International Trade

Stolper-Samuelson Theorem

From FPET, it is clear that when the price of a good (say X) increases, the return of the factor which is intensively used for the production of that good (L) increases.

Therefore, by trade, the return to the scarce factor decreases (because the price of a good which uses the scarce factor intensively decreases by trade), and the return to the abundant factor increases.

This theorem explains why labour unions in developed countries (most of them k-intensive) oppose free trade with less developed countries.

Quantitative Analysis

We make two assumptions:

Zero profit:
  • w + r = (1)
  • w + r = (2)
    • Full employment:
  • x + y =
  • x + y =

    • where = / x, = / x, = / y and = / y.

  • = w / x
  • = w / y
  • = r / x
  • = r / y

    • We would like to know and from and , where "^" denotes the rate of change.

    Differentiating (1) gives:

    wd + dw + rd + dr = d

    implies dw + dr = d

    The Marginal Rate of Technical Substitution is equal to the factor price ratio:

    d / d = -r / w

    implies w+dw/w+ + r+dr/r+ = +d / +

    implies +w/ ++dw/w><> + +r/ ++dr/r+ = d /

    As = /x and = /x:

    implies + /x++w/ ++dw/w+ + + /x++r/ ++dr/r+ = d /

    implies + =

    From (2):

    + =

    implies

    Using Cramer's Rules to solve it for and , then we have:

    As = 1 - and = 1 - :

    = +1 - + / + - +

    = - / + - +

  • positively related to and negatively related to
  • If L-int sector is protected, w increases and r falls
  • If K-int sector is protected, r increases and w falls

    • The change in factor price ratios is

    = + /r+ = - = / + - + =

    There is a magnification effect: The factor prices change more than proportionally when the commodity price changes.

    General Equilibrium Approach

    Let us suppose that Home is labour-abundant, specializing in a labour-intensive good X, and Foreign is capital-abundant, specializing in a capital-intensive good Y. Consider an Edgeworth Box explaining Home's production. At free-trade equilibrium A [1], Isoquants for X [2] and Y [3] must be tangent, and the tangent line represents the relative factor price (W/r) [4].

    X employs LX labour [5] and KX capital [6], and produces a certain amount of X at A. The distance OXA [7] represents the amount of X produced. Y employs LY labour [8] and KY capital [9], and produces a certain amount of Y at A. The distance OYA represents the amount of Y produced [10].

    Now suppose that a tariff on importing Y is imposed. As price of Y at Home goes up, sector Y expands, thus employing more L and K. Sector X releases both L and K (remember that the full employment is one of the assumptions of the neoclassical model). H's production of Y will go up 11] (sector Y employs more L and K) while sector X shrinks [12] (it employs less L and K). A new equilibrium will take place.

    =>Excess demand for capital will raise r (capital rent) while wages w will fall as excess supply of labour drives them down. As a result, w/r ratio decreases, and the tangent line becomes more gradual [13].



    (Question) How do you know wA'/rA' < wA/rA?



    One of the assumptions is that the production function is homogeneous of degree 1. One of the characteristics of the H.D.1 function is that on the same straight ray from the origin, [1] it has the same tangent [2]. In our case, the set of all possible equilibria [3] lies below the ray from the origin to the free-trade equilibrium A [4]. Thus, the tangent at A' will be less steep [5].



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