The name is absent

By substituting the above solution in (7) and (8) we find the optimal solu-
tions for θh and θ_m, respectively, and then by substituting these solutions
in (5) we can solve for the optimal price under autarky:

_рЛ. = 1 + ^cV - 1)                       (10)

Notice that the autarky price does not depend on the size of the budget.
This is because we have focused our attention to the case of an interior
solution for the education policy; i.e. when θι > 0, θ_m > 0 and 0⅛ > 0. In
this case, because preferences are homothetic, the size of the budget does
not affect the ratio of the production levels of the two goods and hence
the equilibrium price. For intermediate values of budget size, as the latter
changes the proportions of the three types of agents adjusts so that the
above ratio stays constant.

By substituting (9) in (8) and differentiating with respect to b we find
that θ_m is increasing as the budget increases. When the budget is sufficiently
low we have ()"_r'_ll = 0. In that case

^_ι' =----,  $m = 0, and θ^ = -

^ι c ^{m                n} C

Using (5) we find that the equilibrium autarky price for this case, is given
^by

Al = ^{c - b} > ^{1 + c}(^{v - 1)} = A.
^l'      bV         v^p

where notice that v does not appear in the above solution because there
are not any type m workers. Also notice that the relative price decreases
as the budget increases. This is because the budget restrains output in the
high-tech sector X. As the budget size increases the proportion of type h
workers increases while the proportion of type I workers decreases. Equating
p^Al with p^A* we find a threshold level for the budget, given by

^l 2 + c(v - 1)

such that when b < bi, ()^. = 0.

There is another threshold level for the budget, b2, such that when the
budget is higher that this threshold θf = 0. In that case (5) implies that
the corresponding autarky price is given by:

∙' = "<^{C - b}) < _pA.

^p     V(b -1) ^p
13

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