Post on 28-Mar-2015
Lecture 13 1
Macroeconomic Analysis 2003
Investment
Blanchard 16.2, Mankiw 17; M&S 14
Lecture 13 2
Contents• Why investment is so volatile?• Investment Decision: Present value and Cost• Marginal productivity theory of investment• A Numerical Example of Investment Problem• Investment tax credit and optimal capital stock• Problem of Manufacturing sector in UK• Long term yield and investment• Multiplier-Accelerator theory of Investment• Marginal productivity, Cost of Capital and Tobin’s Q• Exercises
Lecture 13 3
Growth Rate of Investment and Output
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961P
erce
nt p
er y
ear
InvOutput
Investment is More Volatile than Output: Why?
Lecture 13 4
Change in the Inventory and Change in the Operating Surplus
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Quarters
In m
illio
n P
ound
s
Inventory
Oper surpl
Lecture 13 5
FTSE100 Index
0.00
1000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
Jan-
85
Jan-
86
Jan-
87
Jan-
88
Jan-
89
Jan-
90
Jan-
91
Jan-
92
Jan-
93
Jan-
94
Jan-
95
Jan-
96
Jan-
97
Jan-
98
Jan-
99
Jan-
00
Jan-
01
Jan-
02
Inde
x
FTSE100
Asset Market Bubbles and Collapse
BULL
BEAR
Lecture 13 6
Asset Market Bubbles and Collapses
0.0
2,000.0
4,000.0
6,000.0
8,000.0
10,000.0
12,000.0
Dow
Jon
es
0.0
5,000.0
10,000.0
15,000.0
20,000.0
25,000.0
30,000.0
35,000.0
40,000.0
Nikk
ie
Djones
nikkier
Lecture 13 7
Why Investment is the Most Volatile Component of the GDP?
In advanced economies, where the capital output ratio (K/Y) is around 2.5 on average and share of investment in the GDP is around 20%, the capital stock is 12.5 (=2.5/0.2) times the flow of investment.
This means even a one percentage change in the demand for capital stock brings roughly 13 percent change in the demand for investment.
As explained by perpetual inventory method on average it takes about 13 years of investment flows to generate the total stock of capital of an economy at a given point of time.
Lecture 13 8
Investment Decision AnalysisBreaks even point: PVKr
Annual income from the project: 18000
The value of this investment project: V= r18000
Cost of the Project: 100,000
r 0.05 0.1 0.15
PV 138461.5 100000 78260.87
Project breaks even at 10% interest rate and makes positive
real profit at 5 % interest rate Investment should not be recommended when the interest
rate is 15% because the manufacturer will loose almost 22k.
=0.08
Lecture 13 9
Financing an Investment
Project
Self FinanceBequests
Bonds:Debt Finance
Banks, BuildingSociety, Insurance
Equity FinanceStock Market
(LSE)
NoRisk Risk
HighRisk
MaturityInstalment
MethodRepayment
Method
Financing of an Investment Project
Demand for output
Need for Capital
Lecture 13 10
L
K
r
w
r
w
L
K
Low interest rate induces producers to substitute outlabour by capital
rKwLLPK
01 rLPKK
01 wLPK
L
o
Lecture 13 11
Y = f(K)
Kopt
C = (r+)KMPK
Y
Capital
Output
Optimal Capital Stock for a Firm
MPK=MC
Lecture 13 12
Y = f(K)
Kb
MPKb
Yb
Capital
Output&Cost
Impact of Increase in the Interest rate on the Optimal Capital Stock for a Firm
Ka
Ya
MPKaRa = (r2+)K
Rb = (r1+)K
r2 > r1
Lecture 13 13
r-cost
MPK1
MPK2
K1 K2
Impact of Technological Advancement in the Capital Stock
0
Lecture 13 14
Growth of Lending to Individuals and the Interest Rate, BOE
0.0
5.0
10.0
15.0
20.0
25.0
Oct-87
Oct-88
Oct-89
Oct-90
Oct-91
Oct-92
Oct-93
Oct-94
Oct-95
Oct-96
Oct-97
Oct-98
Oct-99
Oct-00
Oct-01
Oct-02
Gro
wth
Rat
e an
d In
tere
st R
ate
LendingIntrate
Lending is Growing with Lower Interest Rate in Recent Years
Lecture 13 15
Output and Capital Accumulation
KFY and
tItKtK 11
Investment
....
11
11
111
1 ete
tr
tr
et
tr
Iet
VI
and
t
tt K
Y
Optimal investment
kK PrMPK 1
Marginal Productivity Theory of Investment -calculations
Lecture 13 16
r
KPKP
r
KF Kk
1
1
12
1
0
121
11
'
r
KPkPr
KF
K
or Kk PPrMPK 211 1
kK PrMPK 1111 , where
11
2 K
KK
P
P
is the capital gain. 0K
kK PrMPK 1
Marginal Productivity and the User Cost of Capital
Lecture 13 17
Role of Investment Tax Credit in Promoting InvestmentWhy Manufacturers Lobby for a Tax Credit?
Kr 1
Kr
MPK
K1 K20
Lecture 13 18
which is selling each car at 8 thousands had to pay for capital equipment per car about 2 thousands if the nominal interest rate is 6%, inflation (capital gain) is 3% and the depreciation of capital stock is 3% per year assuming that the production function of this
company is given by KY with 75.0 .
What is the optimal capital stock for a car company?
Lecture 13 19
The user cost of capital
Ki = 6% +3%-3% =6% Marginal product of capital:
175.011 75.0' KKKF
Optimal Investment condition
kk iPKFP 11'. =>
%3%3%6200075.08000 175.0 K =>
%6275.0.8 25.0 K ; %626 25.0 K =>
06.0
325.0K 450K = 6.25 million
Optimal Capital Stock for the Car Company
Lecture 13 20
Input and Output Price Inflation in Manufacturing Sector
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
Jan-
91
Jan-
92
Jan-
93
Jan-
94
Jan-
95
Jan-
96
Jan-
97
Jan-
98
Jan-
99
Jan-
00
Jan-
01
Jan-
02Per
cent
cha
nge
InputOutput
Problem of the Manufacturing Sector in the UK
Lecture 13 21
Oil Price Inflation
-100.0
-50.0
0.0
50.0
100.0
150.0
200.0
Jan-
93
Per
cent
oil
Input Prices are Volatile Because of the Volatility of Oil Prices
Lecture 13 22
Arbitrage condition for two periods
ettt iii 1,11
22 111
ett t
iii212 2
1
Higher long-run rate and lower short run interest rate is good for investment.
Yield curve for n period bonds
eeetnt nttt
iiiin
i ...1
321
Rising short run interest rates gives an upward sloping and falling short run interest give downward sloping yield curves
Investment is sensitive to the Long-term Yield than to Short Term Returns
Lecture 13 23
Multiplier Accelerator Theory of Investment 1LAKY
11LAKMPK
K
YMPK
or MPK
YK
Kr
YK
where K represents capital
gains.
Role of investment tax credit
Kr
YK
1
where represents the investment tax credit.
Lecture 13 24
• Change in demand requires change in Capital stock• New Investment meets this requirement• Investment has multiplier effect on income• There is more demand• More demand for capital stock• More investment and more output• This process continues, until the economy reaches
turning point• There is a similar downward movement in output,
investment and capital stock in the recessionary period.
Essence of the Multiplier-Accelerator Theory of Investment
Lecture 13 25
Consumption function: tYcctC10
National income identity: tItCtY
Investment Multiplier: 1
11cI
Y
Investment is Change in Capital Stock 1, tdttn KKI
Capital stock is multiple of output: tt YK ; 0 .
1, tttn YYI = ttn YI ,
Accelerator: t
tn
Y
I
,
Multiplier Acceleration effect on Output:
11 c
YYT
A Simple Illustration of the Multiplier Accelerator Theory of Investment
Lecture 13 26
Tobin’s q theory capitalinstalledofttreplacemen
capitalinstalledofvalueMarketq
cos
Tobin’s q is the ratio of market value of capital stock to its replacement cost and can be stated as:
kP
r
MPKq
1
Investment 0 1 Tobin’s q
Tobin’s q with installation cost:
11
kPr
MPKq Marginal cost
Cost Of Capital And MPK MPK (I/K) (I/K)
Tobin’s q-theory and Investment
Lecture 13 27
Exercises
• Optimal investment with a given production function and user cost of capital
• Impact of investment tax credit
• Whether to take or not take an investment project with a stream of projected revenues and certain cost
• How to deal with uncertainties?
Lecture 13 28
Y= F(K,L)
SC T
Funds
K FA
EquityTreasury
Bonds
DepositBanks
Pension FundsProfit
Link Between Financial System and the Economy
Lecture 13 29
Three Sources of Financing an Investment Project
• Self-financing– Depends on retained earning– Personal savings
• Bonds– Banks, Building Societies and Trusts– Various maturities and risks
• Stocks– Market signals and equity prices
Lecture 13 30
Savers
Households, Corporations and Government
Intermediaries
Banks, Insurance Companies, Building Societies, Trusts, Stock and Bonk Markets
Intermediaries
Banks, Insurance Companies, Building Societies, Trusts, Stock and Bonk Markets
InvestorsSmall, Medium and LargePrivate, Public, Domestic and Foreign
InvestorsSmall, Medium and LargePrivate, Public, Domestic and Foreign
θS=I =95
Transaction Charges (1-θ)S=0.05*100 = 5
S =100
Lecture 13 31
Total equity turnover value as at end September
2,482
2,872
4,1704,383
3,588
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
1998 1999 2000 2001 2002
£b
n
UK International
Lecture 13 32
tLtKtAtY 1
YwL
YrK
YKLK
YrK .1
Y
LLKYwL 1
1
11
11
LKLK
LKLK
LAKLAK
LAKLAK
LKLK
rwrw
LKLK
Investment Income Distribution and Factor Substitution