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Unformatted text preview: Chapter 3 National income: Where It Comes From and Where It Goes 17 7. The effect of a government tax increase of $100 billion on (a) public saving, (b) private
saving, and (c) national saving can be analyzed by using the following relationships: National Saving = [Private Saving] + [Public Saving]
= [Y— T— C(Y— T)] + [T— G]
= Y— C(Y— T) ~ G. a. Public Saving—The tax increase causes a 1for—1 increase in public saving. T
increases by $100 billion and, therefore, public saving increases by $100 billion. b. Private Saving——The increase in taxes decreases disposable income, Y — T, by
$100 billion. Since the marginal propensity to consume (MP0) is 0.6, consumption
falls by 0.6 x $100 billion, or $60 billion. Hence, APrivate Saving = — $1001) — 0.6 (— $10013) = — $4013. Private saving falls $40 billion. 0. National Saving—Because national saving is the sum of private and public sav
ing, we can conclude that the $100 billion tax increase leads to a $60 billion
increase in national saving. Another way to see this is by using the third equation for national saving
expressed above, that national saving equals Y — C(Y — T) — G. The $100 billion
tax increase reduces disposable income and causes consumption to fall by $60 bil
lion. Since neither G nor Y changes, national saving thus rises by $60 billion. d. Investment—To determine the effect of the tax increase on investment, recall the
national accounts identity: in Y: C(Y— T) + 10‘) + G.
Rearranging, we ﬁnd
Y— C(Y— T) — G = 10'). The lefthand side of this equation is national saving, so the equation just says
that national saving equals investment. Since national saving increases by $60
billion, investment must also increase by $60 billion. HOW does this increase in investment take place? We know that investment
depends on the real interest rate. For investment to rise, the real interest rate
must fall. Figure 3—1 illustrates saving and investment as a function of the real
interest rate. r 51 52 Figure 3~1 ‘:
a. Real interest rate r? aid
the
ime I (r) rian
reen
even
duct 1, S
Investment, Saving The tax increase causes national saving to rise, so the supply curve for loan
able funds shifts to the right. The equilibrium real interest rate falls, and invest
ment rises. 18 Answers to Textbook Questions and Problems 8. If consumers increase the amount that they consume today, then private saving and,
therefore, national saving will fall. We know this from the deﬁnition of national saving: National Saving = [Private Saving] + [Public Saving]
= [Y— T— C(Y— T)] + [T— G].
An increase in consumption decreases private saving, so national saving falls.
Figure 3—2 illustrates saving and investment as a function of the real interest
rate. If national saving decreases, the supply curve for loanable funds shifts to the left,
thereby raising the real interest rate and reducing investment. Figure 3—2 Real interest rate 1 (r) I,S Investment, Saving 9. a. Private saving is the amount of disposable income, Y— T, that is not consumed: ;
Sprivate = y_ T_ C { = 5,000 — 1,000 — (250 + 0.75(5,000 — 1,000)) = 750. “ Public saving is the amount of taxes the government has left over after it
makes its purchases: Spublic = T_ G
= 1,000 — 1,000
= 0. Total saving is the sum of private saving and public saving: V S = Sprivate + Spublic
‘ = 750 + 0
i = 750. b. The equilibrium interest rate is the value of r that clears the market for loanable
funds. We already know that national saving is 750, so we just need to set it equal ,
to investment: s = I 750 = 1,000 — 50r 4
Solving this equation for r, we ﬁnd:
r = 5%. c. When the government increases its spending, private saving remains the same as
before (notice that G does not appear in the S Viva” above) while government saving
decreases. Putting the new G into the equations above: Chapter 3 National Income: Where It Comes From and Where It Goes 19 Sprivate =
Spublic = T_ G
= 1,000 — 1,250
= —250.
Thus,
S: Sprivate + Spublic
: + = 500.
Once again the equilibrium interest rate clears the market for loanable funds:
S = I 500 = 1,000 — 50r
Solving this equation for r, we ﬁnd: r = 10%. To determine the effect on investment of an equal increase in both taxes and govern
ment spending, consider the national income accounts identity for national saving: National Saving = [Private Saving] + [Public Saving] = [Y— T— C(Y— T)] + [T— G].
We know that Y is ﬁxed by the factors of production. We also know that the change in
consumption equals the marginal propensity to consume (MPC) times the change in disposable income. This tells us that ANational Saving = [— AT — (MPC >< ( — ATM] + [AT — AG]
= [—AT+(MPC><AT)l +0
= (MPC — 1) AT. The above expression tells us that the impact on saving of an equal increase in T and G depends on the size of the marginal propensity to consume. The closer the MP0
is to 1, the smaller is the fall in saving. For example, if the MP0 equals 1, then the fall
in consumption equals the rise in government purchases, so national saving [Y — C(Y—
T) — G] is unchanged. The closer the MPC is to 0 (and therefore the larger is the
amount saved rather than spent for a one—dollar change in disposable income), the
greater is the impact on saving. Because we assume that the MP0 is less than 1, we expect that national saving falls in response to an equal increase in taxes and govern ment spending.
The reduction in saving means that the supply of loanable funds curve shifts to the left in Figure 3‘3. The real interest rate rises, and investment falls.
r 52 31 Figure 33 Real interest rate I (r) I, S
Investment, Saving 20 Answers to Textbook Questions and Problems 11. a. The demand curve for business investment shifts out to the right because the sub—
sidy increases the number of proﬁtable investment opportunities for any given
interest rate. The demand curve for residential investment remains unchanged. b. The total demand curve for investment in the economy shifts out to the right since
it represents the sum of business investment, which shifts out to the right, and residential investment, which is unchanged. As a result the real interest rate rises
as in Figure 3—4. Figure 3—4 1. An increase
in desired
investment . . . Real interest rate 2. . . . raises
the interest
rate. Investment, Saving 0. The total quantity of investment does not change because it is constrained by the
inelastic supply of savings. The investment tax credit leads to a rise in business
investment, but an offsetting fall in residential investment. That is, the higher
interest rate means that residential investment falls (a movement along the
curve), whereas the rightward shift of the business investment curve leads busi ness investment to rise_by an equal amount. Figure 3—5 shows this change. Note
that IIB+I1R =I§3+IzR =S. Business Residential
investment investment 12. In this chapter, we concluded that an increase in government expenditures reduces
national saving and raises the interest rate; it therefore crowds out investment by the
full amount of the increase in government expenditure. Similarly, a tax cut increases
disposable income and hence consumption; this increase in consumption translates into a fall in national saving—again, it crowds out investment by the full amount of the
increase in consumption. *2
t
g Chapter 3 National Income:Where It Comes From and Where It Goes 21 If consumption depends on the interest rate, then these conclusions about ﬁscal
policy are modiﬁed somewhat. If consumption depends on the interest rate, then so
does saving. The higher the interest rate, the greater the return to saving. Hence, it
seems reasonable to think that an increase in the interest rate might increase saving
and reduce consumption. Figure 3—6 shows saving as an increasing function of the
interest rate. r Sm Figure 3—6 Real interest rate Saving
Consider what happens when government purchases increase. At any given level
of the interest rate, national saving falls by the change in government purchases, as
shown in Figure 3—7. The figure shows that if the saving function slopes upward,
investment falls by less than the amount that government purchases rises by; this hap
pens because consumption falls and saving increases in response to the higher interest
rate. Hence, the more responsive consumption is to the interest rate, the less govern—
ment purchases crowd out investment. r 520’) 510,) Figure 37 Real interest rate
e +5 [(1') Investment, Saving 18. a. Figure 3—8 shows the case Where the demand for loanable funds is stable but the
supply of funds (the saving schedule) ﬂuctuates perhaps reﬂecting temporary
shocks to income, changes in government spending, or changes in consumer conﬁ
dence. In this case, when interest rates fall, investment rises; When interest rates
rise, investment falls. We would expect a negative correlation between investment
and interest rates. 22 Answers to Textbook Questions and Problems S10") Figure 3~8
r
S; (F) (D
E
0
.‘§
s
m [(1’) I, S Investment, Saving b. Figure 39 shows the case Where the supply of loanable funds (saving) does not
respond to the interest rate. Also suppose that this curve is stable, Whereas the
demand for loanable funds varies, perhaps reﬂecting ﬂuctuations in ﬁrms’ expec
tations about the marginal product of capital. We would now ﬁnd a positive corre
lation between investment and the interest rate—When demand for funds rises,
this pushes up the interest rate, so we see investment increase and the real inter
est rate increase at the same time. Figure 3—9 Real interest rate 12 (r) 110’) I, S
Investment, Saving Chapter 3 National Income:Where It Comes From and Where It Goes 23 If both curves shift, we might generate a scatter plot as in Figure 3—10, where the
economy ﬂuctuates among points A, B, C, and D. Depending on how often the
economy is at each of these points, we might ﬁnd little clear relationship between
investment and interest rates. 51(r) Figure 3—10 Real interest rate 12 (2) [1(7) I, S
Investment, Saving Situation (0) seems fairly reasonable—both the supply of and demand for loanable
funds ﬂuctuate over time in response to changes in the economy. ...
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 Fall '10
 Prof.ManluiLau
 Macroeconomics, Interest Rates, Supply And Demand, gross domestic product, government spending

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