Ramanathan - Monetary expansion.pdf

7/26/2019 Ramanathan - Monetary expansion.pdf

1/9

Monetary Expansion, Balance of Trade

and Economic Growth

In recent years there have been a num ber of papers

on

international

trade, investment and growth (Kemp

[6],

Sato

[lo],

Inada

[S], Oniki

and Uzawa

[8]).

Similarly, the literature

on

one-sector monetary growth

models is also fairly extensive (Tobin

[13],

Levhari and Patinkin

[7],

Sidrauski

[ll],

Stein

[12]).

In this paper we attempt to integrate the

two types

of

models by introducing

a

monetary asset in a two-sector

economy which allows international trade and in which accumulation

of capita l and labour takes place.' The working

of

the economy is as

follows. At any given instant, the economy has given stocks of capital

and labour and a stock

of

money supplied by the government as a

transfer payment. The country produces both consumption and capital

goods (i.e., is non-specialized). If at given terms of trade there is an

excess supply of capital (consumption) goods, then, the economy exports

them and

imports

consumption (capital) goods. The output of the

investment goods sector, plus or minus capital goods traded, goes to

increase the stock of capital. Labour force grows at

an

exogenously

determined rate. What role does money play in such an economy? When

the stock of money expands, asset holders' wealth increases. On the

one hand,

ths

increases consumption demand and hence will affect the

amount of capital goods imported or exported, if there is no trade in

securities. This in turn afects the productive capacity of the economy

and hence alters its growth path. Second, if money continuously in-

creases and exchange rates are flexible, then the domestic price level

changes. Since th is alters the relative yields

on

capital and money, the

portfolio composition is afFected, thus afecting capital accumulation

and hence the growth path. It

is

therefore

of

considerable interest to

examine the long-run behaviour

of

such an economy.

For

instance,we

should like to know what effect an increase in the ra te of monetary

expansion will have on the long-run

per

capiru income

as

well as on the

level of trade. A similar question can

be

raised with regard to changes

*John Conl isk , Stuar t McMenamin, Bi l l Rober ts and

a

referee made useful

comments but are not responsible

fo r

e r ro r s .

1R ec en t papers by A llen [ l ] , Fisher and Frenkel [Z], nd Salop [9] a lso

attempt a similar integration, but

our

approach and analysis are quite different .

For instance, Allen s is

a

one-sector (complete specialization) two-country model,

whereas we consider a small country producing both capital and consumption

goods.

Fisher and Frenkel have not considered the monetary

sector

explicitly but

have taken account of trade in securities.

3 1


2/9

32

T H E ECONOMIC RECORD MARCH

in the world terms of trade , in the presence of a monetary asset that

competes with capital assets.

The paper also briefly discusses the implications

of

fixed and

flexible exchange rates

on

the independence

of

monetary policy. It will

be

emphasized that, under pegged exchange rates, the monetary authority

of

a small

open

economy (such as the one we discuss) cannot indepen-

dently determine the rate of monetary expansion.

1 .

The

Model

We assume that there are two sectors, a consumption goods sector

( C )

and an investment (or capital) goods sector

I) .

Let

K

be the

stock of capital,

L

the stock of labour, and

Pk

the price of capital goods

in terms

of

consumption goods. Then it is well known that

if

production

relations are linearly homogeneous in capital and labour, the output

(or supply)

of

the

two

goods can be expressed as follows:

c=

C ( k , P k ) L 1)

I

= ( k ,

P , ) L ,

2)

where

k = K / L ( 3 )

is the capital-labour ratio.

An

increase

in

the price

of

capital will raise

the output

of

the capital goods industry and lower the output of the

consumption goods sector.

Thus

a C / a P ,

0.

By

Rybczynskis

theorem (Kemp

[ 6 ] ) ,

an increase in

k

will result in the

expansion of the industry in which capital is used more intensively and

in the contraction of the other industry. Following the rest of the

literature, we shall assume that the consumption sector is more capital

intensive than the investment sector. Under this

capital intensity

con-

In a closed econom y, the outpu t of the investment sector will

simply augment capital stock and hence increase productive capacity.

If, however, we allow international trade, consumption demand need

not equal the output

of

the consumption goods industry and capital

might flow from o r to the rest of the world. Let consumption demand

be

where Yd s total disposable income. For the time being, we assume

that the saving rate s ) is fixed. This assumption will be relaxed later.

If

I d is the investment demand, then the balance of payments

equilibrium is given by

dition,

Ck > 0 and I k < o.2

D =

1 - s ) Y ~

( 4 )

C D = ( I d )Pk .

(4a )

Since trade is permitted, capital accumulation is given by the

following relation

K P k

= I PI +

C

D

K

P k 5 )

where a dot above a variable denotes its time derivative and

6

is the

constant relative rate

of

depreciation. If there is an excess supply

of

Partial derivatives are denoted by subscripts.


3/9

1975 MONETARY EXPANSION,

TRADE

A N D

GRQWTH 3 3

consumption goods, then the economy will export the surplus and import

investment goods, thus augmenting the domestic production of capital

goods. This situation might be typical of a less developed economy that

exports primary goods an d imp orts cap ita l goods. Similarly,

an

advanced

country might be represented by

an

excess demand for consumption

goods. To ta l labour force is given by

L = Lo ent. ( 6 )

We now add a monetary asset. Let

M

be

the nominal stock of

money.

It

is supplied as a transfer payment by the central bank and is

not a produced commodity. We further assume that money supply

grows at the rate

I-I.

herefore,

p

is treated alternatively as endogenous and exogenous. Since the con-

sumption good is used

as a

numeraire, there will be terms of trade

between money and consumption goods. This is denoted by Pm. he

total wealth of the economy (in terms of consumption goods)

is

8)

Define the ra te of change of the price of money to

be

TT Thus3

Pm/Pm

= R.

9)

We assume that money demand

is

proportional to the communitys

wealth but that the proportionality factor depends on

k ,

R and Pr .

Therefore,

M P , , , = h ( k , x , P , ) W O < h < 1.

Using ( 8 ) this can be rewritten as follows:

where b

= A / 1 ) .

An increase in

k

would induce people to hold a greater proportion

of wealth

in

monetary assets. Therefore

h k

and

bk

are positive. An

increase in the price of money in terms of consumption goods will make

the monetary asset more attractive and hence A,, and b, are negative.

If

Pk

ncreases, individuals would move

in

favour of capital and hence

The disposable income

Y d )

f the economy (again in terms

of

M / M

=

p

W = K PI, M Pm.

M P,

= b ( k , T , P k ) K

Pa

10)

dX/aPk < 0

consumption goods) is given by th e following expression:

Disposable income is thus given by the value

of

domestic output plus

the increase in the value

of

money (through new transfer payments

and increase in

P, )

plus the capital gains due to

a

rise in the price

of capital.

3 Since the numeraire is the consumption

good,

P ,

is the reciprocal of what

is usually called the price level in one-sector models. The inflation rate is there-

fore

-T

and an increase in will induce asset hold ers to hold m o ~ e oney.

B


4/9

34 THE ECONOMIC RECORD MARCH

The above expression can also be derived in another way. Total net

saving is also equal to change in wealth I . Therefore,

From

this and 4)we have

Substituting for

D

from 5 ) in the above relation, we obtain 1 1).

For convenience we will refer to P , as the domestic terms of

trade and

Pk

as the

world

terms of trade.

If,

as

is

common, we assume

that the economy in question is small and that the rest of the world

is in steady state, then we may treat the world terms of trade Pk as

given, in which case P, will be equal to zero for all

t .

In a two-country

model, Pk would of course be determined endogenously. Later on, we

analyse the effects of changes in Pk on the long-run behaviour of the

economy.

Finally we have the exchange rate determination. If P , is the world

price of money, which by the small-country assumption is treated as

given, and P is the exchange rate, we have

( 1 a )

Equations 1) to 1 ) , (4 a) and ( 1 a ) uniquely determine the

time paths

of

the thirteen endogenous variables

C

k , D, ,

L ,

M ,

P,, Yd,W , d , and

p

for given values

of

Pk , P, , R , s, 8 and p . Although

the above formulation treats the exchange rate as flexible and endogen-

ously determined , later we consider the fixed exchange rate case in which

monetary policy is endogenously determined to maintain a stable price

level.

P ,

=

p P,.

2 Long-run Analysis

The long-run properties of the m odel may be derived by reducing

the system to two m e r e n t id equations. From 4), ( l l ) , a nd S ) ,

I(Pk

=

Cf lPk- ( l -S ) Yd-SKPk

(12)

Dividing by K Pk , substituting for

C,

I and M P , and noting that

k / k

=

KIK-n,

we obtain the following differential equation in

k :

= s cfZpk)-- 1 f)(p+T)MPm--6KP,.

Logarithmically differentiating 10) with respect to t , we get

~ / M + T

=

bkk/b+ b , + / b + K / K .

10a)


5/9

1975 MONETARY EXPANSION, TRADE AND GROWTH

35

From this we can obtain the following differential equation in ?r:

where

kbk

a M

7 =

a K -

T

is the partial elasticity of demand for money with respect to the capital

stock and can be shown to be greater than unity. Equations 13) and

14)

constitute the basic differential equations of the system.

3.

Domestic

Price Stability

Is it possible to maintain a stable domestic price level; that is,

can = 0 for all t? The obvious answer is yes, provided the government

pursues an appropriate monetary policy. In this situation, p,

will

become

an endogenous variable, and the system can be completed by adding

=

0

as another equation. It is seen from 14) that for to be zero the

appropriate rate of monetary expansion must be

Therefore, for domestic price stability, the rate of monetary expansion

cannot

be

set arbitrarily but must equal the natural rate

n

plus or minus

a

correction factor which is the product

of

the rate

of

change of the

capital-labour ratio

and

the partial elasticity of demand for money with

respect to capital.

It

should be pointed out that equation 16) gives the

appropriate rate of domestic credit expansion that is consistent with

a

zero balance of payments. If the exchange rate is pegged, the domestic

money supply will always change at the rate that equals the flow

demand for money. The domestic credit creation will affect this to

maintain balance of payments. Thus, what we call the rate

of

monetary

expansion is really the rate of credit expansion. In

this

case, the

system can be reduced to a single differential equation in

k .

Substitute

for p from 16) into 13) and solve for to obtain

where Pk denotes the fixed world terms

of

trade and

is the average product of capital. Since

k =

0 along the balanced

growth path, the steady state condition is

where k* stands for the steady state capital intensity. We assume that

s A ( k * , P k ) 1

- ~ ) n b ( k * , O , P k )

n + 8

19)


6/9

36

THE

E C O N O M I C R E C O RD M A R C H

at least one solution exist^.^ It was shown earlier that bk is positive, and

hence the second term is

a

decreasing function of k . By proceeding as in

Uzawa [14], it can

be

shown that

if

the consumer goods industry

is

more capital intensive than the capital goods industry, then A

k,PI , )

is

a decreasing function of k . Hence , the left-hand side of 1 9 ) will decrease

when

k

increases, implying that the steady state

k*

satisfying (19) is

unique. Will the solution be stable? The necessary and sufficient condi-

tion for t he stability of this case is that + ( k * ) < 0. Differentiating 17)

with respect to

k

an d evaluating at k* (using 19) ), we get

< 0 .

s AB*

1

) n b k *

1 + 1 ) V * b

(/I*)

Therefore the steady state is unique and is also stable.

It is possible to

give

an economic argument for the stability in this

case. Suppose capital stock accumulates faster than labour. Then, as

we saw earlier, the demand for real balances per unit

of

capital will

increase (because

bk > 0 ) .

The portfolio composition therefore moves

in favour

of

monetary assets and away from capital assets. This reduces

investment, and therefore the rate

of

accumulation of capital falls. This

process will continue as long as the capital stock grows faster than

n.

Ultimately, capital accumulation slows to the rate

n

and balanced

growth is achieved. The mechanism is similar when labour grows faster

than capital,

What will be the level of trade (im ports or exports) in the long

run? From

5 )

we have the per capita level of trade as

c D ) / L = ( k / L / L ) P k + K Pk/L.

Since

K / K =

n in the steady state, the long-run per capi ta trade level

is (for the flexible exchange rate case)

T*

=

c* D * ) / L = [ n

+

6 ) k * - ( k * , P k ) ] P k .

Since the right-hand side

is

fixed, the trade level C * D* will grow

in the long run at the same rate as the labour force. But the ratio of

trade level to total output will remain constant.

We now investigate the sensitivities of the long-run capital intensity

(and hence of oth er endogenous variables) with respect t o changes in

the parameters of the system. It is evident from ( 1 7 ) that an increase

in s will

shift

the entire + ( k ) curve upwards and thus a k * / a s > 0.

Similarly,

ak* /an

>

0. These results are the same as in most growth

models. Since monetary policy is endogenously determined to maintain

a stable price level, we cannot examine the long-run effects of changes

in the rate

of

monetary expansion. However, we discuss this issue in the

next section.

4The boundary conditions A ( 0 , Pk) =

03

and

A m ,

P k =

0

re sufficient

to

guarantee the existence of at least one solution.


7/9

1975 MONETARY EXPANSION, TRADE AND GROWTH

37

An

interesting question that arises

in

this model is the effect

of

changes in the world terms of trade

( P k )

on long-run

k*

and also on

the equilibrium level of trade.

Differentiate

19)

partidly with respect to

PI,

and solve for

ak*/aPk to

obtain

The denominator

of the

above expression is negative because

A k < 0 and 6 , >

0.

An increase in the relative price of capital will

increase the wage-rental ratio because of the capital intensity condition.

The marginal product of capital therefore decreases. This will tend to

induce asset holders to favour the monetary asset more. Thus we should

expect

db/dPk

to be positive. It can

be

shown that

db /dP,

0. Even under these conditions the sign of

a T* / d Pk

is

ambiguous. However, it is possible to reach more definite conclusions

if T*

0, which is the same result obtained in neoclassical onesector

monetary

growth

No te also tha t this result is consistent with Allen

[ l ] .

S h e

has

shown that

if

the foreign elasticity

of

demand for t he coun t ry s expor t s i s s f l c i en t ly

large,

then

a k / J p >

0. In our model the elasticity is infinite.


9/9

1975

MONETARY EXPANSION, TRADE AND GROWTH 39

The effect of monetary expansion

on

the level

of

trade is given as

because Zk < 0 and d k * / d p > 0. Thus an increase in the rate of

monetary expansion will increase the trade level unam biguously.

Although we have not explicitly carried out the stability analysis,

it

is

easy to show that, like standard neoclassical models in which

actual rates of inflation are identical with the expected rates

of

inflation,

this model also has some difficulties with stability. The stability problem

could

be

solved in various ways. A well

known

way7

is

to introduce

explicitly

an

adaptive expectation mechanism. Stability is achieved if

the speed

of

revision

of

expectation is small. An alternative way

is

to

introduce a variable saving ratio and impose additional restrictions to

make t he system stable. In this variable saving rate case, an increase in

the rate

of

monetary expansion

decreases

the long-run capital intensity

as

well

as the level of trade, a result in

strong

contrast

to

the simpler

case

of

constant saving ratio.

R. R A M A N A T H A N

University of California,

Sun Diego

Date of Receipt of Final Typescript:

J d y

1974

R E F E R E N C E S

[ l J Allen,

P.

R., Money and Gro wth in Op en Economies,

Review of Econotrric

Stirdies,

Vol.

X X X I X , Apri l 1972,

pp.

213-19.

[ 2 ] Fischer ,

S.,

and

J.

A. Frenkel , Inves tment , the Two-Sector Model and Trade

in Debt and Capital Goods, Journal

of

International Economics, Vol. 2,

M a y 1972, pp. 211-33.

[3] Frenkel , J. A . , A Theory

of

Money Trade and Balance

of

Payments in

a Model of Accumulation, Journal

of

International Econonrics,

Vol. 1 ,

May

1971, pp. 159-87.

[4] Hadj imichalakis , 31. G., Equilibrium and Disequilibrium Gr ow th w ith

Money-The To bin Models, Rninv of Economic Stirdies,

Vol.

S X X V I I I ,

October

1971,

pp.

457-79.

[5] Inada , K., International Trade, Capital Accumulation and Factor Price

Equalization,

Ecoirowtic Rccord, Vol.

44, September 1968, pp. 3 2 - 4 1 ,

[6] Kernp,

M .

C., The Pitrc Theory of Intrmational Trade and

Investment

Prentice-Hall , Englewood Cliffs , N.J., 1 9 6 9 ) .

[7] Levhari ,

D.,

and D. Patinkin, , The Role

of

Money in a Simple Growth

Model, Anzericair Economic Remezu, Vol.

L V I I I ,

September 1968, pp. 713-53.

[ 8 ] Oniki , H., and H. Uzawa, Pat terns of Trade and Inves tment in a Dynamic

Model of Internat ional Trade , R w i c w of Economic Stidies,

Vol.

X X X I I ,

January l?65, pp. 15-38.

[9] Salop, J., T he E xc ha nge R a t e a nd t he T e rms of Trade, manuscript .

[ lo]

Sate,

K., Neo-class ical Economic Growth and Saving: An Extens ion of

I awas

Model, Econoinic Studies

Qiiarterlg,

Vol.

14,

1964, pp. 69-75.

[ 1 1

J

Sidrauski ,

hl.,

Inflation and Economic

Growth,

Journal

of

Political

Eco-

nomy,

Vol.

75, December 1967, pp. 796-810.

[12]

Stein, J . L., Monetary Grow th T heory in Perspect ive, Americon Economic

Rmiezv,

Vol. LX, March 1970,

pp, 85-106.

[

131 Tobin, J., Money and Economic Growth, Econometrica,

Vol.

33, October

[14] Uzawa, H . , On

a

Two-Sector Model of Economic Growth: II, Rerrezv

1965,

pp.

671-84.

o f

Economic Sttrdies,

Vol.

X X X , June 1963, pp. 105-18.

7

See Sidrauski [ l l ] .

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Ramanathan - Monetary expansion.pdf