Globalization, Divergence and Stagnation

and r are constant, this condition is:

∂π (г) 1
да (г) r   ^

Using (11), (10), (7) and normalizing μ = σ (1 — β) β, the previous expression re-
duces to:¹⁵

For the remainder of the paper, define σ ≡ β (e — 1) and assume σ ∈ (0,1). On the
one hand, the assumption σ > 0 (equivalent to e > 1) rules out Bahgwati (1958)
immiserizing growth: the fact that a sector (later on a country) growing faster
than the others would become poorer. On the other hand, the restriction σ < 1
is required to have a stable income distribution across sectors: it implies that if
a sector grows more than another, its relative profitability would fall, discouraging
further innovation.¹⁶ If violated, it would be profitable to innovate in one sector only
and all the other sectors would disappear, a case that does not seem realistic. From
this discussion, it is clear that along the balanced growth path R&D is performed
for all the machines and all the sectors grow at the same rate. But for this to be
the case, the incentive to innovate has to be equalized across sectors. Therefore,
imposing condition (12) for all г, it is possible to characterize the equilibrium profile
of relative productivity across sectors:

_             1

А (г) а (г) φ (г)       φ (г)

A (j) а (j) φ (j) [φ (j)

Equation (13) shows that, as long as σ > 0 (i.e., e > 1), sector specific innovations
amplify the exogenously given productivity differences φ (г) ∕φ (j). As for labor mo-
bility, in order to equalize the returns to innovation, the exogenously more productive
sectors need to have an higher than average а(г).

Finally, using (12), (9) and the Euler equation for consumption growth g = r — ρ,

¹⁶This normalization, where σ is defined below as β (e — 1), is meant to simplify the algebra only.

¹⁶When trade is allowed, this assumption yields a stable distribution of income across countries.
Evidence of stability of the world income distribution is provided by Acemoglu and Ventura (2002),
showing that countries growing faster than the average experienced a deterioration of their terms
of trade.

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