lower range of goods [0, zɪ], region M in an intermediate range [2⅛,Z2] and region
L produces the high-index goods [z2,0]. In this case, the Hrst condition for a trad-
ing equilibrium, deHning the cut-off sectors where it becomes profitable to move
production form one region to another as a function of wages, becomes:
wh _ Φh (¾) and wM _ Φm (¾)
WM Φm (^1) wl Φl (¾) ■
The second equilibrium condition, trade balance, can be written in two equations:
WhLh / P (г)
Zz1
ÇZQ,
wlLl / P (г)
Zo
1—6 j '
аг
1—6 j *
аг
Zzι zZ1
WMLm / P (г)1—6 di + WlLl / р (г)1—6 di,
Jo Jo
whLh / p (г)1—6 аг + wmLm / p (г)1—6 аг.
zZ2 zZ2
The first requires the value of total imports in region H to be equal to the value
of total export from region H ; the second is the equivalent condition for region L.
Trade balance in region M is then redundant. For a given technology and using (7)
to substitute prices away, this system of four equations in four unknown (wh∕wm ,
wm∣wl, zγ and Z2) can be solved to find the static equilibrium. Along the balanced
growth path, innovation has to be equally profitable in all the sectors. In particular,
considering sectors localized in different regions, and allowing θ to vary, the following
condition must hold:
for any г, j, V such that г ≤ zγ ≤ J ≤ Z2 ≤ V. These conditions can be used to
characterize the new trading equilibrium. Leaving the details of the analysis aside,
it is easy to see how the logic of previous results extends to the multi-country
setting: because of specialization, under free trade a tightening of IPRs in a region
(or in a large country of the region) attracts more innovation towards the goods
the region is producing. This translates into a higher wage and a reduction of the
range of activities performed in the region (moving production abroad becomes more
convenient as the domestic labor cost increases). On the contrary, the positive effects
of tighter IPRs in a region in autarky are spread across all sectors and affects only a
small fraction of the market for innovations (the fraction of profits coming from that
specific region) and therefore are less likely to have a significant impact on world
incentives to innovate. The main result of the basic model is therefore reinforced:
∂∏h (г)
∂a(ι)
Θm
∂∏M (J')
∂α(J)
∂∏l(v)
∂a(v') `
19