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