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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

1.1 Comparative advantage

    1.2 The pattern of 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

    trading equilibrium ;

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

    The following trade is impossible:

    aapmpmm;;;0 (1) 11223

    The balance trade

    pmpmm;;,0(2) 11223

    (2)(2)Subtracting from leads to:

    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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