Trade and Factor Price Equalization Hypotheses
2015 Rochana et al.
241
1 ,
1
⎥⎦ ⎤
⎢⎣ ⎡
=
∫
ρ
ρ ρ
n
di i
m M
While the budgetary constraints faced by consumers are:
∫
+ =
n A
di i
m i
p A
p Y
From the results of the consumers’ optimi- zation, the demand functions for manufactured
goods and agriculture goods are:
1 −
− −
=
σ σ
µ G
j p
Y j
m
for
] ,
[ n j ∈
2
A
p Y
A 1
µ −
=
3 By entering the manufacturing demand func-
tion 2 and agriculture 3 into the utility func- tion resulting from the indirect utility function as
follows, we get:
1 1
1
µ µ
µ µ
µ µ
− −
− −
− =
A
p YG
U
4 Where
1 µ
µ −
A
p G
is the cost of living index. Equation 4 shows that consumer utility is af-
fected by the price index. The form of the trans- portation costs in the core periphery models is
iceberg where transportation costs are entered as a multiplier of the home price. As an example, if
the price of goods produced in the North is
M r
p
, and the transportation costs from North to South
is
M rs
T
, then the price of goods delivered to the South will be
M rs
M r
M rs
T p
p =
5 By including the transportation costs 5, the
demand function for manufactured goods is:
M rs
R s
s M
rs M
r s
M r
T G
T p
Y q
∑
= −
−
=
1 1
σ σ
µ
6 On the other hand, companies use the fixed
labour input F and marginal imput C
M
so that the amount of labour used is shown in the following
equation:
M M
M
q c
F l
+ =
The profit function is revenue from the sale of manufactured goods, minus the cost of labour:
M r
M M
r M
r M
r r
q c
F w
q p
+ −
=
π
. The profit maxi- mization is obtained from:
ρ
M r
M M
r
w c
p =
7 By entering the price equation 7 into the
profit function:
⎥ ⎦
⎤ ⎢
⎣ ⎡
− −
= F
c q
w
M M
r M
r r
1 σ
π
8 The balance of the manufacturer at the zero
profit condition is obtained:
M
c F
q 1
− ≡
∗
σ
9
σ
F q
c F
l
M
= +
≡
∗ ∗
10 Using the price equation 7, it can also be
found that the wage of manufacturing workers in the North is as follows:
] ]
[
1 1
1 1
∑
= −
−
=
R s
s M
rs s
M r
G T
Y w
σ σ
σ
11