Globalization, Divergence and Stagnation

to cease. Note that this result, like Proposition 1, requires σ > 0 (i.e., an elasticity
of substitution between goods larger than one): with σ = 0 the cut-off commodity
z and the wage ratio ω would not depend on technology, because every country
and sector would benefit equally from any improvement in a(i), and (23) would not
depend on θ. Also, sector-specific technical process is a key assumption for deriving
Proposition 2. In a setup with factor-specific innovations, as in Acemoglu and Zili-
botti (2001), the market size for any innovation depends on exogenous endowments
that are unaffected by specialization and trade: for this reason, incentives to invest
in R&D would never go to zero even if θ = 0.²¹

Comparing the growth rate in free trade, (23), and autarky, (14), and noting
that (23) is a continuous function of θ with limθ→θ*>θ g^FT = 0, proves the following:

Proposition 2 For any σ ∈ (0,1), there exists a level θ such that, if θ < θ, the
world growth rate is lower in free trade than in autarky.

What happens during the transitional dynamics from autarky to the free trade
equilibrium? Since technology adjusts slowly, initially the equilibrium is determined
by equations (19) and (20) using the pre-trade values of α(z). In general, the wage in
both countries will jump up, as specialization increases the overall efficiency of the
whole economy. Then, if the instantaneous wage ratio falls short of its long run free-
trade value, there will be a period in which innovation is biased towards Northern
sectors. During the transition, the Northern relative wage will rise and at the same
time firms will move to the South where production costs are lower. Note that in a
trading environment with asymmetric IPRs protection, divergence and stagnation
are closely related: it is the growing cost of production in the wealthier North that
induces the relocation of production towards the South (an important phenomenon
in recent years) which in turn makes more sectors subject to weak IPRs and lowers
the global incentives for innovation.

2.3 Why Are IPRs Not Protected in the South?

The previous analysis suggests that Southern countries may benefit from the en-
forcement of IPRs: it would attract more appropriate innovations and foster world
growth. It is then interesting to ask why these policies are often not adopted. A first

²¹As a consequence, in Acemolgu and Zilibotti (2001) trade opening has no effect on the world
growth rate.

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