ñòð. 58 |

G 1 (X 2 IM)â€”crosses the 45Â° line. The 45Â° line is signif- still more spending, and so on.

icant because it marks off points at which spending and

12. The multiplier is the same for an autonomous increase

output are equalâ€”that is, at which Y 5 C 1 I 1 G 1

in consumption, investment, government purchases, or

(X 2 IM), which is the basic condition for equilibrium.

net exports.

5. An income-expenditure diagram can be drawn only for

13. A simple formula for the multiplier says that its numeri-

a specific price level. Thus, the equilibrium GDP so de-

cal value is 1/(1 2 MPC). This formula is too simple to

termined depends on the price level.

give accurate results, however.

6. Because higher prices reduce the purchasing power of con-

14. Rapid (or sluggish) economic growth in one country

sumersâ€™ wealth, they reduce total expenditures on the 45o

contributes to rapid (or sluggish) growth in other coun-

line diagram. Equilibrium real GDP demanded is therefore

tries because one countryâ€™s imports are other countriesâ€™

lower when prices are higher. This downward-sloping re-

exports.

lationship is known as the aggregate demand curve.

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

Licensed to:

Part 2

192 The Macroeconomy: Aggregate Supply and Demand

| KEY TERMS |

Equilibrium 176 Full-employment level of GDP Multiplier 185

(or potential GDP) 182

Expenditure schedule 179 Induced increase in

Recessionary gap 183 consumption 189

Induced investment 179

Inflationary gap 183 Autonomous increase in

Y 5 C 1 I 1 G 1 (X 2 IM) 179

consumption 189

Coordination of saving and

Income-expenditure (or 45Â° line)

investment 183-184

diagram 180

Coordination failure 184

Aggregate demand curve 180

| TEST YOURSELF |

1. From the following data, construct an expenditure On a piece of graph paper, use these data to construct an

schedule on a piece of graph paper. Then use the aggregate demand curve. Why do you think this exam-

income-expenditure (45Â° line) diagram to determine the ple supposes that consumption declines as the price

equilibrium level of GDP. level rises?

4. (More difficult)8 Consider an economy in which the

Government Net consumption function takes the following simple alge-

Income Consumption Investment Purchases Exports braic form:

$3,600 $3,220 $240 $120 $40

C 5 300 1 0.75DI

3,700 3,310 240 120 40

3,800 3,400 240 120 40

and in which investment (I) is always $900 and net ex-

3,900 3,490 240 120 40

ports are always 2$100. Government purchases are

4,000 3,580 240 120 40

fixed at $1,300 and taxes are fixed at $1,200. Find the

equilibrium level of GDP, and then compare your

Now suppose investment spending rises to $260, and answer to Table 1 and Figure 2. (Hint: Remember that

the price level is fixed. By how much will equilibrium disposable income is GDP minus taxes: DI 5 Y 2 T 5

GDP increase? Derive the answer both numerically and Y 2 1,200.)

graphically.

5. (More difficult) Keep everything the same as in Test

2. From the following data, construct an expenditure Yourself Question 4 except change investment to I 5

schedule on a piece of graph paper. Then use the $1,100. Use the equilibrium condition Y 5 C 1 I 1 G 1

income-expenditure (45Â° line) diagram to determine the (X 2 IM) to find the equilibrium level of GDP on the de-

equilibrium level of GDP. Compare your answer with mand side. (In working out the answer, assume the price

your answer to the previous question. 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

Government Net

multiplier?

Income Consumption Investment Purchases Exports

6. (More difficult) An economy has the following con-

$3,600 $3,280 $180 $120 $40

sumption function:

3,700 3,340 210 120 40

3,800 3,400 240 120 40

C 5 200 1 0.8DI

3,900 3,460 270 120 40

4,000 3,520 300 120 40

The government budget is balanced, with government

purchases and taxes both fixed at $1,000. Net exports are

3. Suppose that investment spending is always $250, gov- $100. Investment is $600. Find equilibrium GDP.

ernment purchases are $100, net exports are always $50, What is the multiplier for this economy? If G rises by

and consumer spending depends on the price level in $100, what happens to Y? What happens to Y if both G

the following way: and T rise by $100 at the same time?

Price Consumer

Level Spending

90 $740

95 720

100 700

105 680

110 660 The answer to this question is provided in Appendix A to this

8

chapter.

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

Licensed to:

Chapter 9 193

Demand-Side Equilibrium: Unemployment or Inflation?

7. Use both numerical and graphical methods to find the

Consumption Consumption

multiplier effect of the following shift in the consump-

Income before Shift after Shift

tion function in an economy in which investment is

$1,080 $ 880 $ 920

always $220, government purchases are always $100,

1,140 920 960

and net exports are always 2$40. (Hint: What is the mar-

1,200 960 1,000

ginal propensity to consume?)

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 ex- give a mechanical answer to this question. Explain the

ceeded exports in the U.S. economy. Many people con- economic mechanism involved.

sider this imbalance to be a major problem. Does this 3. Does the economy this year seem to have an inflationary

chapter give you any hints about why? (You may want gap or a recessionary gap? (If you do not know the an-

to discuss this issue with your instructor. You will learn swer from reading the newspaper, ask your instructor.)

more about it in later chapters.)

4. Try to remember where you last spent a dollar. Explain

2. Look back at the income-expenditure diagram in how this dollar will lead to a multiplier chain of in-

Figure 3 (page 179) and explain why some level of real creased income and spending. (Who received the dollar?

GDP other than $6,000 (say, $5,000 or $7,000) is not an What will he or she do with it?)

equilibrium on the demand side of the economy. Do not

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

we can solve for the equilibrium value of Y by substi-

The model of demand-side equilibrium that the chap-

tuting 1,500 1 0.75Y for C 1 I 1 G 1 (X 2 IM) to get

ter presented graphically and in tabular form can also

be handled with some simple algebra. Written as an

Y 5 1,500 1 0.75Y

equation, the consumption function in our example is

To solve this equation for Y, first subtract 0.75Y

C 5 300 1 0.75DI

from both sides to get

5 300 1 0.75(Y 2 T)

0.25Y 5 1,500

because, by definition, DI 5 Y 2 T. This is simply the

Then divide both sides by 0.25 to obtain the answer:

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 ex- Y 5 6,000

ample, the intercept is 2600 and the equation can be

This, of course, is precisely the solution we found by

written more simply as follows:

graphical and tabular methods in the chapter.

C 5 2600 1 0.75Y We can easily generalize this algebraic approach to

deal with any set of numbers in our equations. Sup-

Investment in the example was assumed to be 900,

pose that the consumption function is as follows:

regardless of the level of income, government pur-

chases were 1,300, and net exports were 2100. So the C 5 a 1 bDI 5 a 1 b(Y 2 T )

sum C 1 I 1 G 1 (X 2 IM) is

(In the example, a 5 300, T 5 1,200, and b 5 0.75.)

C 1 I 1 G 1 (X 2 IM) 5 2600 1 0.75Y 1 900 Then the equilibrium condition that Y 5 C 1 I 1 G 1

1 1,300 2 100 (X 2 IM) implies that

5 1,500 1 0.75Y

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

This equation describes the expenditure curve in 5 a 2 bT 1 bY 1 I 1 G 1 (X 2 IM)

Figure 3. Because the equilibrium quantity of GDP de-

Subtracting bY from both sides leads to

manded is defined by

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

Y 5 C 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:

Part 2

194 The Macroeconomy: Aggregate Supply and Demand

By comparing this expression with the previous ex-

and dividing through by 1 2 b gives

pression for Y, we see that a one-unit change in any

a 2 bT 1 I 1 G 1 1 X 2 IM 2

component of spending changes equilibrium GDP by

Y5

12b

a 2 bT 1 I 1 G 1 1 X 2 IM 2 1 1

Change in Y 5

This formula is valid for any numerical values of a, b,

12b

T, G, I, and (X 2 IM) (so long as b is between 0 and 1).

a 2 bT 1 I 1 G 1 1 X 2 IM 2

From this formula, it is easy to derive the oversim- 2

12b

plified multiplier formula algebraically and to show

that it applies equally well to a change in investment, or

autonomous consumer spending, government pur- 1

Change in Y 5

chases, or net exports. To do so, suppose that any of 12b

the symbols in the numerator of the multiplier for-

Recalling that b is the marginal propensity to con-

mula increases by one unit. Then GDP would rise

sume, we see that this is precisely the oversimplified

from the previous formula to

multiplier formula.

a 2 bT 1 I 1 G 1 1 X 2 IM 2 1 1

Y5

12b

| TEST YOURSELF |

1. Find the equilibrium level of GDP demanded in an econ- Imagine also that investors want to spend $500 at every

level of income (I 5 $500), net exports are 0 (X 2 IM

omy in which investment is always $300, net exports are

always 2$50, the government budget is balanced with 5 0), government purchases are $300, and taxes are

purchases and taxes both equal to $400, and the con- $200.

sumption function is described by the following alge- a. What is the equilibrium level of GDP?

braic equation:

b. If potential GDP is $3,000, is there a recessionary or

inflationary gap? If so, how much?

C 5 150 1 0.75DI

c. What will happen to the equilibrium level of GDP if

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

investors become optimistic about the countryâ€™s fu-

2. Referring to Test Yourself Question 1, do the same for an ture and raise their investment to $600?

economy in which investment is $250, net exports are 0,

d. After investment has increased to $600, is there a re-

government purchases and taxes are both $400, and the

cessionary or inflationary gap? How much?

consumption function is as follows:

5. Fredonia has the following consumption function:

C 5 250 1 0.5DI

C 5 100 1 0.8DI

3. In each of these cases, how much saving is there in equi-

Firms in Fredonia always invest $700 and net exports

librium? (Hint: Income not consumed must be saved.) Is

are 0, initially. The government budget is balanced with

saving equal to investment?

spending and taxes both equal to $500.

4. Imagine an economy in which consumer expenditure is

a. Find the equilibrium level of GDP.

represented by the following equation:

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

C 5 50 1 0.75DI

c. Now suppose that an export-promotion drive suc-

ceeds in raising net exports to $100. Answer (a) and

ñòð. 58 |