Globalization, Divergence and Stagnation

because of specialization, regulations of even small countries become more effective
in an integrated economy.

The introduction of non-traded goods gives rise to a regime that combines ele-
ments of both the free-trade and autarky equilibrium. Following Dornbusch et al.
(1977), assume that a fraction t of income is everywhere spent on internationally
traded goods and a fraction (1 — t) is spent in each country on non-traded goods.²²
Assume also that the range of traded goods is represented by the familiar [0,1]
interval, maintaining all the characteristics already discussed. More explicitly, con-
sumption and investment are now made out of a new output aggregate, (Y)^t (Y*)^1-t,
defined over the bundle Y of traded goods and a non-traded good Y*, denoted by
an asterisk. The non-traded good Y * can be thought of as another range [0,1] of
commodities similar to that in the traded sector, although it is simpler to treat
it here as a single good, with a production function similar to that of any single
y(t).²³ Given the Cobb-Douglas specification, a fraction (1 — t) of total labor force
is allocated to the non-traded sector: L* = (1 — t) L. As before, the price index
of the traded good Y is set equal to one.²⁴ The rest of the analysis follows the
steps of the basic model, with the difference that now the costs of machines and
innovation are not defined in terms of the numeraire, but in terms of final output,
with a price index proportional to (P*)^1-t. In turn, from the equivalent of equation
(7), the price of non-traded goods is found to be proportional to the wage rate:
w = ξ (P*)^t(^1-β)∕^β A*, where ξ is a constant and A* is productivity of labor in the
non-traded sector. After redoing all the intermediate caluclations, the condition for
efficient specialization in the traded sector, in (z~) = ps (z~), becomes:

²²Non-traded goods can also arise endogenously in the presence of a trade cost. However, mod-
elling a trade cost explicitly would complicate the analysis. More simply, in this setup a reduction
of trade cost can be thought of as an expansion of the traded sector. See Dornbusch et al. (1977)
for more details.

²³By treating Y * as a single good, the analysis abstract from the issue of “appropriateness”
of technology in the non-traded sector (i.e., the fact that different countries may desire different
technologies for non-traded goods). In order to study the impact of θ₁ on income differences, this
simplification is innocuous as long as Southern countries are small compared to the world economy.
In this case, a change of θi would attract better technologies only for the traded goods produced
by country i, where specialization neutralizes the small country assumption.

²⁴Final output cannot be taken as the numeraire because, in the presence of non-trade goods, its
price index will not be equalized across countries.

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