced expenditure, equilibrium expenditure is equal to the length of which further increases real GDP and thus creates the double-headed arrow, $2 trillion. further increases in (induced) expenditure. Induced ♦ The change in real GDP is less than the shift in the expenditure occurs because the increase in real AD curve. In Figure 10.5 the shift in the AD curve GDP created by the increase in autonomous ex- is $2 trillion. The increase in the price level reduces penditure raises disposable income. For instance, an the increase in GDP; in the short run, real GDP in increase in investment purchases of personal com- the figure increases by only $1 trillion. puters raises the incomes of workers who are hired to manufacture the additional computers. Then, 152 CHAPTER 10 (25) the increase in disposable income increases these 1 19. The multiplier equals . workers’ (induced!) consumption expenditures. ()1− MPS 3. THE MULTIPLIER AND THE AGGREGATE SUPPLY 10. The larger the marginal propensity to consume, the CURVE : The multiplier shows the change in equi- smaller the multiplier. librium expenditure. So, if the multiplier is 5.0 and investment (a component of autonomous expendi- 11. If the marginal propensity to consume is 0.8 and ture) increases by $10 billion, the equilibrium ex- there are no income taxes nor imports, the multi- penditure increases by $50 billion. plier equals 5.0. However, an increase in the equilibrium expendi- The Multiplier and the Price Level ture of $50 billion does not necessarily mean that 12. An increase in investment shifts the AE curve up- equilibrium real GDP also increases by $50 billion. The change in equilibrium real GDP depends on ward and the AD curve rightward. the interaction of aggregate demand and aggregate 13. In the short run, an increase in investment expen- supply. The $50 billion increase in equilibrium ex- diture of $1 billion increases equilibrium GDP by penditure implies that the AD curve shifts right- more than $1 billion. ward by $50 billion, but this shift is one part of the picture. Depending on the aggregate supply curve, 14. In the long run, an increase in investment expen- real GDP could increase by an amount close to $50 diture of $1 billion increases equilibrium GDP by billion (if the SAS curve is relatively flat) or by an more than $1 billion. amount less than $50 billion (how much less de- pends on the steepness of the SAS curve).
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