1. The trade theorems The construction of the production possibility curve shown in Figures 12.2 and 12.3 can be used to illustrate three important ‘theorems’ in international trade theory. To get started, notice in that the efficiency line
Ox,Oy
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, (k l
)x
> (k l
)y
no matter how much of the goods are produced. Demonstration of the trade theorems assumes that the price ratio,
p
=
px
/py, 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 equalisation theorem: Use 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 labour-intensive good).