production in that sector and thus it keeps exporting the primary commodity
Y. ■
The proposition identifies four type of economies. Sub-cases (la), (2a)
and (3a) identify economies for which it is always optimal to export the
high-tech product while sub-cases (lc), (2b) and (3c) identify economies for
which it is always optimal to export the primary commodity. In contrast,
sub-cases (lb) and (3b) identify economies for which a change in the patterns
of trade is optimal.
Moving up the chain: Notice that case lb is the only instance where it
would be optimal for the government to adjust its education policy in order
to reverse the patterns of trade so that the economy ‘moves up the chain’.
What prevents the government from pursuing such a policy is the binding
budget constraint. We show below that if the government is able to borrow
from abroad it would be beneficial to do so. The following proposition
demonstrates that the welfare gains resulting from a change in the patterns
of trade will be higher than the welfare loss incurred from a lump-sum tax
imposed to finance the loan.
Proposition 4 Suppose that pA > p* > pA*. Then it is optimal to finance
increased educational expenditures and move up the chain of comparative
advantage.
Proof. We know that in this case it is optimal for the economy to
maximize the production of the high-tech product; thus Θa = fifλ, θpn =
0, and Θa = ð. Define welfare without borrowing as Wn and welfare
with increased educational expenditures financed by foreign borrowing as
Wft.Using (6) we find that
Wn
∣(p∙)
+ Vbp*
c
The new welfare level after an increase in the budget by ∆b that is financed
by a lump-sum tax, is equal to
Wft = ∣(p*)"1
c — b — ∆b b + ∆b .
---------(1 — ∆b) +--(Vp — ∆b)
c c
where the increase in the budget allows for a greater proportion of agents
receiving the high level of education. Subtracting the former expression from
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