A higher productivity in the non-traded sector makes a country more competitive
because machines are produced with Hnal output, which incorporates also non-traded
goods. Trade balance and the arbitrage condition in R&D, [∂∏n (i)∕∂α(i)] (PN)*-1 =
θ [∂∏s(j)∕∂a(j)] (PJ)*-1 ∀i,j ∈ [0,1] with i ≤ z ≤ j, now yield:
-tσ
ω = θ (l-σ)t+σ
σ -, t(1—σ
Ls Jp Φn (i)~σ di ^-σ>t+σ ΓA↑,-
ln fz1 φs (i)1-σ di _ As -
σP-t)
(1 — σ)t+σ
(25)
Note that, as t → 1 the economy approaches the free trade equilibrium; conversely,
as t → 1 the wage ratio converges to the relative productivity of labor in the non-
traded sector of the two countries, AN/AJ (as in the autarky case, where A* was
a more complicated function of technology). Further, it is easy to see that the
presence of non-traded goods makes the two schedules (24) and (25) flatter; given
that the absolute value of the exponent of θ in (25) is increasing in t, it follows that
the relative wage, ω, is more elastic to a change of the IPRs regime, θ, the higher
the share of traded goods, t, in the economy. Considering the wage ratio in real
terms, ω (PJ∕PN)1-*, reinforces this result: since the price of non-traded goods is
proportional to the wage level, for a given change of ω real income difference reacts
more the higher is t.
2.5 Empirical Predictions
The key mechanism of the model is the interaction between trade-driven specializa-
tion and the ability of a country to attract better technologies by changing the level
of protection of IPRs. Given an elasticity of substitution across sectors larger than
one (e > 1 or σ > 0), more innovation targeted to a sector translates into higher
sectoral income, both in absolute terms and relative to the rest of the economy.
Because of this, a country unambiguously gains from innovations on the goods it is
producing. Innovation, in turn, can be stimulated by protecting more the rewards
of inventors. In this setup, specialization has two effects. First, by increasing a
country’s share of world production (and profits) in the sectors of specialization, it
increases the impact of country policies on global profitability of innovations directed
to those sectors, thereby increasing the ability of a country to attract technologies
tailored to its needs. Second, by reducing the number of countries producing a spe-
cific good, it limits the benefits of innovations directed to that good on the rest of
the world. For these reasons, the model suggests the positive effect of raising θ on
21