320 A.K. Parai International Review of Economics and Finance 8 1999 317–326
section 3, export-cum-on-site-production phenomenon is incorporated in the Brander- Spencer model, and rent-shifting power of tariff and corporate profit tax is examined.
In section 4, I present a numerical solution of the model to exemplify the implications of the tariff and the profit tax. The paper ends with some concluding remarks in
section 5.
2. Tariff and rent-shifting: The Brander-Spencer result
The foreign corporation maximizes its profits P by engaging in export x
2
to the host country. It pays a specific tariff on its export at the rate of t, 0 t , 1. The host
firm produces y amount of the same product, and maximizes its profit p. Two firms face a linear demand function
P 5 P x
2
1 y
, P9 ,
0, P
″ 5
0. 1
Both the firms produce under increasing marginal cost conditions. Their profit func- tions are as follows:
P 5 Px
2
2 C
x
2
2 tx
2
. 2
p 5 Py 2 C
y. 3
Each firm’s profit maximization would yield the following first order conditions. P
2
5 x
2
P9 1 P 2 C9
2
2 t 5
0. 4
p
y
5 yP9 1 P 2 C9
y
5 0.
5 One can derive the reaction functions of the foreign and home firm from Eqs. 4
and 5 respectively. Now I differentiate Eqs. 4 and 5 totally and derive the following comparative static derivatives.
dx
2
dt|D| 5 2P9 2 C9
y
, 0. 6
dydt|D| 5 2P9 . 0. 7
d[yx
2
1 y
]dt|D| 5 [x
2
dydt 2 ydx
2
dt]x
2
1 y
2
. 0.
8 d
x
2
1 y
dt|D| 5 P9 2 C9
y
, 0. 9
dPdt|D| 5 P9P9 2 C9
y
. 0. 10
dPdt|D| 5 2x
2
1 1 P9
2
, 0. 11
dpdt|D| 5 yP92P9 2 C ″
y
. 0. 12
Note that C ″
is the slope of the marginal cost function, C ″
. 0. And |D| is the
coefficient determinant of Eqs. 4 and 5, and |D| ; 3P9
2
2 2P9 C
″
2
1 C
″ y
1 C
″
2
C ″
y . 0.
From Eqs. 6–12 it is evident that an increase in the tariff rate would decrease the export and profit of the foreign firm, while it will raise the sales, market share,
and profit of the host firm. This is the rent-shifting effect of tariff in Brander-Spencer
A.K. Parai International Review of Economics and Finance 8 1999 317–326 321
model. The tariff, as under perfect competition here too, will raise the domestic price and reduce aggregate sales.
3. Export-cum-direct investment regime: Extension of Brander-Spencer
The foreign firm is now assumed to be a multiplant duopolist. It serves the host market in two ways, one through export x
2
from its plant in source country, the other from its production x
1
in the host country. The multiplant production is assumed to be the result of “tariff-jumping” by the MNC. The host firm produces y amount
of the same product
1
. The linear inverse demand function
2
will now be written as follows.
P 5 P x
1
1 x
2
1 y
, P9 ,
0, P
″ 5
0. 13
The MNC now pays a specific tariff at the rate of t per unit of x
2
, and also a proportional tax at the rate of t on its profits from on-site production, x
1
. The host firm also pays a tax on its profits at the same rate t, 0 t , 1.
So the net profit functions of the two firms will be as follows: P 5
1 2 t[x
1
P x
1
1 x
2
1 y
2 Cx
1
] 1 [x
2
P x
1
1 x
2
1 y
2 Cx
2
2 tx
2
]. 14
p 5 1 2 t[yPx
1
1 x
2
1 y
2 Cy]. 15
Under the Cournot quantity competition assumption, the first order conditions for profit maximization by the duopolists are as follows:
dP dx
1
5 1 2 t[P 1 x
1
P9 2 C9
1
] 1 x
2
P9 5 0.
16 dP
dx
2
5 1 2 tx
1
P9 1 P 1 x
2
P9 2 C9
2
2 t 5
0. 17
dp dy 5 1 2 t[yP9 1 P 2 C9
y
] 5 0. 18
Here P9,0 and C9
j
.0 are the first derivatives of the demand and cost functions respectively. Furthermore, from Eq. 16, [P 1 x
1
P9 2 C9
1
] . 0. Now I differentiate Eqs. 16–18 totally to obtain the following.
1 2 t2P9 2 C ″
1
dx
1
1 P9
2 2 tdx
2
1 1 2 tP9dy 5 [P 1 x
1
P9 2 C9
1
]dt. 19
P9 2 2 tdx
1
1 2P9 2 C
″
2
dx
2
1 P9 dy 5 x
1
P9dt 1 dt .
20 P9dx
1
1 P9dx
2
1 2P9 2 C
″
y
dy 5 0. 21
Here C ″
.0 stands for the slope of the marginal cost function. The Cournot-Nash equilibrium is assumed to be locally strictly stable so that the coefficient determinant
|D9| of the system given by Eqs. 19–21 is negative. It is also assumed that in the absence of on-site production the duopoly market remains stable. The latter assump-
tion basically reiterates that |D| . 0 see Bulow, Geanakoplos, Klemperer, 1985 for details. Specifically, I have
|D| ; 3P9
2
2 2P9C
″
2
1 C
″ y
1 C ″
2
C ″
y . as in section 2, and
322 A.K. Parai International Review of Economics and Finance 8 1999 317–326
|D9| ; 2|D|[C ″
1
1 2 t 1 P9t] 2 [C ″
2
2 P9t
][3 2 tP9
2
2 C
″
y
2 2 tP9]. 22
Thus the system is stable, that is, |D9| , 0 if [C ″
1
1 2 t1 P9t] . 0. I assume stability, and solve Eqs. 19–21 to derive the following comparative static derivatives.
3.1. Case 1: Tariffs [dx
1
dt] 5 2|D9|
2
1
[3 2 tP9
2
2 P9
2 2 tC ″
y
] . 0. 23
[dx
2
dt] 5 |D9|
2
1
1 2 t[3P9
2
2 2P9C
″
1
1 C
″
y
1 C ″
1
C ″
y
] , 0. 24
[dx
1
1 x
2
dt] 5 2|D9|
2
1
[C ″
1
1 2 t 1 P9t][2P9 2 C ″
y
] , 0. 25
[dydt] 5 |D9|
2
1
[C ″
1
1 2 t 1 P9t]P9 . 0. 26
[dx
1
1 x
2
1 y
dt] 5 2|D9|
2
1
[C ″
1
1 2 t 1 P9t][P9 2 C ″
y
] , 0. 27
[dPdt] 5 2P9|D9|
2
1
[C ″
1
1 2 t 1 P9t][P9 2 C ″
y
] . 0. 28
[dPdt] 5 [dPdydydt 1 dPdt] 5 [x
1
1 2 t 1 x
2
]P9dydt 2
x
2
, 0.
29 [dpdt] 5 [dpdx
1
dx
1
dt 1 dpdx
2
dx
2
dt] 1
dpdt 5 1 2 tyP9[dx
1
1 x
2
dt] . 0. 30
Assuming stability, Eqs. 23–30, especially Eqs. 29 and 30, once again establish the rent-shifting power of tariff. In an export-cum-on-site production regime, tariff
would reduce MNC export and increase its on-site production, but it would reduce its overall sale and net profit in the host country. The host firm’s output and net
profits, on the contrary, would rise as a result of tariff.
3.2. Case 2: Corporate profit tax [dx
1
dt] 5 |D9|
2
1
{P 1 x
1
P9 2 C9
1
|D| 2 x
1
P9 [3 2 tP9
2
2 P9
2 2 tC ″
y
]} , 0. 31
[dx
2
dt] 5 2|D9|
2
1
{P 1 x
1
P9 2 C9
1
[3 2 tP9
2
2 P9
2 2 tC ″
y
] 2
x
1
P9 1 2 t[3P9
2
2 2P9C
″
1
1 C
″
y
1 C ″
1
C ″
y
]} . 0. 32
[dx
1
1 x
2
dt] 5 2|D9|
2
1
{2P9 2 C ″
y
}{x
1
P9 [C
″
1
1 2 t 1 P9t ]
1 [P 1 x
1
P9 2 C9
1
C ″
2
2 P9t
]}. 33
[dydt] 5 |D9|
2
1
P9 {x
1
P9 [C
″
1
1 2 t 1 P9t] 1
[P 1 x
1
P9 2 C9
1
C ″
2
2 P9t
]}. 34
[dx
1
1 x
2
1 y
dt] 5 2|D9|
2
1
{P9 2 C ″
y
}{x
1
P9 [C
″
1
1 2 t 1
P9t ] 1 [P 1 x
1
P9 2 C9
1
C ″
2
2 P9t
]}. 35
[dPdt] 5 P9[dx
1
1 x
2
1 y
dt]. 36
[dPdt] 5 [dPdydydt] 1 dPdt 5 [x
1
1 2 t 1 x
2
][P9dydt] 2
[Px
1
2 C
x
1
]. 37
[dpdt] 5 [dpdx
1
dx
1
dt] 1 [dpdx
2
dx
2
dt] 1 dpdt 5
1 2 tyP9[dx
1
1 x
2
dt] 2 [Py 2 Cy]. 38
A.K. Parai International Review of Economics and Finance 8 1999 317–326 323
Assuming stability, Eqs. 31 and 32 ensure that an increase in corporate profit tax would decrease the MNC’s on-site production, and increase its export. But the effects
of the tax on the total sales of the MNC and of the host firm are not so clear cut. A sufficient condition for dx
1
1 x
2
dt , 0, or dydt . 0 is {x
1
P9 [C
″
1
1 2 t 1 P9t] 1 [P 1 x
1
P9 2 C9
1
C ″
2
2 P9t
]} . 0. 39
Once Eq. 39 is assumed, Eqs. 35–38 would show that dx
1
1 x
2
1 y
dt , 0, dP dt .
0, dPdt , 0, and dpdt _ 0. Under condition of Eq. 39, the corporate profit tax will have the same effects as the tariff on aggregate sales, price, and the net profit
of the MNC. The tax will increase the host firm’s market share and gross profit, but it may reduce its net profit. Thus, unlike a tariff, the corporate profit tax may fail to
shift rent away from the foreign to the host firm.
In the following section, I provide a numerical example where a rise in profit tax rate is shown to lower the net earnings of both firms. In this example, then, a cut in
the rate of profit tax would increase the market output and also the net earnings of the firms.
4. Numerical example: Export-cum-on-site-production
