
35 
APPENDIX
t t t t C B A T T + + + = 0
A_{t }= Ae^{at }, B_{t }= Be^{bt },C_{t }= Ce^{ct }
.
T T
=
T T 0
aAe^{at }+bBe^{bt }+ cCe^{ct }
+
Ae^{at }+ Be^{bt }+Ce^{ct }
=
T T 0
c b a c w b w a w + + +
where w_{i }is the share of the i^{th }patent flow component
If a is the dominant r.o.g. in the limit the result will be
w_{a }→1, w_{b }→ 0, w_{c }→ 0,
0 T T
→0
.
and so ^{T }→ a . T
i.e. the rate of growth of the technology stock will be determined by the highest among the rates of growth of the patent flows and only the fastest growing patent component will, in the limit determine the accumulation of technology. This might not be the rate of growth of domestic patents. Hence the role of distance as representing the capacity to attract innovations is crucial in order to allow for technology accumulation to take place through diffusion, even if the domestic production of technology is negligible.
In the nonlimit solution, on the contrary, all variables grow at the same rate. To this case we now turn.
Initial levels of technology are equal to
i T *
=
Pat µ _{pati }* .i
in order to allow µ_{pati }
to be the r.o.g, as can
be derived by integrating eq (7) for each country. Herein, for simplicity we assume 3 interacting countries and one representing the rest of the world.
For sake of clarity and simplicity in illustrating the steady state solution we will refer to the case of three countries plus the United States. The list of exogenous and endogenous variables for the application of the undetermined coefficient method (see Gandolfo 1981, 1997) is the following:
Exogenous:
( 1 0 ) H K e H K H K 0 1 1 ρ =
_{1}t
( 1 1 ) H K e H K H K 0 2 2 ρ =
_{2}t