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International Trade - Theory and Policy, 2010a

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Adding these two equations vertically yields<br />

0QC − 5QS = −180,<br />

which implies QS=−180−5=36. Plugging this into the first equation above (any equation will do) yields<br />

2QC + 3∗36 = 120. Simplifying, we get QC=120−1082=6. Thus the new solutions are QC = 6 <strong>and</strong> QS = 36.<br />

The Rybczynski theorem says that if the capital endowment rises, it will cause an increase in output of the<br />

capital-intensive good (in this case, steel) <strong>and</strong> a decrease in output of the labor-intensive good (clothing).<br />

In this numerical example, QS rises from 24 to 36 <strong>and</strong> QC falls from 24 to 6.<br />

Percentage Changes in the Endowments <strong>and</strong> Outputs<br />

The magnification effect for quantities ranks the percentage changes in endowments <strong>and</strong> the percentage<br />

changes in outputs. We’ll denote the percentage change by using a ^ above the variable (i.e., X∧=<br />

percentage change in X).<br />

Table 5.4 Calculating Percentage Changes in the Endowments <strong>and</strong> Outputs<br />

K∧=150−120120∗100=+25%<br />

The capital stock rises by 25 percent.<br />

QS∧=36−2424∗100=+50%<br />

QC∧=6−2424∗100=−75%<br />

L∧=+0%<br />

The quantity of steel rises by 50 percent.<br />

The quantity of clothing falls by 75 percent.<br />

The labor stock is unchanged.<br />

The rank order of the changes in Table 5.4 "Calculating Percentage Changes in the Endowments <strong>and</strong> Outputs" is<br />

the magnification effect for quantities:<br />

QS∧>K∧>L∧>QC∧.<br />

The effect is initiated by changes in the endowments. If the endowments change by some percentage,<br />

ordered as above, then the quantity of the capital-intensive good (steel) will rise by a larger percentage<br />

than the capital stock change. The size of the effect is magnified relative to the cause.<br />

The quantity of cloth (QC) changes by a smaller percentage than the smaller labor endowment change. Its<br />

effect is magnified downward.<br />

Although this effect was derived only for the specific numerical values assumed in the example, it is<br />

possible to show, using more advanced methods, that the effect will arise for any endowment changes that<br />

are made. Thus if the labor endowment were to rise with no change in the capital endowment, the<br />

magnification effect would be<br />

QC∧>L∧>K∧>QS∧.<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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