The name is absent

4 Autarky

We derive the equilibrium under autarky in two stages. Under the assump-
tion that all markets are competitive, we begin by deriving the equilibrium
price and the corresponding production and consumption allocations for
an arbitrary education policy. Then, we derive the education policy that
maximizes aggregate welfare. The following preliminary result significantly
simplifies the equilibrium analysis.

Proposition 1 If the government is financially constrained, efficiency re-
quires that type I and type m workers are employed in the Y sector and type
h workers are employed in the X sector.

Proof. Suppose not. Then one of the following must be true:

a) Aggregate production of the X sector is less than Vθh. But this
implies that some type h workers are employed in the Y sector. Further,
a binding government constraint means that θι > 0. Then the government
could have enhanced welfare by reducing 0⅛ and increasing θ_m as this change
in policy would result in a higher output of the primary commodity with-
out any reduction in the production of the high-tech product. We have a
contradiction.

b) Aggregate production of the X sector is more than W⅛. But this
implies that some type m workers are employed in the X sector. Consider
a small increase in the proportion of type h workers. Then the budget con-
straint implies that the proportion of type m workers has to be reduced with
^g^ = —c. Now suppose that after this change you keep the production in
sector X constant. Given that all type h workers are employed in sector
X then the proportion of type m workers employed in this sector will be
reduced and j^ç- = — —. But since — > c the reduction in the proportion
of type m workers in sector X is higher than the reduction in the over-
all proportion of type m workers in the economy and therefore after the
above change the government can increase production in sector Y without
decreasing production in sector X. We have a contradiction. ■

The above result implies that given the government’s education policy
production in sector X will be equal to W⅛ while production in sector Y
will be equal to θι + vθ_m.

Using the primary commodity Y as the numeraire let p^A denote the
autarky price. Further let ∕_y' denote the income of a type i worker. Maxi-
mization of (3) subject to the budget constraint yields the demand functions:

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