Walters & Layard CH 4Application to international trade1 INTRODUCTION 1-In this chapter we are going to apply general equilibrium analysis to the subject

Walters & Layard CH 4 Application to international trade 1

INTRODUCTION

INTRODUCTION

1-In this chapter we are going to apply general equilibrium analysis to the subject of international trade . 2-When Tariff is levied , we want to investigate that who loose and who gain , and how the pattern of trade will be determined . 3-In the first place we assume that the country is small and accept the world price . In this manner the behavior of citizens can not affect the world price .4-After that we release this assumption and assume that the country is not small in the world trade and terms of trade is not fixed and will be determined endogenously and we will find out about the mechanism of determination.


WORLD PRICES CONSTANT , ONE COUNTRY’S GAIN FROM TRDE WORLD PRICES CONSTANT , ONE COUNTRY’S GAIN FROM TRDE

Y

X

P

d

E

x0

Y0

U0

U1

U=U(X,Y)

dXp

Yp

C

xc

Yc

(∏x / ∏y) =(px/py)

Domestic price before trade=(px/py)’

E= No trade equilibrium point E= No trade equilibrium point

Consumption of x&y after trade= (xConsumption of x&y after trade= (x00, , yy00 ) )

C= after trade equilibrium pointC= after trade equilibrium point

World price = World price = (∏x / ∏y) =domestic =domestic

price after trade =(Pprice after trade =(Pxx/P/Pyy) )

Production point after trade = PProduction point after trade = P

Consumption point after trade = CConsumption point after trade = Cexport

import


WORLD PRICES CONSTANT ,

ONE COUNTRY’S GAIN FROM TRDE WORLD PRICES CONSTANT ,

ONE COUNTRY’S GAIN FROM TRDE At point E , (X0,Y0) → MRSxy = MRTxy = (px/py)’When trade takes place , production moves from point E to point P in order to ;

Max GNP = Y Py + X Px

S.T. G( X , Y ) =0 P.P.F. → Yp & Xp is the solution .At point P we notice that

Rate of transformation through trade= (∏x/∏y)=(px/py) =MRT MRT = domestic rate of transformation .

domestic rate =(Pdomestic rate =(Pxx/P/Pyy)’ > (∏)’ > (∏xx/∏/∏yy)= foreign rate → )= foreign rate →

Y can be produced domestically cheaper and X can be obtained cheaper Y can be produced domestically cheaper and X can be obtained cheaper through foreign trade ( import) through foreign trade ( import) . Domestic production of Y increase and domestic production of X decrease . Production point moves to point P and consumption point moves to point C . Consequently social welfare

will increase to U1 .


WORLD PRICES CONSTANT ,ONE COUNTRY’S GAIN FROM TRDE

WORLD PRICES CONSTANT ,ONE COUNTRY’S GAIN FROM TRDE

Since social welfare ( welfare of capital and labor Since social welfare ( welfare of capital and labor owners )has increased , there is a potential Pareto owners )has increased , there is a potential Pareto improvement by moving from point E to point C . improvement by moving from point E to point C .

In moving from point E to C relative price of X or (Px/Py) decrease and make labor owners worse off and capital owners better off ( Stopler – Samulson Theorem ) .

There is a possibility for government intervention , and levy tax on capital and subsidize on labor .


THE EEFECT OF A TARRIF ,WORLD PRICE CONSTANT .THE EEFECT OF A TARRIF ,WORLD PRICE CONSTANT .

Efficient compensation is rare , and disadvantaged groups may seek for inefficient way of compensation , namely tariff.

The effect of tariff is to increase the domestic price of x (Px/Py) . → (Px/Py) = ( ∏x/∏y) (1+t)

( ∏x/∏y)= foreign rate or foreign price of x .

t = tariff rate .

After tariff x becomes more profitable , and production moves from point P to point P’ on the PPF .

At P’ → MRT = (Px/Py) = (∏x/∏y ) (1+t) > MRTf = (∏x/∏y ) → production inefficiency


THE EEFECT OF A TARRIF ,WORLD PRICE CONSTANT . THE EEFECT OF A TARRIF ,WORLD PRICE CONSTANT .

Y

X

C

C’P’

P

R

Slope = ∏x/∏y

Slope = Px/Py

From P’ , trade take place along PR . Consumption equilibrium point will be C’ . So ;

MRS = ( Px/Py)= (∏x/∏y)(1+t)>MRTf



I - Production inefficiency

In moving from point P to point P’ , cost of producing additional x ( MRTxy) is greater than cost of buying it through foreign trade ( MRTf ).

II – consumption inefficiency;

In moving from point P to P’ , value of additional x to consumers (MRSxy) is greater than cost of providing it through international trade (MRTf= international value).

Consumption and production inefficiency could be seen clearly in the following diagram per unit diagramm.



S

D

Px/Py

x

∏x/∏y

(∏x /∏y)(1+t)

P P’ C’ C

Sf

Sf + t

a b c d

Total demand for x Without income effect

Domestic supply

Foreign supply

Import before tariffImport after tariff



As it is shown from the figure , after tariff consumption decrease from OC to OC’ , and production increase from OP to OP’ , and import will decrease too . Welfare changes are as follows ;

Consumer surplus decrease = - ( a+b+c+d) Producer Surplus increase = + aTaxpayers gain = +c Total welfare change = - (b+d)-b = production inefficiency from producing PP’ units more

expensive at home .-d = consumption inefficiency from consuming PP’ units less at

home .Considering the above argument , is there any argument in favor of

tariff .



Since X is labor intensive and y is capital intensive , after tariff (Px/Py) increase , and labor will be better off and capital becomes worse off . Since total welfare decrease , if whole gain goes to capital owners , still capital owners will loose .

If the intension of the tariff was raising the welfare of labor owners, tariff is not the proper way . Free trade with subsidy and taxes is the proper one .

If the intention is to encourage the development of the production of x (infant industry) , the best way is to set a minimum production level ( at P’ ) with providing a production subsidy instead of levying tariff .with production subsidy the producer’s price will raise to (1+t)∏x/∏y . Domestic production increase to OP’ , while the consumer’s price remain at the lower international price of (∏x/∏y) . So consumption will not be reduced . Intended production inefficiency is present while , unintended consumption inefficiency is not present .



If the intention is to lower the consumption of luxuries, the alternative policy tariff is to levy the consumption tax on luxuries. This will increase the price of x from

Px/Py = ∏x/∏y to (1+t)∏x/∏y . This will lower the consumption to C’ . But production price remain at ∏x/∏y and production inefficiency is not present . But intended consumption inefficiency is present .

Now suppose that there is a export tax on Y . This means to lower the price of Y in compare to international price of Y . This means lowering Py in ( Px/Py ) which means increasing ( Px/Py ) ,which acts like an import tax on X ,and consequently increasing the production of X and decreasing the production of Y .


THE DETERMINATION OF THE DETERMINATION OF WORLD PRICE WORLD PRICE THE DETERMINATION OF THE DETERMINATION OF WORLD PRICE WORLD PRICE

terms of trade is not fixed and it is variable . Not even large countries , but also small countries could have significant effect on the terms of trade, if small countries produce a large portion of the world production .

In order to see how the terms of trade are affected by commercial policies ( tariffs , export subsidies ) we need to know how the world prices are determined . For analyzing these effects we consider the case of pure exchange .

Consider the following diagram.


THE DETERMINATION OF WORLD PRICE

THE DETERMINATION OF WORLD PRICE

E

(∏x/∏y)=(px / py )

X imported by AX imported by A

Y e

xpor

ted

by A

Y e

xpor

ted

by A

OA

OB

Offer curve B

Offer curve APP

Is P an unique equilibrium point ? Or does a rise in (∏x /∏y ) always decrease the excess demand for x ? When (∏x/∏y ) increase substitution effect in both countries reduce the excess demand for x . there will be income gain to the one who export x and income lose to the one who import x . Until marginal propensity to spend on x differ sharply, these effects will be canceled out And excess demand will be reduced.

E =

initi

al e

quili

briu

m


OPTIMUM TARIFF, OPTIMUM TARIFF, WORLD WORLD PRICE variablePRICE variable OPTIMUM TARIFF, OPTIMUM TARIFF, WORLD WORLD PRICE variablePRICE variable

Neither of the countries is price taker . A will impose tariff to lower the relative world price of importing good X assuming that B does not retaliate ; it is assumed that after tariff world price will change from (∏x/∏y) to (∏x/∏y)1 and domestic price will change from Px/Py to ( Px/Py ) 1

Before tariff → (∏x/∏y) = Px/Py

After tariff → new world price = (∏x/∏y)1 = ( Px/Py ) 1 / (1+t) ,

New domestic price = ( Px/Py ) 1 = (1+t) (∏x/∏y)1

A’s

exp

ort

of Y A’s offerB’s offer

P

(∏(∏xx/∏/∏yy) = (P) = (Pxx/P/Pyy))

(∏(∏xx/∏/∏yy)) 1 1 =(P=(Pxx/P/Pyy) ) 1 1 // (1+t) (1+t) A’s import of X

TA1

TA0 = trade indifference curve

E

R

The best that The best that A could do is A could do is to bring the to bring the trade to point trade to point RR


OPTIMUM TARIFF, WORLD PRICE variable

OPTIMUM TARIFF, WORLD PRICE variable

Y per x

A’s import of X

B’s supply of X

MC of import to A

X1

e

f

X1*

(Px /Py)1

(∏x / ∏y)1

A’s demand for x

g

An individual importer who buys more imports forces up the price faced by other importers.

The externality mentioned above could be overcome by government through imposing tax on imports .

An individual importer who buys more imports forces up the price faced by other importers.

The externality mentioned above could be overcome by government through imposing tax on imports .

ef= optimum tariff rate ef= optimum tariff rate


OPTIMUM TARIFF, WORLD PRICE CONSTANT


If M = volume of importsΠ = (Πx/c)= international terms of trade . ΠM= total cost of imports (social cost of imports).d(ΠM)/dM = Π + M dΠ/dM = Π(1+1/ μs) μs = supply elasticity of imports .d(ΠM)/dM = additional cost imposed because of buying one

more unit of x .(externality imposed ).Π = (Πx/Πy)= the cost which will be paid by the importer for

one more unit of X .((ΠΠ//μμs s ) = the cost which will be imposed on others when ) = the cost which will be imposed on others when

one more unit of x will be bought.one more unit of x will be bought.the optimum tariff rate = 1/the optimum tariff rate = 1/μμs s

When country is price taker → μs = ∞ → tariff rate =0




for optimality we should have ;Marginal cost the importer impose on society [Π(1+1/ μs)]= marginal value which the society puts on X { demand

price}Export subsidy to Y → domestic price of Y (Py) < world

price of Y (Πy ) → ( Px/Py )↑ → the same effect will result as increase in domestic price of X with respect to tariff imposed on import of X

We had (K/L)x < (K/L)y or X is labor intensive , so when relative price of x will increase , this will lead to increase in (WL/WK) → real wage of labor increase, or real wage of capital decrease .

Tariffs usually is imposed by poor countries, and will be only justified by the notion of equity ground .


WORLD INCOME DISTRIBUTION AND TRADE PATTERN WORLD INCOME DISTRIBUTION AND TRADE PATTERN

Factor price equalization and Heckscher-Ohlin theorem

How far can a theory explain the pattern of world trade and income distribution in the world and what will be the welfare implications of free trade and international migration . Theorems will be built based upon the following assumptions ;

1- Technology (production function) is the same in both of the countries.

2-constant return to scale is present.3-perfect competition is prevailing.4-no factor intensity reversal is present5- no specialization is present ( each country produce some

of each good )


WORLD INCOME DISTRIBUTION AND

TRADE PATTERN WORLD INCOME DISTRIBUTION AND

TRADE PATTERN Above five assumptions we will have unique relation

between (Px/Py) and MPL and MPK in each industry .Each (Px/Py) → unique (K/L) in each industry → unique MPL

and MPK in each industry → (WL/WK) will be unique.Under free trade (Px/Py) is the same in both countries , so

(WL/WK) will be the same in both countries .Given assumptions 1 through 5 , free movements of goods

will bring the equality in factor prices and movement of the factors of production is not necessary .

once (WL/WK) is known in each country , (K/L) is known in each industry . Knowing (K0/L0) and the following relation, the product mix will be known . The equilibrium point on the contract curve will be known , so the product mix will be known )

(K0/L0) = (K/L)x (Lx/L) + (K/L)y (Ly/L)




TRADE PATTERN in a country where (K0/L0) is high ( capital rich country like

country A in page 22 ) and knowing that x is labor intensive , [(K/L)x < (K/L)y ] , higher weights should be attached to (K/L)y . So, (Ly /L0) > (Lx /L0) → production of Y with respect to X is high . So more Y will be produced with respect to X ( in country A with respect to country b in page 22 )

Weak version of Hecscher-Ohlin theorem ;Under free trade and given assumptions 1-5 , the

capital rich country will produce relatively more of the capital intensive good.

But this says nothing about the pattern of trade (export and imports). We need to introduce the strong version of the theorem .




TRADE PATTERN

Having strong taste (demand) for capital intensive good , the capital intensive country could import the capital intensive goods except when taste are the same in each country . When taste are the same , for given (Px/Py) the same proportion will be spent for each good in each country. This will happens when we assume homothetic utility functions in the countries.

Strong version of the H.O. theorem ;Given free trade ,assumption 1-5 , and identical

homothetic tastes in both countries, the capital rich country will export the capital – intensive goods and vise versa.




TRADE PATTERN

OA

OBYA

XA

XB

YB

P

C

C’.

A,s import

B’s export

A’s

ex

po

rt B’s

im

po

rt

P=world production equilibrium point

C= world consumption equilibrium point

Under free trade MRTA

xy=MRTBxy=(Πx/Πy)=Px/Py

As it is seen world equilibrium is prevailing → world excess demand for each good is zero.

X is labor intensive and y is capital intensive . If A is capital abundant country and B is labor abundant country , we expect that (Y/X)A>(Y/X)B→P should lie above the diagonal → if c lies below the diagonal , H.O. theory is working .




TRADE PATTERN This is the special case of the more general theory of

comparative advantage which says that that country which has comparative advantage in any good will produce that good when free trade is prevailing .

We should note that point C , the equilibrium consumption point should not lie above the point P ( like C’ ). Since in this case the capital rich country would import capital intensive good. This happens if taste differ sharply in two countries. That is , consumers should have very strong preference for capital intensive goods in country A and very strong preference for labor intensive good in country B . This will not happen if taste were homothetic in both countries.




TRADE PATTERN What does the theory says about optimality of trade of free

trade ?

Even without the five assumption that we have made any competitive equilibrium would be fully efficient , if all agents were free to do the best for themselves . But there are international barriers on migration of labor or sometimes for capital movements .

When these barriers are present , the five assumptions would guarantee the efficiency of world economy under free trade . Because they insure that the marginal product of given factor is the same in all countries. The equality of marginal product is needed for he equality of real wages .




TRADE PATTERN How realistic is all this ? How realistic is the strong version of

the Hecher Ohlin theorem . Do countries export goods which is intensive in their abundant factor ?

Taking into account labor and capital as two relevant factor ,we would expect the densely populated countries to import grain from sparsely populated countries .it is found that they do .

However Leontief calculated the capital labor ratio for US export and found that it is 25 percent lower than for US import competing goods . The first problem with this analysis was dismissing the natural resource as a factor. The second problem is heterogeneity of the labor .




TRADE PATTERN These factors are very difficult to measure . Concerning the

heterogeneity of labor more research has shown that US export are more skill intensive than US imports .

The evidence of factor price equalization is very weak . The real wage of a given quality of labor is much higher in capital rich countries .

These evidence against the theorem may happen because of the failure of the assumptions which we were made .

First – we relax the assumption about the factor intensity reversal ;Agricultural sector (x) is labor intensive in labor abundant countries and is

capital intensive in capital intensive countries. This would mean that at

given world product price (Px / Py) , relative factor prices differ between

countries .




TRADE PATTERN

(Px/Py)0

XXYY

))WWLL/W/WKK((00

((K/L)x0

(K/L)(K/L)y0y0))K/LK/L((y1y1

))K/L(x1

agriculture

manufacture

1 = capital abundant country 0 = labor abundant country

(W(WLL / W / WKK ) )11 > (W > (W LL / W / WKK ) )00

In capital abundant country In capital abundant country (1) , capital labor ratio is (1) , capital labor ratio is higher in x and y industries higher in x and y industries compared to labor compared to labor abundant country (0)abundant country (0)

X is labor intensive in labor abundant country , so x will be exported by country 0 . X is also capital intensive in capital abundant country , so x will also be exported by capital abundant country .theory breaks down .

An inefficiency will be present in the world economy since relative factor prices differ in two countries .

X is labor intensive in labor abundant country , so x will be exported by country 0 . X is also capital intensive in capital abundant country , so x will also be exported by capital abundant country .theory breaks down .

An inefficiency will be present in the world economy since relative factor prices differ in two countries .

(W(WLL / / WWKK ) )11




TRADE PATTERN Inefficiency will also be present if either of the countries

specialize entirely in any of the commodities .

O

XX

yy

(K/L)x)K/L(y(Px/Py)0

(WL/WK)0

(K/L)A

/(K/L)B

World prices

Country B is starving of Country B is starving of capital so that she is capital so that she is not able to produce not able to produce capital intensive good , capital intensive good , and will be specialized and will be specialized on producing labor on producing labor intensive good (x) . As intensive good (x) . As it is seen , there should it is seen , there should be two different relative be two different relative wage rates. Inefficiency wage rates. Inefficiency will be present . Theory will be present . Theory does not work does not work

(WL/WK)’


WORLD INCOME DISTRIBUTION

AND TRADE PATTERN WORLD INCOME DISTRIBUTION

AND TRADE PATTERN When wages are differ in two countries , labor migration will

be encouraged and if it is allowed this may eliminate the wage differential in two countries . But the very fact that unsatisfied migration pressure will exist , this suggest that free trade is not sufficient to produce efficiency in the world .

If taste differ or if expenditure patterns differ with income, we may get different pattern of trade than the one predicted by Heckscher-Ohlin theorem . But the income distribution predictions and efficiency implications of the theory will be unaffected.




AND TRADE PATTERN Allowing differences in technology can make more difference .

One country may excel over others in all industries or only in some .

Suppose that Swiss can make 25 percent more than the others with any given input bundles in either industries ( X or Y ). This would not alter the shape of Swiss transformation curve , but push it only out along every ray from origin to a point 25 percent beyond that occupied by another country with the same endowment .

So production pattern would follow the H.O. theorem .but the real marginal product of all factors will be 25 percent higher in Swiss than another country .




AND TRADE PATTERN But suppose that Swiss is better in 25 percent in labor

intensive good ( Watch making) only . K

LXS

XN

Y=1

(K/L)XN

(K/L)XS(K/L)YS

(K/L)YN

)WL/WK(s > (WL/WK)N

Iso-quant for watch map in Swiss is the same as elsewhere but each Is-oquant correspond to a higher output.

32

WORLD INCOME DISTRIBUTION AND TRADE PATTERN WORLD INCOME DISTRIBUTION AND TRADE PATTERN Xs shows the one dollar value of Swiss watches ( y=income)

XN shows one dollar value of other country watches .

As it is seen Swiss use less Labor and Capital for producing one unit of X, because Swiss is more efficient in watch making. As it is seen (K/L) is also higher for Swiss in both industries ( X ,Y ). This will imply higher real wage in Swiss in compare to other country.

Having higher (K/L) in labor intensive commodity (X) in Swiss compared to other country, Swiss will employ higher fraction of both factors in Watch making industry since it employs higher fraction of capital and its productivity is higher in watch industry ). Since Swiss is more efficient in making watches, it would produce higher ratio of watches to other goods. With identical homothethic taste Swiss will export watches.




AND TRADE PATTERN Now suppose that the assumption concerning constant

return to scale relaxed.

Increasing return to scale certainly help to explain the fact of some inter-country specialization in production . But assuming that the scale economies are the same for all countries , they do not explain which country concentrate on which products . The country that will reap the economies of scale in particular industries will be the one that has comparative advantage in it , due to its endowments or its relative technological superiorities .

THE END

Documents

Walters & Layard CH 4Application to international trade1 INTRODUCTION 1-In this chapter we are going to apply general equilibrium analysis to the subject