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expenditure schedule”defined as the sum of C 1 I 1 for another person, and this additional income leads to
G 1 (X 2 IM)”crosses the 45° line. The 45° 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 equal”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
sumers™ 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 country™s imports are other countries™
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 45° 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 (45° 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 (45° 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 country™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

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