Globalization, Divergence and Stagnation



producing the cut-off commodity z: pn (z) = ps (z). Using (7), this latter condition
identi
fies the cut-off sector z as a function of the relative wage under free trade ω:

φN (z) =
φS (z)

(19)


Since comparative advantage of the North is decreasing in z, condition (19) traces
a downward sloping curve, Φ, in the space (z,
ω). The second equilibrium condition
is trade balance, i.e., imports and exports have to be equal in value. Since total
output in a country is proportional to the wage bill and the share of consumption
allocated to a set [0, z] of goods is
ʃj p (i)1-e di, trade balance can be written as:

Wn Ln


J^ p (i)1 e di = wsLs


Z p (i)1-e


di


Note that, by homogenous tastes, the origin of demand (and R&D spending) is
irrelevant. Using (7) the trade balance condition can be rewritten as:

wNLn [ A (i)σ di = wSLs [ A (i)σ di
Zz                       Jo

(20)


Along a balanced growth path, the profits generated by innovation in any pair of
sectors must be equal. In particular, considering innovations for the Northern and
the Southern markets, i and j, the following condition must hold:
∂∏n(i)∕α(i) =
θ∂πs(j)∕α(j). Substituting (11) for profits, noting that under free trade the op-
timal allocation of labor (10) is
In (i) = LnAn (i)σ ∕ JJZ An (^)σ dv and Is (j) =
L
sAs (j)σ ʃj As (u)σ dv and using (20), yields the equilibrium sectoral productiv-
ity pro
file:

an (i) = φN (i)
As (j)     θφs (j)_


1∕(1-σ)

(ω)σAσ-1l i, j [0,1] with i z j (21)

Compared to the autarky case, the relative productivity of sectors under free trade
still depends on the exogenous
φ (i), but also on the IPRs regime of the country
where the innovation is sold. Technology is still biased towards the exogenously more
productive sectors (as
σ (0,1), original differences Φn (i) ∕Φs (j) are amplified) but
also against the Southern sectors where some rents from innovation are lost (
θ < 1).
Integrating i over [0, z] and j over [z, 1] in (21) and using (20), the trade balance

14



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