The name is absent

Then it is clear that if p^A > p* the economy will export the primary com-
modity and if p^A < p* it will export the high-tech product. However, the
government can further enhance welfare by adjusting its education policy
after the change in the trade regime.

By substituting the world price for the autarky price in (6) we obtain
the government’s problem under trade.

max|(p*)^_1 (θι + vθ_m + Vθ_hp* )

θι 2

which using (7) and (8) can be written as:

Differentiating with respect to θι we get

j(p*Γ² (1 — v ^C — Vp* + Vp*ɪ)          (11)

2 C C — 1              c — IJ

Notice that the above expression is independent of θι which implies that we
obtain corner solutions. The intuition is that under free trade it is optimal
for the economy to specialize as long it is allowed by the budget constraint.
When the budget is sufficiently high so that the corresponding constraint
is not binding we also allow the government to redistribute any budgetary
surplus.

The optimal education policy under trade depends on the sign of the
expression in (11) that is in brackets. The expression is equal to 0 when the
world price p* is equal to p^A*. The following proposition defines the optimal
production patterns under trade.

Proposition 2 (Optimal Production Patterns) (a) If p* > p^A* it is optimal
that the economy produces as much as possible of the high-tech product,
X (the budget will not allow complete specialization), (b) If p* < p^A* it
is optimal that the economy specializes in the production of the primary
commodity, Y,

Proof, (a) In this case (11) is greater than 0 which implies that θι must
be set as high as possible. This is because, given the budget constraint, the
only way that the economy can increase the production of X is by increasing
θh that can only be accomplished by increasing θι while decreasing θ_m. At
the optimum we have θι = ^ç_^-,θ_m = 0, and θh = ð. (b) In this case (11)

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