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# Chapter1 The theory of international trade

By Janet Kennedy,2014-08-17 12:44
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Chapter1 The theory of international trade

Chapter 1 The theory of international trade

In two-product case

aS:the set gives the relative prices in autarky p1 any relative prices :p2

a?)paa1:bb the slope of the line in figure indicate 1.1??p2(，

relative prices in autarky

1?)p111:bb: the slope of the trade balance line in figure ??p(，2

1.1 indicate relative prices in trade (0,0):the origin must correspond to an allocation which

is preferred to any allocations corresponding to any other

aSpoint in ;

a(,):mm the allocations corresponds to any point in 12

a(0,0)S:but ;

1(,):mm the allocations corresponds to any point in 12

The main result :

a

(0,0)(,)mm12

1a (,)(0,0)(,)mmmm1212

aIt follows that for(/)(/)pppp, the country will export 1212

a(/)(/)ppppgood 1 and import good 2, and conversely for. 1212

The equilibrium price ratio must therefore lie between the

two autarky price ratios; in which case it is obvious that the

country with the lower relative price of good 1 in autarky

will export that good, and vice versa. In three-product case

Suppose there are three goods, let good be the numeraire, 3

the superscript a denote autarky value then ppp,,: the price of the goods 123

mmm,,: the quantities imported 123

aapmpmm；；；0 (1) 11223

pmpmm；；，0(2) 11223

aa()()0ppmppm？；？； (3) 111222

m0?)1??am0?)()0pp？！(，211 ???a()0pp？！m0?)22(，1??m02(，

The possibility that both goods 1 and 2 will be imported is ruled out

1.2.1 Factor abundance

bb1112,the factor intensity of good 1; bb1211

bb2221,: the factor intensity of good 2; bb2122

1.2.2 Product prices and factor prices:the

Stolper-Samuelson

1.2.2.1The definition

():pp be the output prices; 1,2

(,):ww the factor prices; 12

b(1,2) the input coefficients denoting the amount of factor ij

ij,(1,2)~jrequired for unit output of good,i ,it is fixed .

In competitive equilibrium , each output price equals the average cost ,which equals the average cost under constant returns to scale , so we have the equations of production equilibrium:

pbwbw，；1111122

(4)pbwbw，；2211222

()bb(1112

(5)()bb(2122

pw11，(，，,Where

pw22

()bb(1112lglglg()lg()，，；？；bbbb，((11122122()bb(2122

ddbbdbblglg()lg()，；？；，((11122122

dbdb()()d((1121，？()()bbbb；；11122122，((

1dbb1121，？dbbbb()()；；，(((11122122

11，？ (6)(/)(/)；；bbbb((12112221

bbbb//22211211(/)(/)；；bbbb12112221((

bb1112,the factor intensity of good 1; bb1211

bb2221,: the factor intensity of good 2; bb2122

(/)(/)0((；；！bbbb?)1d121122211).0?！??bbbb//0？！d，(22211211(，

bbbb22121121！?！bbbb21111222

(/)(/)0((；；！bbbb?)1d121122212).0?，??bbbb//0？，d，(22211211(，

bbbb22121121，?，bbbb21111222

(/)(/)0((；；！bbbb?)1d121122213).0?？??bbbb//0？？d，(22211211(， bbbb22121121？?？bbbb21111222

1.2.3 Production and factor supply:

the Rybzyski theorem ():xx The output of product 1,2 ; 1,2

(,):vv The factor endowment 1,2 ; 12

(,):ccthe consumption of product 1,2 12

vxbxb，；1111221

(7) vxbxb，；2121222

vbxxb((/))1111221

vbxxb((/))2121222

v1d()

vbbxxbbbxxb((/))((/))；？；211121222121112212x((/))bxxb1121222d()

x2

v1d()

vbbxxbbbbxxbb((/))((/))；？；2111212112211121221122x((/))bxxb1121222d()

x2

v1d()

vbbbb2112221122x((/))bxxb1121222d()

x2

vbb12212dbb()()1121vbb22111 (8)2x((/))bxxb1121222d()

x2

bb

22121)0？！bb

2111

vbb

12212dbb()()

1121vbb

22111，！0

2x((/))bxxb 1121222d()

x

2

bb

22122)0？，bb

2111

vbb

12212dbb()()

1121vbb

22111，，0

2x((/))bxxb1121222d()

x

2

bb

22123)0？？bb

2111

vbb12212dbb()()1121

vbb22111，？02x((/))bxxb1 121222d()

x2

dvdxbdxb，；1111222

(8)dvdxbdxb，；2121222

bdvbdv221211dx1

bbbb11222112

？；bdvbdv121111 (9)dx2

bbbb11222112

b1.2.3.Input substitution: is variable 22ij

case

1) The effect of a small change in relative factor price on the relative output prices

the effect of a small change in relative factor price on the relative output prices depend on which goods is relatively more intensive in which factor at the initial point.

?)wbbvxp11121111????,?? wbbvxp(，21222222

2) The effect of a large change in relative factor price on the relative output prices : factor intensity reversals

w1();bbww，，ijij w2

?)bb;11211):ww？！ ??bb(，1222

?)bb;11212):ww！？ ??bb1222(，

1.2.4.Several good and factors: mn

The generalization of the factor abundance hypothesis:

nm1) the number of goods is large than the number of factors

mmThis gives us equation in unknowns which in an

overdetermined system ,the economic point is that

(1) inter-industry substitution ,i.e changing the output mix, is not by itself sufficient to ensure full employment of all factors, or to maintain it in the face of changes in factor supplies

(2) with intra-industry substitution possible by changing the factor mix, there is the possibility of full

employment ,however ,changes in factor supplies will now entails changes in the input coefficients to preserve this states of

affairs,

nmthe number of goods is large than the number of 2)

factorsthis is an undedetermined system,in other words ,the supply side of the economy is insufficient to determine quantities produced .

1.3 Factor price equalization

1.3.1The two-by-two case

w1The relative factor prices map uniquely into relative ()w2

product prices and vice versa----- there is no factor intensity

wp0011reversals ()()? wp22

The only possibilities are specialization or complete factor price equalization

Figure 1.3a

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