Baumol & Blinder MACROECONOMICS (11th ed)

LICENSED TO:

CHAPTER 9

Demand-Side Equilibrium: Unemployment or Inflation?

187

Suppose that Microhard—a major corporation in our hypothetical country—decides to

spend $1 million on a new office building. Its $1 million expenditure goes to construction

workers and owners of construction companies as wages and profits. That is, the $1 million

becomes their income.

But the construction firm’s owners and workers will not keep all of their $1 million in

the bank; instead, they will spend most of it. If they are “typical” consumers, their spend-

ing will be $1 million times the marginal propensity to consume (MPC). In our example,

the MPC is 0.75, so assume they spend $750,000 and save the rest. This $750,000 expendi-

ture is a net addition to the nation’s demand for goods and services, just as Microhard’s original

$1 million expenditure was. So, at this stage, the $1 million investment has already pushed

GDP up by some $1.75 million. But the process is by no means over.

Shopkeepers receive the $750,000 spent by construction workers, and

TABLE 4

they in turn also spend 75 percent of their new income. This activity ac-

The Multiplier Spending Chain

counts for $562,500 (75 percent of $750,000) in additional consumer

(1)

(2)

(3)

spending in the “third round.” Next follows a fourth round in which the

recipients of the $562,500 spend 75 percent of this amount, or $421,875,

Round

Spending in

Cumulative

and so on. At each stage in the spending chain, people spend 75 percent

Number

This Round

Total

of the additional income they receive, and the process continues—with

1

$1,000,000

$1,000,000

2

750,000

1,750,000

consumption growing in every round.

3

562,500

2,312,500

Where does it all end? Does it all end? The answer is that, yes, it does

4

421,875

2,734,375

eventually end—with GDP a total of $4 million higher than it was before

5

316,406

3,050,781

Microhard built the original $1 million office building. The multiplier is

6

237,305

3,288,086

indeed 4.

7

177,979

3,466,065

8

133,484

3,599,549

Table 4 displays the basis for this conclusion. In the table, “Round 1”

9

100,113

3,699,662

represents Microhard’s initial investment, which creates $1 million in in-

10

75,085

3,774,747

come for construction workers. “Round 2” represents the construction

O

O

O

workers’ spending, which creates $750,000 in income for shopkeepers. The

20

4,228

3,987,317

rest of the table proceeds accordingly; each entry in column 2 is 75 percent

O

O

O

“Infinity”

0

4,000,000

of the previous entry. Column 3 tabulates the running sum of column 2.

We see that after 10 rounds of spending, the initial $1 million invest-

ment has mushroomed to $3.77 million—and the sum is still growing. After 20 rounds,

the total increase in GDP is over $3.98 million—near its eventual value of $4 million. Al-

though it takes quite a few rounds of spending before the multiplier chain nears 4, we

see from the table that it hits 3 rather quickly. If each income recipient in the chain waits,

say, two months before spending his new income, the multiplier will reach 3 in only

FIGURE 11

about ten months.

How the Multiplier

Figure 11 provides a graphical presentation of the

Builds

numbers in the last column of Table 4. Notice how the

multiplier builds up rapidly at first and then tapers

off to approach its ultimate value (4 in this example)

$4.0

gradually.

And, of course, all this operates exactly the same—

but in the opposite direction—when spending falls.

Total

3.0

For example, when the boom in housing in America

ended in 2005 and 2006, spending on new houses be-

Spending

gan to decline. As this process progressed, the slow-

2.0

down in housing created a negative multiplier effect

on everything from appliances and furniture to carpet-

Cumulative

ing and insulation. Indeed, the big macroeconomic

1.0

concern in 2007 and 2008 was whether housing would

“pull” the whole economy into a recession.

0

2

4

6

8

10

15

20

Algebraic Statement of the Multiplier

Spending

Round

Figure 11 and Table 4 probably make a persuasive case

that the multiplier eventually reaches 4. But for the

NOTE: Amounts are in millions of dollars.

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

188

PART 2

The Macroeconomy: Aggregate Supply and Demand

remaining skeptics, we offer a simple algebraic proof.5 Most of you learned about something called an infinite geometric progression in high school. This term refers to an infinite series of numbers, each one of which is a fixed fraction of the previous one. The fraction is called the common ratio. A geometric progression beginning with 1 and having a common ratio of 0.75 looks like this:

1 1 0.75 1 10.7522 1 10.7523 1 . . .

More generally, a geometric progression beginning with 1 and having a common ratio R would be

1 1 R 1 R2 1 R3 1 . . .

A simple formula enables us to sum such a progression as long as R is less than 1.6 The

formula is7

1 Sum of infinite geometric progression 5 1 2 R

We now recognize that the multiplier chain in Table 4 is just an infinite geometric progression with 0.75 as its common ratio. That is, each $1 that Microhard spends leads to a (0.75) 3 $1 expenditure by construction workers, which in turn leads to a (0.75) 3 (0.75 3 $1) 5 (0.75)2 3 $1 expenditure by the shopkeepers, and so on. Thus, for each initial dollar of investment spending, the progression is

1 1 0.75 1 10.7522 1 10.7523 1 10.7524 1 . . .

Applying the formula for the sum of such a series, we find that

1	1
Multiplier 5 1 2 0.75 5 0.25 5		4

Notice how this result can be generalized. If we did not have a specific number for the marginal propensity to consume, but simply called it MPC, the geometric progression in Table 4 would have been

1 1 MPC 1 1MPC22 1 1MPC23 1 . . .

This progression uses the MPC as its common ratio. Applying the same formula for summing a geometric progression to this more general case gives us the following general result:

Oversimplified Multiplier Formula

1

Multiplier 5 1 2 MPC

We call this formula “oversimplified” because it ignores many factors that are important in the real world. You can begin to appreciate just how unrealistic the oversimplified formula is by considering some real numbers for the U.S. economy. The MPC is over 0.95. From our oversimplified formula, then, it would seem that the multiplier

should be at least

1 1 Multiplier 5 1 2 0.95 5 0.05 5 20

In fact, the actual multiplier for the U.S. economy is less than 2. That is quite a discrepancy!

5Students who blanch at the sight of algebra should not be put off. Anyone who can balance a checkbook (even many who cannot!) will be able to follow the argument.

6If R exceeds 1, no one can possibly sum it—not even with the aid of a modern computer—because the sum is not a finite number.

7The proof of the formula is simple. Let the symbol S stand for the (unknown) sum of the series:

S 5 1 1 R 1 R2 1 R3 1 . . .

Then, multiplying by R,

RS 5 R 1 R2 1 R3 1 R4 1 . . .

By subtracting RS from S, we obtain

1

S 2 RS 5 1 or S 5 1 2 R

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

NOTE: Figures are in billions of dollars per year.

LICENSED TO:

CHAPTER 9

Demand-Side Equilibrium: Unemployment or Inflation?

189

But this discrepancy does not mean that anything we have said about the multiplier so far is incorrect. Our story is simply incomplete. As we progress through this and subsequent chapters, you will learn why the multiplier in the United States is less than 2 even though the country’s MPC is over 0.95. One such reason relates to international trade—in particular, the fact that a country’s imports depend on its GDP. We deal with this complication in Appendix B to this chapter. A second factor is inflation, a complication we will address in the next chapter. A third factor is income taxation, a point we will elaborate in Chapter 11. The last important reason arises from the financial system and, after we discuss money and banking in Chapters 12 and 13, we will explain in Chapter 14 how the financial system influences the multiplier. As you will see, each of these factors reduces the size of the multiplier. So:

Although the multiplier is larger than 1 in the real world, it cannot be calculated accurately with the oversimplified multiplier formula. The actual multiplier is much lower than the formula suggests.

THE MULTIPLIER IS A GENERAL CONCEPT

Although we have used business investment to illustrate the workings of the multiplier, it should be clear from the logic that any increase in spending can kick off a multiplier chain. To see how the multiplier works when the process is initiated by an upsurge in consumer spending, we must distinguish between two types of change in consumer spending.

	To do so, look back at Figure 4 on page 181. When C rises because income rises—that
	is, when consumers move outward along a fixed consumption function—we call the increase								An induced increase
	in C an induced increase in consumption. (See the brick-colored arrows in the figure.)
									in consumption is an
	When C rises because the entire consumption function shifts upward (such as from C0 to C2								increase in consumer
	in the figure), we call it an autonomous increase in consumption. The name indicates that								spending that stems from
	consumption changes independently of income. The discussion of the consumption func-								an increase in consumer in-
	tion in Chapter 8 pointed out that a number of events, such as a change in the value of the								comes. It is represented on
									a graph as a movement
	stock market, can initiate such a shift.
									along a fixed consumption
	If consumer spending were to rise autonomously by $200 billion, we would revise our
									function.
	table of aggregate demand to look like Table 5. Comparing this new table to Table 3, we
	note that each entry in column 2 is $200 billion higher than the corresponding entry in								An autonomous increase
	Table 3 (because consumption is higher), and each entry in column 3 is $200 billion lower								in consumption is an in-
									crease in consumer spend-
	(because in this case investment is only $900 billion).
									ing without any increase in
	Column 6, the expenditure schedule, is identical in both tables, so the equilibrium level
									consumer incomes. It is
	of income is clearly Y 5 $6,800 billion once again. The initial rise of $200 billion in con-
									represented on a graph
	sumer spending leads to an eventual rise of $800 billion in GDP, just as it did in the case of
									as a shift of the entire
	higher investment spending. In fact, Figure 10 (page 186) applies directly to this case once								consumption function.
	we note that the upward shift is now caused by an au-
	tonomous change in C rather than in I. The multiplier
				TABLE 5
	for autonomous changes in consumer spending, then,
				Total Expenditure after Consumers Decide to Spend
	is also 4 (5 $800/$200).
				$200 Billion More
	The reason is straightforward. It does not matter
				(1)	(2)	(3)		(4)	(5)	(6)
	who injects an additional dollar of spending into the
								Government
	economy—business investors or consumers. Whatever
				Income	Consumption	Investment		Purchases	Net Exports	Total
	the source of the extra dollar, 75 percent of it will be
				(Y )	(C )	(I )		(G)	(X 2 IM)	Expenditure
	respent if the MPC is 0.75, and the recipients of this
				4,800	3,200	900		1,300	2100	5,300
	second round of spending will, in turn, spend 75 per-
				5,200	3,500	900		1,300	2100	5,600
	cent of their additional income, and so on. That contin-
				5,600	3,800	900		1,300	2100	5,900
	ued spending constitutes the multiplier process. Thus			6,000	4,100	900		1,300	2100	6,200
	a $200 billion increase in government purchases (G) or			6,400	4,400	900		1,300	2100	6,500
	in net exports (X 2 IM) would have the same multi-			6,800	4,700	900		1,300	2100	6,800
				7,200	5,000	900		1,300	2100	7,100
	plier effect as depicted in Figure 10. The multipliers

are identical because the logic behind them is identical.

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

190

PART 2

The Macroeconomy: Aggregate Supply and Demand

The idea that changes in G have multiplier effects on GDP will play a central role in the discussion of government stabilization policy that begins in Chapter 11. So it is worth noting here that

Changes in the volume of government purchases of goods and services will change the equilibrium level of GDP on the demand side in the same direction, but by a multiplied amount.

To cite a recent example, heavy federal government spending on the war in Iraq since 2003 has boosted the G component of C 1 I 1 G 1 (X 2 IM), which had a multiplier effect on GDP.

				Applying the same multiplier idea to exports and imports teaches us another important
				lesson: Booms and recessions tend to be transmitted across national borders. Why is that? Sup-
				pose a boom abroad raises GDPs in foreign countries. With rising incomes, foreigners will
				buy more American goods—which means that U.S. exports will increase. But an increase
	FIGURE 12
				in our exports will, via the multiplier, raise GDP in the United States. By this mechanism,
	Two View of the
								rapid economic growth abroad con-
	Multiplier
								tributes to rapid economic growth here.
								And, of course, the same mechanism
					45°			also operates in reverse. Thus:
						C + I1 + G + (X – IM )		The GDPs of the major economies
				E1		C + I0 + G + (X – IM )		are linked by trade. A boom in one
								country tends to raise its imports and
								hence push up exports and GDP in
	Expenditure							other countries. Similarly, a recession
								in one country tends to pull down
								GDP in other countries.
		$200 billion
	Real			E0
								THE MULTIPLIER AND
								THE AGGREGATE
								DEMAND CURVE

	0	6,000	6,800			One last mechanical point about the mul-
						tiplier: Recall that income-expenditure
						diagrams such as Figure 3 (page 179) can
						be drawn only for a given price level.
	D0	D1				Different price levels lead to different to-
						tal expenditure curves. This means that
						our oversimplified multiplier formula in-
						dicates the increase in real GDP demanded
						that would occur if the price level were fixed.
Level						Graphically, this means that it measures
						the horizontal shift of the economy’s ag-
Price		E0		E1		gregate demand curve.
	100					Figure 12 illustrates this conclusion
				D1	(I = $1,100)	by supposing that the price level that
						underlies Figure 3 is P 5 100. The top
			D0	(I = $900)		panel simply repeats Figure 10 (page
						186) and shows how an increase in in-
						vestment spending from $900 to $1,100
		6,000	6,800			billion leads to an increase in GDP from
						$6,000 to $6,800 billion.
			Real GDP			The bottom panel shows two
						downward-sloping aggregate demand
NOTE: Figures are in billions of dollars per year.						curves. The first, labeled D0D0, depicts

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

CHAPTER 9

Demand-Side Equilibrium: Unemployment or Inflation?

191

the situation when investment is $900 billion. Point E0 on this curve corresponds exactly to point E0 in the top panel. It indicates that, at the given price level (P 5 100), the equilibrium quantity of GDP demanded is $6,000 billion. The second aggregate demand curve, D1D1, depicts the situation after investment has risen to $1,100 billion. Point E1 on this curve indicates that the equilibrium quantity of GDP demanded when P 5 100 has risen to $6,800 billion, which corresponds exactly to point E1 in the top panel.

As Figure 12 shows, the horizontal distance between the two aggregate demand curves is exactly equal to the increase in real GDP shown in the income-expenditure diagram—in this case, $800 billion. Thus:

An autonomous increase in spending leads to a horizontal shift of the aggregate demand curve by an amount given by the oversimplified multiplier formula.

So everything we have just learned about the multiplier applies to shifts of the economy’s aggregate demand curve. If businesses decide to increase their investment spending, if the consumption function shifts upward, or if the government or foreigners decide to buy more goods, then the aggregate demand curve moves horizontally to the right—as indicated in Figure 12. If any of these variables moves downward instead, the aggregate demand curve moves horizontally to the left.

Thus, the economy’s aggregate demand curve cannot be expected to stand still for long. Autonomous changes in one or another of the four components of total spending will cause it to move around. But to understand the consequences of such shifts of aggregate demand, we must bring the aggregate supply curve back into the picture. That is the task for the next chapter.

| SUMMARY |

1.The equilibrium level of GDP on the demand side is the level at which total spending just equals production. Because total spending is the sum of consumption, investment, government purchases, and net exports, the condition for equilibrium is Y 5 C 1 I 1 G 1 (X 2 IM).

2.Output levels below equilibrium are bound to rise because when spending exceeds output, firms will see their inventory stocks being depleted and will react by stepping up production.

3.Output levels above equilibrium are bound to fall because when total spending is insufficient to absorb total output, inventories will pile up and firms will react by curtailing production.

4.The determination of the equilibrium level of GDP on the demand side can be portrayed on a convenient income-expenditure diagram as the point at which the expenditure schedule—defined as the sum of C 1 I 1

G 1 (X 2 IM)—crosses the 45° line. The 45° line is significant because it marks off points at which spending and output are equal—that is, at which Y 5 C 1 I 1 G 1 (X 2 IM), which is the basic condition for equilibrium.

5.An income-expenditure diagram can be drawn only for a specific price level. Thus, the equilibrium GDP so determined depends on the price level.

6.Because higher prices reduce the purchasing power of consumers’ wealth, they reduce total expenditures on the 45o line diagram. Equilibrium real GDP demanded is therefore lower when prices are higher. This downward-sloping relationship is known as the aggregate demand curve.

7.Equilibrium GDP can be above or below potential GDP, which is defined as the GDP that would be produced if the labor force were fully employed.

8.If equilibrium GDP exceeds potential GDP, the difference is called an inflationary gap. If equilibrium GDP falls short of potential GDP, the resulting difference is called a recessionary gap.

9.Such gaps can occur because of the problem of coordination failure: The saving that consumers want to do at full-employment income levels may differ from the investing that investors want to do.

10.Any autonomous increase in expenditure has a multiplier effect on GDP; that is, it increases GDP by more than the original increase in spending.

11.The multiplier effect occurs because one person’s additional expenditure constitutes a new source of income for another person, and this additional income leads to still more spending, and so on.

12.The multiplier is the same for an autonomous increase in consumption, investment, government purchases, or net exports.

13.A simple formula for the multiplier says that its numerical value is 1/(1 2 MPC). This formula is too simple to give accurate results, however.

14.Rapid (or sluggish) economic growth in one country contributes to rapid (or sluggish) growth in other countries because one country’s imports are other countries’ exports.

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

192 PART 2 The Macroeconomy: Aggregate Supply and Demand

| KEY TERMS |

	Equilibrium 176			Full-employment level of GDP			Multiplier 185
	Expenditure schedule	179		(or potential GDP)		182	Induced increase in
	Induced investment	179		Recessionary gap	183		consumption	189
	Y 5 C 1 I 1 G 1 (X 2 IM)		179	Inflationary gap	183		Autonomous increase in
							consumption	189
	Income-expenditure (or 45° line)			Coordination of saving and
				investment 183-184
	diagram 180
	Aggregate demand curve		180	Coordination failure		184

| TEST YOURSELF |

1.From the following data, construct an expenditure schedule on a piece of graph paper. Then use the income-expenditure (45° line) diagram to determine the equilibrium level of GDP.

				Government	Net
	Income	Consumption	Investment	Purchases	Exports
	$3,600	$3,220	$240	$120	$40
	3,700	3,310	240	120	40
	3,800	3,400	240	120	40
	3,900	3,490	240	120	40
4,000		3,580	240	120	40

Now suppose investment spending rises to $260, and the price level is fixed. By how much will equilibrium GDP increase? Derive the answer both numerically and graphically.

2.From the following data, construct an expenditure schedule on a piece of graph paper. Then use the income-expenditure (45° line) diagram to determine the equilibrium level of GDP. Compare your answer with your answer to the previous question.

				Government	Net
	Income	Consumption	Investment	Purchases	Exports
	$3,600	$3,280	$180	$120	$40
	3,700	3,340	210	120	40
	3,800	3,400	240	120	40
	3,900	3,460	270	120	40
4,000		3,520	300	120	40

3.Suppose that investment spending is always $250, government purchases are $100, net exports are always $50, and consumer spending depends on the price level in the following way:

Price	Consumer
Level	Spending
90	$740
95	720
100	700
105	680
110	660

On a piece of graph paper, use these data to construct an aggregate demand curve. Why do you think this example supposes that consumption declines as the price level rises?

4.(More difficult)8 Consider an economy in which the consumption function takes the following simple algebraic form:

C 5 300 1 0.75DI

and in which investment (I) is always $900 and net exports are always 2$100. Government purchases are fixed at $1,300 and taxes are fixed at $1,200. Find the equilibrium level of GDP, and then compare your answer to Table 1 and Figure 2. (Hint: Remember that disposable income is GDP minus taxes: DI 5 Y 2 T 5 Y 2 1,200.)

5.(More difficult) Keep everything the same as in Test Yourself Question 4 except change investment to I 5 $1,100. Use the equilibrium condition Y 5 C 1 I 1 G 1 (X 2 IM) to find the equilibrium level of GDP on the demand side. (In working out the answer, assume the price level is fixed.) Compare your answer to Table 3 and Figure 10. Now compare your answer to the answer to Test Yourself Question 4. What do you learn about the multiplier?

6.(More difficult) An economy has the following consumption function:

C 5 200 1 0.8DI

The government budget is balanced, with government purchases and taxes both fixed at $1,000. Net exports are $100. Investment is $600. Find equilibrium GDP.

What is the multiplier for this economy? If G rises by $100, what happens to Y? What happens to Y if both G and T rise by $100 at the same time?

8 The answer to this question is provided in Appendix A to this chapter.

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

CHAPTER 9

Demand-Side Equilibrium: Unemployment or Inflation?

193

7.Use both numerical and graphical methods to find the multiplier effect of the following shift in the consumption function in an economy in which investment is always $220, government purchases are always $100, and net exports are always 2$40. (Hint: What is the marginal propensity to consume?)

		Consumption	Consumption
	Income	before Shift	after Shift
	$1,080	$ 880	$ 920
	1,140	920	960
	1,200	960	1,000
	1,260	1,000	1,040
	1,320	1,040	1,080
	1,380	1,080	1,120
	1,440	1,120	1,160
	1,500	1,160	1,200
1,560		1,200	1,240

| DISCUSSION QUESTIONS |

1.For over 25 years now, imports have consistently exceeded exports in the U.S. economy. Many people consider this imbalance to be a major problem. Does this chapter give you any hints about why? (You may want to discuss this issue with your instructor. You will learn more about it in later chapters.)

2.Look back at the income-expenditure diagram in Figure 3 (page 179) and explain why some level of real GDP other than $6,000 (say, $5,000 or $7,000) is not an equilibrium on the demand side of the economy. Do not

give a mechanical answer to this question. Explain the economic mechanism involved.

3.Does the economy this year seem to have an inflationary gap or a recessionary gap? (If you do not know the answer from reading the newspaper, ask your instructor.)

4.Try to remember where you last spent a dollar. Explain how this dollar will lead to a multiplier chain of increased income and spending. (Who received the dollar? What will he or she do with it?)

| APPENDIX A | The Simple Algebra of Income Determination and the Multiplier

The model of demand-side equilibrium that the chapter presented graphically and in tabular form can also be handled with some simple algebra. Written as an equation, the consumption function in our example is

C 5 300 1 0.75DI

5 300 1 0.75(Y 2 T )

because, by definition, DI 5 Y 2 T. This is simply the equation of a straight line with a slope of 0.75 and an intercept of 300 2 0.75T. Because T 5 1,200 in our example, the intercept is 2600 and the equation can be written more simply as follows:

C 5 2600 1 0.75Y

Investment in the example was assumed to be 900, regardless of the level of income, government purchases were 1,300, and net exports were 2100. So the sum C 1 I 1 G 1 (X 2 IM) is

C 1 I 1 G 1 (X 2 IM) 5 2600 1 0.75Y 1 900 1 1,300 2 100

5 1,500 1 0.75Y

This equation describes the expenditure curve in Figure 3. Because the equilibrium quantity of GDP demanded is defined by

Y 5 C 1 I 1 G 1 (X 2 IM)

we can solve for the equilibrium value of Y by substituting 1,500 1 0.75Y for C 1 I 1 G 1 (X 2 IM) to get

Y 5 1,500 1 0.75Y

To solve this equation for Y, first subtract 0.75Y from both sides to get

0.25Y 5 1,500

Then divide both sides by 0.25 to obtain the answer:

Y 5 6,000

This, of course, is precisely the solution we found by graphical and tabular methods in the chapter.

We can easily generalize this algebraic approach to deal with any set of numbers in our equations. Suppose that the consumption function is as follows:

C 5 a 1 bDI 5 a 1 b(Y 2 T )

(In the example, a 5 300, T 5 1,200, and b 5 0.75.) Then the equilibrium condition that Y 5 C 1 I 1 G 1 (X 2 IM) implies that

Y 5 a 1 bDI 1 I 1 G 1 (X 2 IM)

5 a 2 bT 1 bY 1 I 1 G 1 (X 2 IM)

Subtracting bY from both sides leads to

(1 2 b)Y 5 a 2 bT 1 I 1 G 1 (X 2 IM)

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

194

PART 2

The Macroeconomy: Aggregate Supply and Demand

and dividing through by 1 2 b gives

a 2 bT 1 I 1 G 1 1X 2 IM2

Y 5

1 2 b

This formula is valid for any numerical values of a, b, T, G, I, and (X 2 IM) (so long as b is between 0 and 1).

From this formula, it is easy to derive the oversimplified multiplier formula algebraically and to show that it applies equally well to a change in investment, autonomous consumer spending, government purchases, or net exports. To do so, suppose that any of the symbols in the numerator of the multiplier formula increases by one unit. Then GDP would rise from the previous formula to

a 2 bT 1 I 1 G 1 1X 2 IM2 1 1

Y 5

1 2 b

By comparing this expression with the previous expression for Y, we see that a one-unit change in any component of spending changes equilibrium GDP by

a 2 bT 1 I 1 G 1 1X 2 IM2 1 1

Change in Y 5

1 2 b

a 2 bT 1 I 1 G 1 1X 2 IM2

2

1 2 b

or

1 Change in Y 5 1 2 b

Recalling that b is the marginal propensity to consume, we see that this is precisely the oversimplified multiplier formula.

| TEST YOURSELF |

1.Find the equilibrium level of GDP demanded in an economy in which investment is always $300, net exports are always 2$50, the government budget is balanced with purchases and taxes both equal to $400, and the consumption function is described by the following algebraic equation:

C 5 150 1 0.75DI

(Hint: Do not forget that DI 5 Y 2 T.)

2.Referring to Test Yourself Question 1, do the same for an economy in which investment is $250, net exports are 0, government purchases and taxes are both $400, and the consumption function is as follows:

C 5 250 1 0.5DI

3.In each of these cases, how much saving is there in equilibrium? (Hint: Income not consumed must be saved.) Is saving equal to investment?

4.Imagine an economy in which consumer expenditure is represented by the following equation:

C 5 50 1 0.75DI

Imagine also that investors want to spend $500 at every level of income (I 5 $500), net exports are 0 (X 2 IM 5 0), government purchases are $300, and taxes are $200.

a.What is the equilibrium level of GDP?

b.If potential GDP is $3,000, is there a recessionary or inflationary gap? If so, how much?

c.What will happen to the equilibrium level of GDP if investors become optimistic about the country’s future and raise their investment to $600?

d.After investment has increased to $600, is there a recessionary or inflationary gap? How much?

5.Fredonia has the following consumption function:

C 5 100 1 0.8DI

Firms in Fredonia always invest $700 and net exports are 0, initially. The government budget is balanced with spending and taxes both equal to $500.

a.Find the equilibrium level of GDP.

b.How much is saved? Is saving equal to investment?

c.Now suppose that an export-promotion drive succeeds in raising net exports to $100. Answer (a) and

(b) under these new circumstances.

| DISCUSSION QUESTIONS |

1.Explain the basic logic behind the multiplier in words. Why does it require b, the marginal propensity to consume, to be between 0 and 1?

2.(More difficult) What would happen to the multiplier analysis if b 5 0? If b 5 1?

| APPENDIX B | The Multiplier with Variable Imports

In the chapter, we assumed that net exports were a fixed number, 2100 in the example. In fact, a nation’s imports vary along with its GDP for a simple reason:

Higher GDP leads to higher incomes, some of which is spent on foreign goods. Thus:

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

CHAPTER 9

Demand-Side Equilibrium: Unemployment or Inflation?

195

Our imports rise as our GDP rises and fall as our GDP falls.

Similarly, our exports are the imports of other countries, so it is to be expected that our exports depend on their GDPs, not on our own. Thus:

Our exports are relatively insensitive to our own GDP, but are quite sensitive to the GDPs of other countries.

This appendix derives the implications of these rather elementary observations. In particular, it shows

TABLE 6

that once we recognize the dependence of a nation’s imports on its GDP,

International trade lowers the value of the multiplier.

To see why, we begin with Table 6, which adapts the example of our hypothetical economy to allow imports to depend on GDP. Columns 1 through 4 are the same as in Table 1; they show C, I, and G at alternative levels of GDP. Columns 5 and 6 record revised assumptions about the behavior of exports and imports.

Equilibrium Income with Variable Imports

(1)		(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Gross
	Domestic	Consumer		Government			Net	Total
	Product	Expenditures	Investment	Purchases	Exports	Imports	Exports	Expenditure
	(Y)	(C)	(I)	(G)	(X)	(IM)	(X 2 IM)	(C 1 I 1 G 1 [X 2 IM])
	4,800	3,000	900	1,300	650	570	180	5,280
	5,200	3,300	900	1,300	650	630	120	5,520
	5,600	3,600	900	1,300	650	690	240	5,760
	6,000	3,900	900	1,300	650	750	2100	6,000
	6,400	4,200	900	1,300	650	810	2160	6,240
	6,800	4,500	900	1,300	650	870	2220	6,480
7,200		4,800	900	1,300	650	930	2280	6,720

NOTE: Figures are in billions of dollars per year.

FIGURE 13

The Dependence of Net Exports on GDP

	950							IM
Imports	850
	750					Negative net
							exports
and
	650
Exports		Positive net						X
	550	exports
Real	450
	0	4,800 5,200		5,600	6,000	6,400	6,800	7,200
				Real GDP
	200
Exports	100Positive net
	0	exports
		4,800			6,000	6,400	6,800	7,200
			5,200
Net
	–100			5,600			Negative net
Real							exports
	–200
	–300							X – IM
				Real GDP

NOTE: Figures are in billions of dollars per year.

Exports are fixed at $650 billion regardless of GDP. But imports are assumed to rise by $60 billion for every $400 billion rise in GDP, which is a simple numerical example of the idea that imports depend on GDP. Column 7 subtracts imports from exports to get net exports, (X 2 IM), and column 8 adds up the four components of total expenditure, C 1 I 1 G 1 (X 2 IM). The equilibrium, you can see, occurs at Y 5 $6,000 billion, just as it did in the chapter.

Figures 13 and 14 display the same conclusion graphically. The upper panel of Figure 13 shows that exports are fixed at $650 billion regardless of GDP, whereas imports increase as GDP rises, just as in Table 6. The difference between exports and imports, or net exports, is positive until GDP approaches $5,300 billion, and negative once GDP surpasses that amount. The bottom panel of Figure 13 shows the subtraction explicitly by displaying net exports. It shows clearly that

Net exports decline as GDP rises.

Figure 14 carries this analysis over to the 45° line diagram. We begin with the familiar C 1 I 1 G 1 (X 2 IM) line in

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

LICENSED TO:

196

PART 2

The Macroeconomy: Aggregate Supply and Demand

FIGURE 14

Equilibrium GDP with Variable Imports

	45	C + I + G + (X – IM )
		(fixed imports)
		C + I + G + (X – IM )
Real Expenditure	E	(variable imports)
Positive net
exports	Negative net exports
	6,000	X – IM
	Real GDP

FIGURE 15

The Multiplier with Variable Imports

		45
		C + I + G + (X1 – IM )
		A
		C + I + G + (X0 – IM )
Real Expenditure	Rise in
	exports = $160
	E
		Rise in GDP = $400
	6,000	6,400
		Real GDP

TABLE 7

Equilibrium Income after a $160 Billion Increase in Exports

(1)		(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Gross
	Domestic	Consumer		Government			Net	Total
	Product	Expenditures	Investment	Purchases	Exports	Imports	Exports	Expenditure
	(Y)	(C)	(I)	(G)	(X)	(IM)	(X 2 IM)	(C 1 I 1 G 1 [X 2 IM])
	4,800	3,000	900	1,300	810	570	1240	5,440
	5,200	3,300	900	1,300	810	630	1180	5,680
	5,600	3,600	900	1,300	810	690	1120	5,920
	6,000	3,900	900	1,300	810	750	160	6,160
	6,400	4,200	900	1,300	810	810	0	6,400
	6,800	4,500	900	1,300	810	870	260	6,640
7,200		4,800	900	1,300	180	930	2120	6,800

NOTE: Figures are in billions of dollars per year.

black. Previously, we simply assumed that net exports were fixed at 2$100 billion regardless of GDP. Now that we have amended our model to note that net exports decline as GDP rises, the sum C 1 I 1 G 1 (X 2 IM) rises more slowly than we previously assumed. This change is shown by the brick-colored line. Note that it is less steep than the black line.

Let us now consider what happens if exports rise by $160 billion while imports remain as in Table 6. Table 7 shows that equilibrium now occurs at a GDP of Y 5 $6,400 billion. Naturally, higher exports have raised domestic GDP. But consider the magnitude. A $160 billion increase in exports (from $650 billion to $810 billion) leads to an increase of $400 billion in GDP (from $6,000 billion to $6,400 billion). So the multiplier is 2.5 (5 $400/$160).9

9 Exercise: Construct a version of Table 6 to show what would happen if imports rose by $160 billion at every level of GDP while exports remained at $650 billion. You should be able to show that the new equilibrium would be Y 5 $5,600.

This same conclusion is shown graphically in Figure 15, where the line C 1 I 1 G 1 (X0 2 IM) represents the original expenditure schedule and the line C 1 I 1 G 1 (X1 2 IM) represents the expenditure schedule after the $160 billion increase in exports. Equilibrium shifts from point E to point A, and GDP rises by $400 billion.

Notice that the multiplier in this example is 2.5, whereas in the chapter, with net exports taken to be a fixed number, it was 4. This simple example illustrates a general result: International trade lowers the numerical value of the multiplier. Why is this so? Because, in an open economy, any autonomous increase in spending is partly dissipated in purchases of foreign goods, which creates additional income for foreigners rather than for domestic citizens.

Thus, international trade gives us the first of what will eventually be several reasons why the oversimplified multiplier formula overstates the true value of the multiplier.

Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.