Globalization, Divergence and Stagnation

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

^φN ^(z) =
^φS ^(z)

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:

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:

wN^+σLn [ A (i)^σ di = wS^+σLs [ A (i)^σ di
Zz                       Jo

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) =
LsAs (j)^σ ∕ ʃj As (u)^σ dv and using (20), yields the equilibrium sectoral productiv-
ity profile:

¹∕(^1-σ)

(ω)^σA^σ-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

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