is less than O and optimality requires to set θι as low as possible so that θm
is at the maximum possible level. If b ≤ 1, θm = b and if b > 1,θm = 1
(budget surplus). ■
Notice that the above optimal production decisions do not depend on the
price under autarky. This is in contrast to traditional trade models where
the optimal production decisions and hence the patterns of trade depend on
the difference between the autarky price and the world price. The reason
is that in traditional models the production possibilities frontier is fixed.
In the present model, when the government changes the education mix it
also changes the production possibilities frontier. We will see shortly that
this is crucial for understanding patterns of trade reversals. The following
proposition defines the patterns of trade before and after the change in
education policy for all possible autarky prices. Let X- or Y denote the
good that was exported before the change in education policy and X+ or
Y+ denote the good that is exported after the change.
Proposition 3 Optimal trade patterns before and after the change in edu-
cation policy are as follows:
Case 1: b < bɪ
|
1a: If p* > pA then 1b: If pA > p* > pA* 1c: If pA > pA* > p* |
X- and X+ | |
|
then Y then Y- |
and Y+ | |
|
Case 2: b1 < b < b2 | ||
|
2a: If p* > pA = pA* |
then X- |
and X+ |
|
2b: pA = pA* > p* = |
then Y- |
and Y+ |
|
Case 3: b2 < b | ||
|
3a: If p* > pA* > pA |
then X- |
and X+ |
|
3b: If pA* >p* >pA |
then X- |
and Y+ |
|
3c: If pA* > pA > p* |
then Y- |
and Y+ |
Proof. Consider the patterns of trade before the change in education
policy. Then it is clear that when p* > pA was optimal for the economy
to export the high-tech product X while when p* < pA was optimal to
export the primary commodity Y. Next, consider the patterns of trade after
the change in education policy. With only exception case lb, they depend
on the patterns of specialization derived in proposition 2. In case lb the
education policy is determined by proposition l and welfare is maximized
when the economy specializes in the high-tech product X. However, the
binding budget constraint does not allow the government to further increase
16