Globalization, Divergence and Stagnation

' Φn (»)^J/<1-a) dr
fà Φn (rΓ^w^^rt Φs (≈)^σ dr

First, note that ∂ω∕∂φN (r) > 0 and ∂ω∕∂φs (r) < 0∙ Intuitively, the relative wage
is proportional to the exogenous productivity of the two regions, Φ_n and Ss∙ More
important, the Appendix shows that the sectoral prohle of technology is optimal for
the North, in the sense that it maximizes Yn, and is appropriate for the South only in
the limit case when the two regions have the same sectoral distribution of φ (φs (r) =
αφN (r), ∀i, with α equal to a constant of proportionality^¹⁹ This result mirrors, in a
different setup, that of Acemoglu and Zilibotti (2001)∙ Further, the Appendix shows
that ∀σ ∈ (0,1) ω is bounded by max {Φn (r) ∕Φs (r)} = Φn (0) ∕Φs (0)∙ Lastly, since
growth is due to the expansion of the a(ι) that are identical across countries, equation
(14) for the North gives also the growth rate of the South∙

Consider now the case of imperfect protection of IPRs in the South∙ To keep the
analysis a simple as possible, assume that the owner of a patent can extract only
a fraction θ of the profits generated by its patent in the South∙²° Therefore, θ can
be interpreted as an index of the strength of IPRs protection∙ The profitability of
an innovation is now the sum of the rents generated both in the North and in the
South, and the marginal condition for buying innovations becomes:

∂∏S (r) "I 1 =
да (r)   r ^

Substituting the expressions for profits and solving for a (r) yields:

in poor countries. This trade-off, studied extensively in the literature, is particularly important for
welfare analysis, which is not the main concern of the paper. On the contrary, positive rents from
innovation in the South are crucial to study the case of partial protection of IPRs. This latter case
seems realistic, since companies do receive royalties from developing countries.

¹⁹Remember that it is optimal to have high quality machines in sectors where the exogenous
productivity is already high. Copying the technology from the North, the South is using high
quality machines in sectors that are originally not productive. This inefficiency lowers the wage in
the South.

²⁰This description of IPRs is both simple and general. It can also capture practices such as
licensing, where rent sharing is necessary to deter default or imitation on behalf of the licensee. See
Yang and Maskus (2001) on this.

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