Macroeconomic Analysis 2003
Investment
Blanchard 16.2, Mankiw 17; M&S 14
Lecture 13
1
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
2
Investment is More Volatile than Output: Why?
Lecture 13
3
Lecture 13
4
Asset Market Bubbles and Collapse
FTSE100 Index
8000.00
7000.00
6000.00
FTSE100
BEAR
4000.00
3000.00
BULL
2000.00
1000.00
0.00
Ja
n8
Ja 5
n8
Ja 6
n8
Ja 7
n8
Ja 8
n8
Ja 9
n9
Ja 0
n9
Ja 1
n9
Ja 2
n9
Ja 3
n9
Ja 4
n9
Ja 5
n9
Ja 6
n9
Ja 7
n9
Ja 8
n9
Ja 9
n0
Ja 0
n0
Ja 1
n02
Index
5000.00
Lecture 13
5
Asset Market Bubbles and Collapses
40,000.0
35,000.0
Djones
nikkier
8,000.0
6,000.0
30,000.0
25,000.0
20,000.0
15,000.0
10,000.0
4,000.0
2,000.0
5,000.0
0.0
0.0
19
85
19
86
19
8
19 7
8
19 8
89
19
90
19
9
19 1
9
19 2
93
19
94
19
9
19 5
9
19 6
97
19
98
19
99
20
0
20 0
01
20
02
Dow Jones
10,000.0
Lecture 13
6
Nikkie
12,000.0
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
7
Investment Decision Analysis
Breaks even point:


r    K  PV
Annual income from the project: 18000
The value of this investment project: V= 18000
r 
Cost of the Project: 100,000
r
0.05
0.1
=0.08
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.
Lecture 13
8
Financing of an Investment Project
Demand
for output
Self
Finance
Bequests
Maturity
Need for Capital
Financing an
Investment
Project
Equity Finance
Stock Market
(LSE)
Bonds:
Debt Finance
Banks, Building
Society, Insurance
Instalment Repayment
Method
Method
Lecture 13
No
Risk
High
Risk
Risk
9


  PK L  wL  rK
K
L
Low interest rate induces
producers to substitute out
labour by capital
K
 w

L
 r

  1
 PK L  w  0
L

 PK  1 L  r  0
K
o
w
r
Lecture 13
10
Optimal Capital Stock for a Firm
MPK
Output
C = (r+)K
Y = f(K)
Y
MPK=MC
Kopt
Lecture 13
Capital
11
Impact of Increase in the Interest rate on
the Optimal Capital Stock for a Firm
MPKb
MPKa
Output
&
Cost
Yb
Ra = (r2+)K
Rb = (r1+)K
Y = f(K)
r2 > r1
Ya
Ka
Kb
Capital
Lecture 13
12
Impact of Technological Advancement in the Capital Stock
MPK2
MPK1
r-cost
0
K1
Lecture 13
K2
13
Lending is Growing with Lower Interest Rate in Recent Years
Growth of Lending to Individuals and the Interest Rate, BOE
20.0
Lending
Intrate
15.0
10.0
5.0
0.0
O
ct
-8
7
O
ct
-8
8
O
ct
-8
9
O
ct
-9
0
O
ct
-9
1
O
ct
-9
2
O
ct
-9
3
O
ct
-9
4
O
ct
-9
5
O
ct
-9
6
O
ct
-9
7
O
ct
-9
8
O
ct
-9
9
O
ct
-0
0
O
ct
-0
1
O
ct
-0
2
Growth Rate and Interest Rate
25.0
Lecture 13
14
Marginal Productivity Theory of Investment -calculations
Output and Capital Accumulation
Y  F K  and K t  K t 1 1     I t
Investment

 1
I V   e   I 
e 
  t 
t 1
1

r
1 r

t
t



1
1    te  1  ....
1  r e 

t 


 
 Yt
 t  
and
 Kt
Optimal investment





MPK  r     P
K
Lecture 13
k
1
15
Marginal Productivity and the User Cost of Capital
K


P


1
F K 
k
2 K
 P1 K 

1  r 
1 r
'
F K 

 Pk 

K 1  r  1
1   P2K
1 r
MPK  1  r P1  1   P
k
or
0


K
2
MPK  1  r   1    1  
K
K
P
k
1
, where
P2K
K
 K 1
is the capital gain.   0
P1


MPK  r     P
K
k
1
Lecture 13
16
Role of Investment Tax Credit in Promoting Investment
Why Manufacturers Lobby for a Tax Credit?
r     
K
1  r     K 
0
MPK
K1
K2
Lecture 13
17
What is the optimal capital stock for a car
company?
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 Y  K with   0.75 .
Lecture 13
18
Optimal Capital Stock for the Car Company
The user cost of capital
i   
K
= 6% +3%-3% =6%
Marginal product of capital:
 1
F ' K1   K
 0.75K
Optimal Investment condition

P.F ' K1   P1k i     k
0.751
 =>
80000.75K 0.751  20006%  3%  3% =>
8.0.75K 0.25  26% ; 6K
 3 
K 0.25  

 0.06 
0.25
K  50
4
=
 26% =>
6.25 million
Lecture 13
19
Problem of the Manufacturing Sector in the UK
Input and Output Price Inflation in Manufacturing Sector
20.0
Input
Output
15.0
5.0
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
-5.0
Jan-92
0.0
Jan-91
Percent change
10.0
-10.0
-15.0
Lecture 13
20
Input Prices are Volatile Because of the Volatility of Oil Prices
Lecture 13
21
Investment is sensitive to the Long-term Yield than to Short
Term Returns
Arbitrage condition for two
periods
2
e
2t
1t
1,t 1
1  i   1  i 1  i
1
i  i  i 
Yield curve for n period bonds


1 e e
e
int  i1t  i 2t  i 3t  ...  i nt
n

Rising short run interest rates
gives an upward sloping and
2t
1t
2t
2
falling short run interest give
Higher long-run rate and lower downward sloping yield curves
short run interest rate is good
for investment.
e
Lecture 13
22
Multiplier Accelerator Theory of Investment

1
Y  AK L
MPK  AK  1 L1
Y
Y
Y
r     K 
where
MPK 
K
K
or
MPK
K
K
represents capital
gains.
Role of investment tax credit
Y
K
1   r     K 
where  represents the investment tax credit.
Lecture 13
23
Essence of the Multiplier-Accelerator Theory of Investment
• 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.
Lecture 13
24
A Simple Illustration of the Multiplier Accelerator
Theory of Investment
Consumption function:
National income identity:
Investment Multiplier:
Ct  c  c Yt
0 1
Yt  Ct  It
Y  1
I 1 c
1
Investment is Change in Capital Stock
Capital stock is multiple of output:
I n,t  K td  K t 1
  0.
  Yt 
K t  Yt ;
I n,t  Yt  Yt 1 = I n,t
Accelerator:

I n ,t
Yt
 Y 

YT

Multiplier Acceleration effect on Output:
1  c1
Lecture 13
25
Tobin’s q-theory and Investment
Market value of installed capital
replacem ent cost of installed capital
Tobin’s q is the ratio of market value of
Tobin’s q with installation cost:
capital stock to its replacement cost and
MPK
k
q

P
 1    Marginal cost
can be stated as:
1  r 
MPK
q
Pk
1  r 
Cost
Of
Capital
And
Investment
MPK
MPK
0
1
Tobin’s q
Tobin’s q theory q 
(I/K)
Lecture 13
(I/K)
26
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
27
Link Between Financial System and the Economy
Y= F(K,L)
C
T
S
Funds
K
Profit
FA
Equity
Lecture 13
Treasury
Bonds
Deposit
Banks
Pension Funds
28
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
29
S =100
Savers
Households, Corporations and
Government
Transaction Charges Intermediaries
(1-θ)S=0.05*100 = 5
Banks, Insurance Companies, Building Societies,
Trusts, Stock and Bonk Markets
θS=I =95
Investors
Small, Medium and Large
Private, Public, Domestic
and Foreign
Lecture 13
30
T otal equity turnover value
as at end September
5,000
4,500UK
International 4,383
4,170
4,000
3,588
3,500
2,872
£bn
3,000
2,500
2,482
2,000
1,500
1,000
500
0
1998
1999
2000
Lecture 13
2001
2002
31
Investment Income Distribution and Factor Substitution


Yt  At Kt Lt



1
rK

K
L
.
K
 
Y
Y
rK  wL  1
Y
Y


1


K
L
L
wL


Y
Y
K L
K L
K L
K L
 KL 
 K L 1


w r 
K L


1




1


 AK L
AK
L 
wr
K L




1




1
AK L
AK
L
Lecture 13
32