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Ch4: Consumption, Saving,
and Investment
Abel & Bernake: Macro Ch3
Mankiw: Macro Ch3
1
Chapter Outline
Appendix: micro-foundation of Macro
 Consumption and Saving
 Investment
 Goods Market Equilibrium

2
Aggregate Demand:
Demand for goods & services
Assume a closed economy: NX=0, NFP=0
Components of aggregate demand:
AD = Cd+Id+G+NX = Cd+Id+G
 Desired consumption (Cd)
 Desired investment (Id)
3
Consumption C
Traditional: Keynesian setup

Disposable income
total income minus total taxes:
Yd ≡ Y – T.

Consumption function: C = C(Yd) = a+bYd
assume Yd   C 

Marginal propensity to consume (MPC)
C
MPC 
Yd
4
Appendix: Intertemporal analysis
utility maximization over-time

With micro-foundation:
Cd = optimal C*
= C (lifetime wealth, real interest rate)
= C (current income, future income, real interest rate)

Desired consumption and saving: function of r
Sd = Y – Cd – G
(4.1)
5
Saving is for future consumption

Trade-off between current consumption and future
consumption
 The price of 1 unit of current consumption is
(1 + r) units of future consumption,
where r is the real interest rate
 Consumption-smoothing motive:
the desire to have a relatively even pattern of
consumption over time
6
Consumption and Saving

S≡Y-C
If C=Y, S=0
If C<Y, S>0
If C>Y, S<0

C=a+Y: no-borrowing, no-lending
C< a+Y: lender, with interest income
C< a+Y: borrower, with interest payment
7
Effect of changes in current income

Increase in current income (IE):
both consumption and saving increase
 Marginal propensity to consume (MPC)
MPC≡ (△C/△Y), 0≦MPC≦1
 Aggregate level:
When current income (Y) rises, Cd rises,
but not by as much as Y, so Sd rises
8
Effect of changes in expected future income

Higher expected future income
leads to more consumption today, so saving falls.
9
Application:
The Idiosyncrasy of Singapore Aggregate Consumption

Does consumption spending remain stable over time?
 Table 4.1 shows that APC remains stable for all countries
except Singapore
 Consumption ratio in Singapore falls steadily as income
increases (Fig 4.1)


2 explanations: the rise in loans and withdrawals from the
Central Provident Fund (CPF) to finance housing and car
purchases
This is cause for policy concern as it means that consumption
will not be able to play its role as stabilizer and Singapore will
become more susceptible to experience cyclical fluctuations of
larger amplitude.
10
Table 4.1 Average Propensity to Consume ( APC)
in selected economies
11
Fig 4.1 APC in Singapore (1960–2008)
12
Saving S = S (r)

r↑: 2 opposing effects
 ISE: Positive effect on saving, since rate of return is
higher; greater reward for saving elicits more saving
 IE:
 For a saver (lender): Negative effect on saving,
since it takes less saving to obtain a given amount in
the future (target saving)
 For a borrower: Positive effect on saving, since the
higher real interest rate means a loss of wealth
 Empirical studies have mixed results;
probably a slight increase in aggregate saving
13
Taxes and the real return to saving

Expected after-tax real interest rate:
ra-t = (1 – t)i – e
(4.2)
14
Table 4.1 Calculating After-Tax Interest Rates
15
In touch with data and research: interest rates

different interest rates, default risk, term structure (yield curve),
and tax status
 Since interest rates often move together, we frequently refer
to “the” interest rate
 Yield curve:
relationship between life of a bond and interest rate
殖利率曲線:零息債券的殖利率與其到期日的關係
橫軸為各到期期限(time to maturity)，
縱軸為相對應之到期殖利率(yield to maturity)，
用以描述兩者之關係。
16
In Touch Yield Curve
17
Fiscal policy 財政政策: △G, △T  △Sd



Directly affects desired national saving,
Sd = Y – Cd – G
Affects desired consumption
through changes in current and expected future income
Assume △Y=0: may need revision
18
Fiscal policy:
Government purchases (temporary G↑)

Higher G financed by higher current taxes
reduces after-tax income, lowering desired consumption
 Even true if financed by higher future taxes,
if people realize how future incomes are affected
 Since Cd declines less than G rises,
national saving (Sd = Y – Cd – G) declines
 So government purchases reduce
both desired consumption and desired national saving.
19
Fiscal policy: Tax cut (T↓, △G=0)
Ricardian equivalence proposition (Appendix)
Lump-sum tax cut today,
??
If tax change affects only the timing of taxes,
not their ultimate amount (present value)
no change in consumption
(Ricardian equivalence proposition)
 ???

20
Ricardian equivalence proposition

In practice, people may not see that future taxes will rise
if taxes are cut today;
then a tax cut leads to increased desired consumption and
reduced desired national saving.
21
Application:
How consumers respond to tax rebates

The government provided a tax rebate in 2008,
hoping to stimulate the economy.
2008年5月美國國稅局 (IRS)會有特別退稅
（個人300-600元，17歲以下小孩每位300元)：
美國振興經濟(Economic Stimulus Act of 2008)法案的一部分

Research by Shapiro and Slemrod suggests that
consumers did not increase spending much in 2001,
when the government provided a similar tax rebate.
22
Application:
How consumers respond to tax rebates




New research by Agarwal, Liu, and Souleles have different
findings from their study on credit-card payments, purchases,
and debt over time.
People getting the tax rebates initially made additional payments
on their credit cards, paying down their balances; but after nine
months they had increased their purchases and had more creditcard debt than before the tax rebate.
Younger people, who were more likely to face binding
borrowing constraints, increased their purchases on credit cards
the most of any group in response to the tax rebate.
People with high credit limits also spent less, behaved more in
the manner suggested by Ricardian equivalence.
23
Summary 5
24
Investment


Investment plays a crucial role in economic growth.
Investment fluctuates sharply over the business cycle,
so we need to understand investment to understand the
business cycle.
25
Firm’s intertemporal analysis:
profit maximization over-time (Varian Ch17)

Max   t
t 0
St. BC (production function and capital accumulation)
Kt 1  (1   ) Kt  I t
Net investment: I t - K t =K t+1 - K t
(4.5)

Over-time optimal K = desired capital stock (K*)

Πt ??
Trade-off between dividends over time
26
Desired capital stock (K*)
MB= future benefit of investment = MPKf
 MC= user cost of capital = r+d
1. Opportunity cost: interest rate ( r )
股利原可存銀行賺利息或借錢融資需繳利息
2. Depreciation cost: d
the value loss as capital wears out (capital resale price ↓)
 Real-side comparison:
MPKf = r+d  optimal K*

 Earlier: one-time period decision rule:
MPK 
Re
P
27
課本將MPKf視為名目
若MPKf視為實質
Nominal-side comparison:
uc = PK (r + d)
(4.3)
P‧MPKf = PK (r + d)  optimal K*
If P = PK  same as real-side comparison


以下採用課本：將MPKf視為名目
If MPKf > uc  profits rise as K ↑
If MPKf  uc profits rise as K ↓
With diminishing MPKf ,
profits are maximized where MPKf = uc
28
Fig 4.3 Determination of the desired capital stock
（Nominal MPKf）
29
Changes in the desired capital stock (△K*)
△r, △d, △PK  △uc
 Technological changes  △ MPKf

Factors that change user cost of capital (Fig. 4.4)
 Or factors that shift the MPKf curve (Fig. 4.5)
 the desired capital stock to change

30
Fig 4.4 A decline in the real interest rate
raises the desired capital stock
31
Fig 4.5 An increase in the expected future MPK
raises the desired capital stock
32
△τ(tax rate on capital return)△K*
taxes, MB = (1 – ) MPKf
(1 – ) MPKf = uc
Or
MPKf = uc/(1 – ) = PK (r + d) /(1 – )
 With
(4.4)
user cost of capital is uc/(1 – )
 An increase in τ raises the tax-adjusted user cost and
reduces the desired capital stock
 Tax-adjusted
33
the effective tax rate

In reality, there are complications to the tax-adjusted user cost
 We assumed that firm revenues were taxed
 In reality, profits, not revenues, are taxed
 So depreciation allowances reduce the tax paid by firms,
because they reduce profits
 Investment tax credits reduce taxes when firms make new
investments
 Summary measure: the effective tax rate—the tax rate on firm
revenue that would have the same effect on the desired capital
stock as do the actual provisions of the tax code
 Table 4.2 shows effective tax rates for many different countries
34
Table 4.2 Effective Tax Rate on Capital, 2007
35
Application:
measuring the effects of taxes on investment


Do changes in the tax rate have a significant effect on
investment?
A 1994 study by Cummins, Hubbard, and Hassett found
that after major tax reforms, investment responded strongly;
elasticity about –0.66 (of investment to user cost of capital)
36
From the desired capital stock to investment

Gross investment It = Kt+1 – Kt + dKt
 If firms can change their capital stocks in one period,
then Kt+1 = K* (the desired capital stock)
 It = K* – Kt + dKt
(4.6)
 Investment has two parts
 Desired net increase in the capital stock over the year
(K* – Kt)
 Investment needed to replace worn-out capital (dKt)
 With adjustment costs  lags
? -- partial adjustment
37
The investment function:
r↓ K*↑ Id↑
r
I (r )
I
38
Fig 4.6 Gross and net investment, 1929-2008
Sources: GDP, gross private domestic investment, and net private domestic investment from BEAWeb
site, Tables 1.1.5, 5.1, and 5.2.5.
39
Tobin’s q theory of investment
V
Tobin ' s q 
Pk K
V: stock market value of the firm
PkK: replacement cost of firm’s capital stock
 If
V < PkK , q < 1  K↓
If V > PkK , q > 1 K↑
If V = PkK , q=> 1 optimal K*
40
Tobin’s q theory of investment

Firms change investment
in the same direction as the stock market.
r↓? ,
q > 1  K↑
 If Pk↓ ?
q > 1  K↑
 MPKf ↑  V ↑  q > 1
 K↑
Data show general tendency of investment to rise when
stock market rises; but relationship isn’t strong because
many other things change at the same time (Figure 4.7)
 If

41
Fig 4.7 Investment and Tobin’s q, 1987-2009
Source: Investment from St. Louis Fed Web site at research.stlouisfed.org/fred2/series/PNFIC1; Tobin’s from Federal
Reserve Flow of Funds Accounts, Table B.102, for nonfarm nonfinancial corporate business, market value plus liabilities
divided by assets.
42
Investment in inventories and housing

Marginal product of capital and user cost also apply,
as with equipment and structures
43
Summary 6
44
Government spending, G
G = govt spending on goods and services.
 G excludes transfer payments
(e.g., social security benefits,
unemployment insurance benefits).
 Assume government spending and total taxes are
exogenous:

G G
and
T T
45
Goods market equilibrium

Aggregate demand:

Aggregate supply:
Y

Equilibrium:
Y  C (Y  T , r )  I (r )  G

The real interest rate adjusts
to equate demand with supply.
Y d  C (Y  T , r )  I (r )  G
s
 F (K , L )
46
Goods Market Equilibrium

The real interest rate adjusts to bring the goods market into
equilibrium
 Y = Cd + Id + G
(4.7)
goods market equilibrium condition
 Differs from income-expenditure identity,
as goods market equilibrium condition need not hold;
undesired goods may be produced,
so goods market won’t be in equilibrium.
47
Goods Market Equilibrium

Alternative representation for a closed economy:
Y= Cd + Id + G
Sd = Y – Cd – G,
 Sd = Id
(4.8)
saving-investment diagram (Fig. 4.8)
48
Fig 4.8 Goods market equilibrium
49
Table 4.3 (△r to reach equilibrium)
Components of Aggregate Demand for Goods
50
Shifts of the saving curve

Y ?, expected Yf ?, wealth ?,
G ?, T ? (unless Ricardian equivalence holds)
 Sd↑: Saving curve shifts right

Example:
Temporary G↑(Fig. 4.8)
 S↓: shifts S left
 r↑: causing crowding out of I
51
Fig 4.9 A decline in desired saving
52
Shifts of the investment curve

r↓, d↓, PK↓,Tax rate τ↓, MPKf ↑(Fig. 4.9)
 K*↑
 Id↑:shift to the right
 r↑, S↑= I ↑
53
Fig 4.10 An increase in desired investment
54
Application: Macroeconomic consequences
of the boom and bust in stock prices

Sharp changes in stock prices
affect consumption spending (a wealth effect)
and capital investment (via Tobin’s q)
 Data in Fig. 4.11
55
Fig 4.11 Real U.S. stock prices and
the ratio of consumption to GDP, 1987-2009
Source: S&P 500 from Yahoo finance Web site, finance.yahoo.com; real S&P 500 calculated as S&P 500 divided by GDP
deflator; GDP deflator, consumption spending, and GDP from St. Louis Fed Web site at research.stlouisfed.org/fred2.
56
Consumption and the 1987 crash
 When
the stock market crashed in 1987, wealth declined
by about $1 trillion
 Consumption fell somewhat less than might be expected,
and it wasn’t enough to cause a recession
 There was a temporary decline in confidence about the
future, but it was quickly reversed
 The small response may have been because there had
been a large run-up in stock prices between December
1986 and August 1987, so the crash mostly erased this
run-up
57
1987年美股崩盤
重回1987年…美股崩盤 相當今跌3200點 編譯王錦時／特譯




紐約股市在1987年10月19日當天出現崩盤走勢，道瓊工業平均指數暴跌五○八點，跌
幅高達22.6％。主要是因當時美國的貿易及預算雙赤字攀升至新高峰，引發市場疑慮；
同時當天的電腦程式交易，加重了大盤跌勢。
美國在1987年的經濟情勢，剛好是1980年代經濟繁榮的高峰期。美國已故前總統雷根
當時大力推展「供給面經濟學」，實施減稅政策，活絡民間消費及投資，帶動美國經
濟強勁擴張。美國股市也自1982年開始，展開一波多頭行情。而股市持續上揚自然吸
引更多游資聚集，到最後過多的資金在股市瘋狂炒作，漲勢逐漸脫離基本面，形成越
來越大的泡沫。而伴隨當時美國經濟景氣擴張而來的是，貿易及預算赤字連袂攀升至
新高峰，並引發通膨上揚。
當時美國聯邦準備理事會（Fed）為抑制通膨，採取升息及緊縮信用的行動，使債券吸
引力大幅上升，同時也引發股市投資人對股價高估的疑慮。10月16日道瓊工業指數已
出現重挫91點（約5％）的盤勢，同時也有分析師警告指出，紐約股市即將大跌。果然，
在10月19日星期一股市開盤後，龐大的殺盤賣壓有如潮水般湧出，收盤時道瓊工業指
數竟暴跌了508點；亞洲及歐洲股市也都連鎖遭到波及，應聲劇跌。
當時剛接掌Fed主席不久的葛林斯潘，立即發佈強而有力的聲明表示：「聯邦準備體系
為支持經濟及金融體系，已經完成提供市場流動性資金的準備。」成功化解了一場全
球股市風暴。1987年這場股災雖然並未如同1927年那次，引發經濟大蕭條。
58
Investment and the declines in the stock market
in the 2000s



Investment and Tobin’s q were correlated in 2000 and 2008,
when the stock market fell sharply
Investment tended to lag the decline in the stock market,
reflecting lags in the process of making investment decisions
The financial crisis of 2008
 Stock prices plunged in fall 2008 and early 2009, and
home prices fell sharply as well, leading to a large
decline in household net wealth
 Despite the decline in wealth, the ratio of consumption
to GDP did not decline much
59
Investment and Tobin’s q
 Investment
and Tobin’s q were not closely correlated
following the 1987 crash in stock prices
 But the relationship has been tighter in the 1990s and
early 2000s, as theory suggests (Fig. 4.11)
60