(4)
where proposition 1 implies that Ia — 1, Ia — v, and Ia — pAV. Equilib-
rium under autarky requires that the following market clearing conditions
for sectors X and Y respectively, are satisfied:
V0ft — 2
PA ($l + v@-m) + V@h
θι + vθm — 1 ∖θl + vθm + pAV0h\
where in both conditions the left-hand side equals the supply of that good
and the right-hand side equals the corresponding demand. Solving either of
the above market clearing conditions for the equilibrium autarky price we
get:
A θι + vθm
(5)
p Vθh
It also follows from proposition 1 that 1 > pA > υ∣V.
4.1 Optimal education policy
The optimal education policy corresponds to the solution of the following
program:
1
max|{(θι + vθm) ( ɪɔ + Vθh (pA) 2 }
Oi 2 pA J
— ∖(p'''' 2 ∖θl + υθm + V0hpA\ (6)
subject to (5),
θh — 1 - θι - θm (7)
and
βm — C(1 - ,, >- b (S)
c — 1
where the last two constraints follow from (1) and (2).
The optimal proportion of type I workers under autarky is:
«A —
1 — b — c + be — bv + 2cv — bcv
2(1 — c + cυ)
(9)
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