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UXfi
1
n ifpi$pˆi
0 ifpi <pˆi
(
ð9Þ
764 R. A. Araujo and G. T. Lima
Where pˆi > pi we can take natural logarithms on both sides of equation (7) and
differentiate them with respect to time. By adopting the following convention: _pi
pi
¼ sUi
;
_pˆi
pˆi
¼ sAi
; _yA
yA
¼ sAy
;
_X
ˆn
Xˆn
¼ ˆg; this procedure yields the following growth rate of per capita export
demand for commodity i:
_ai ˆn
ai ˆn
¼
hiðsU
i
sA
i ÞþbisA
y þðbi
1Þˆg ifpi$pˆi
0 ifpi <pˆi

ð10Þ
By adopting the same procedure with respect to equation (9) in the case of pi > pˆi; and by
adopting the convention that _yU
yU
¼ sUy
and
_X
n
Xn
¼ g; we obtain the following growth rate of
the per capita import demand coefficient for commodity i:
_aˆin
aˆin
¼
ciðsA
i
sU
i ÞþfisU
y þðfi
1Þg ifpˆi$pi
0 ifpˆi <pi

ð11Þ
Let us assume that g ¼ ˆg ¼ 0; which means that the population in both countries remains
constant, and that sUi
¼ sAi
; which means that the rate of change of price of commodity i is
equal in both countries. In the aggregate BP-constrained growth model developed in
Thirlwall (1979), this assumption about relative prices is justified by claiming that even
though the terms of trade or real exchange rate may fluctuate in the short run, it appears to
remain relatively stable in the long run. In this case, expressions (10) and (11) can be
respectively reduced to:
_ai ˆn
ai ˆn
¼bisA
y ð12Þ
_aˆin
aˆin
¼fisU
y ð13Þ
In fact, only one of the two above equations is valid. Equilibrium in the balance of payment
is given by expression (3), and in order for this equilibrium to be maintained, it is necessary
that its time rate of change be equal to zero. Formally:
+
n
1
i¼1
ðj _ai ˆn
_aˆinÞani þ +
n
1
i¼1
ðjai ˆn
aˆinÞ _ani ¼0 ð14Þ
Let us consider the case in which there is no technical progress, that is, _aniðtÞ ¼ 0: In this
case expression (14) simplifies to:
+
n
1
i¼1
ðj _ai ˆn
_aˆinÞani ¼0 ð15Þ
By substituting equations (12) and (13) into equation (15) we obtain, after some algebraic
manipulation:
sU
y ¼
+
n
1
i¼1
jbiai ˆnani
+
n
1
i¼1
fiaˆinani
sA
y ð16Þ
Equation (16) is the first important result of this paper, as it shows the relationship between
the growth rate of per capita income in countries U and A. Let us define D as:
A structural economic dynamics approach to BP-constrained growth 765
D¼
+
n
1
i¼1
jbiai ˆnani
+
n
1
i¼1
fiaˆinani
ð17Þ
Where D < 1, a situation of uneven development will follow, that is, the per capita income
of the advanced country grows at a higher rate than the per capita income of the
underdeveloped one. After some algebraic manipulation it本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。