The construction of the production possibility curve shown in Figures 13.2 and
13.3 can be used to illustrate three important "theorems" in international
trade theory. To get started, notice in Figure 13.2 that the efficiency line
\(O_{x}, O_{y}\) is bowed above the main diagonal of the Edgeworth box. This
shows that the production of good \(x\) is always "capital intensive" relative
to the production of good \(y\). That is, when production is efficient,
\(\left(\frac{5}{7}\right)_{x}>\left(\frac{5}{1}\right)\), no matter how much of
the goods are produced. Demonstration of the trade theorems assumes that the
price ratio, \(p=p_{x} / p_{y}\) is determined in international markets-the
domestic economy must adjust to this ratio (in trade jargon, the country under
examination is assumed to be "a small country in a large world").
a Factor price equalization theorem: Use Figure 13.4 to show how the
international price ratio, \(p\), determines the point in the Edgeworth box at
which domestic production will take place. Show how this determines the factor
price ratio, \(w / v\). If production functions are the same throughout the
world, what will this imply about relative factor prices throughout the world?
b. Stolper-Samuelson theorem: An increase in \(p\) will cause the production to
move clockwise along the production possibility frontier \(-x\) production will
increase and \(y\) production will decrease. Use the Edgeworth box diagram to
show that such a move will decrease \(k / l\) in the production of both goods.
Explain why this will cause \(w / v\) to decrease. What are the implications of
this for the opening of trade relations (which typically increases the price
of the good produced intensively with a country's most abundant input).
c. Rybczynski theorem: Suppose again that \(p\) is set by external markets and
does not change. Show that an increase in \(k\) will increase the output of \(x\)
(the capital-intensive good) and reduce the output of \(y\) (the labor-intensive
good).
