Globalization, Divergence and Stagnation

Note that the endogenous component of sectoral productivity is now proportional
to a weighted average of the two exogenous indexes Φ_n (г) and Φ_s (г), with weights
that depend on country size, the strength of property rights and relative income.
The general expression for the relative Northern wage becomes:

{₁            r                                            -∣σ∕(l-σ)    ʌ l∕^σ

J₀ ^φN ^(гГ ^LN^φN ^(гГ + ^θlS^φs ^(гГ (N)"          ^di I

~---------r---------------------------------,₁σ∕(l-σ)    f

Jo ^φs W^σ [^ln^φN W^{σ + θl}s^φs W^σ <ω )^σ ] dɪ

Whether technology is closer to the Northern or Southern optimum, depends on
which of the two markets for innovations, Ln and θL_s, is larger (see also the Ap-
pendix). As θLs/Ln → 0, equations (17) reduces to (15). Therefore, the case of no
IPRs protection dehnes an upper bound for ω in autarky.

Finally, using (16), (9) and the Euler equation g = r — ρ, the growth rate of the
world economy for the general case when θ = 0 can be found as:

g = {jo h^φN ^{(г) + GL}s^φs ^(г)" ^(φN ^(г) ω^,' "] ∕( ) ^di}

Note that the world growth rate increases with θ because stronger IPRs translate
into higher prohts for innovation. As θ → 0, the growth rate declines to (14),
dehning a lower bound for the growth rate in autarky.

2.2 Trading Equilibrium

Trade takes place because of the Ricardian element of the model: even if techno-
logical progress is endogenous, productivity differences across countries are com-
pletely exogenous and so is comparative advantage. Recall that the ordering of
sectors г ∈ [0,1] is decreasing in the comparative advantage of the North, so that
Φn (г) /Φs (г) > Φn (^φ) /Φs (^φ) if and only if г < j. Further, for analytical tractabil-
ity, the comparative advantage schedule, i.e., the ratio of exogenous productivity
Φn (г) /Φs (г), is assumed to be continuous. The static equilibrium under free trade
can be found imposing two conditions. The first is that each good is produced only
in the country where it would have a lower price. Therefore, the North specializes
in the sectors [0, z] where its comparative advantage is stronger and the South pro-
duces the remaining range of goods [z, 1]. Given the continuity assumption on the
comparative advantage schedule, the North and the South must be equally good at

13

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