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.

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Copyright © 1997, 1998, 2001 Dr MoonJoong Tcha
(mtcha@ecel.uwa.edu.au)

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