244 A.K. Basu, N.H. Chau International Review of Economics and Finance 8 1999 239–252
2. K
1
is strictly increasing in s. 3. K
j
is strictly decreasing in s, for every j . 1, if and only if mK
j
wL
j
, e
w
, where e
w
. 0 denotes the elasticity of the competitive wage, w, with respect to the uniform subsidy ]w]sw.
4. The proportion of low productivity capital imports, S
j i
5
a
i
K
i
S
n i
5
a
i
K
i
, is strictly increasing in s, if, for every k j , h n, ,
k
,
h
. K
k
K
h
. Contrary to the case of an increase in s
i
, which has the effect of unambiguously increasing the absolute as well as the relative level of capital imports from high and
low productivity firms, a uniform subsidy, on the other hand, can in fact perform quali- tatively the same role as a subsidy to low productivity firms, by increasing the absolute
and relative levels of capital imports from low productivity foreign firms and reducing the supply of capital from their high productivity counterparts. To see the intuition
behind this result, Eq 3 and 4 can be manipulated to obtain, for every i . j,
2 ]
K
i
]w ]
K
i
]s 5 ,
i
; 2
] K
j
]w ]
K
j
]s 5 ,
j
, ,
i
] K
i
]s . 0 represents the direct effect of an increase in s on the amount of foreign capital imports by type i firms. ]K
i
]w, on the other hand, represents the negative indirect effect of a uniform subsidy as a result as a result of the attendant increase
in the competitive wage rate. The relative magnitude of these two effects thus depends only on the labor intensity of the typical i-type firm. In particular, since ,
i
. ,
j
, whenever g
i
. g
j
, the negative indirect effect always takes a relatively larger toll on high productivity firms. It follows, therefore, that K
1
increases in both absolute and relative terms in response to a uniform subsidy. Meanwhile, whether K
i
rises or falls depends on the magnitude of the wage increase triggered by the implementation of
a uniform capital import subsidy in addition to the labor intensity of high productivity firms. In particular, the larger is g
i
and hence ,
i
, relative to g
j
,
j
, the more likely it is that the absolute amount of high productivity capital declines upon an increase
in s. The same intuition applies to part 4 of the propositions. The proportion of low productivity capital import of type k j rises with s whenever ,
k
is sufficiently larger than ,
h
for every h . j.
6
The use of a uniform subsidy to encourage foreign capital inflow, therefore, suffers from adverse selection among foreign firms with differing productivities. In particular,
an increase in s serves to increase the absolute as well as the proportion of low productivity capital imports. Competition for home country labor between high and
low productivity firms, in turn, guarantees that as long as the condition stated in part 3 of proposition 2 is satisfied the absolute amount of high productivity capital imports
is reduced in response to a uniform subsidy.
3. Optimal policy under perfect information
The analysis section 2 demonstrates the equilibrium allocation of capital between the home country and the rest of the world. To evaluate the national welfare conse-
A.K. Basu, N.H. Chau International Review of Economics and Finance 8 1999 239–252 245
quences of capital import subsidies and to demonstrate the possibility that asymmetric information may indeed lead to a reversal of the optimal policy measures targeting
high productivity firms, we shall proceed in two stages. Consider first the case where the government has perfect information about firm types. Accordingly, let the n-tuple,
{s
i
}
n i
5
1
, denote the productivity specific subsidies for each firm type i, which maximize national income, G
p
, in the absence of asymmetric information: G
p
5 N
o
n i
5
1
[a
i
wL
i
2 ms
i
K
i
] 1 XT, L
x
5 N
o
n i
5
1
a
i
[MK
i
, g
i
L
i
2 m 1 C9
i
K
i
] 1 XT, L
X
. 6
The first line of Eq. 6 expresses national income as the sum total of the income of all domestic factor inputs. The second line of Eq. 6 follows from the linear
homogeneity of the production function, M, and the profit maximization condition of foreign firms, as stated in Eq. 3. Hence, G
p
is simply the value of total output, evaluated at international prices, net of repatriated foreign capital earnings and subsidy
payments. In particular, m 1 C9
i
K
i
, should be interpreted as the supply price of K
i
units of foreign capital from a typical i-type firm. Therefore, dG
p
ds
i
5 Na
i
M
K
i
2 m 2 C9
i
2 C ″
i
K
i
] K
i
] s
i
1 N
o
j?i
a
j
M
K
j
2 m 2 C9
j
2 C ″
j
K
j
] K
j
] s
i
7 5 2Na
i
ms
i
1 C ″
i
K
i
] K
i
] s
i
2 N
o
j?i
a
j
ms
j
1 C ″
j
K
j
] K
j
] s
i
. 8
From Eq. 7, whether national welfare improves in response to a subsidy to type 1 firms depends once again on a direct and an indirect effect. The term M
K
i
denotes the marginal contribution of foreign capital, while m 1 C9
i
1 C ″
i
K
i
represents the corresponding change in the amount of repatriated foreign capital earnings. From Eq.
3, foreign firms set M
K
i
2 m 2 C9
i
1 ms
i
to zero in their profit maximization calculus. It follows, therefore, that beginning with s
i
5 0 the first term in of Eq. 7, indicating the direct effect on an increase in s
i
on national welfare is always negative. The indirect effect, which arises as a result of the reduction in capital imports from firm type j ?
i proposition 1 constitutes the possibility of a welfare improvement as a result of
an increase in s
i
beginning with s
j
5 0. To see this, note that 2ms
j
1 C ″
j
K
j
]K
j
]s
i
5 2C
″
j
K
j
]K
j
]s
i
. 0. Making use of Eq. 8, an obvious candidate for the n-tuple, {s
i
}
n i
5
1
, which equates the n first order condition to zero is that:
s
i
5 2 C
″
i
K
i
m 5 2
M
K
i
m h
i
, for every i, where h
i
denotes the elasticity of the supply price foreign capital with respect to K
i
, dlog m1 2 s 1 C9
i
d log K
i
. It is perhaps of interest to note that Eq. 8 implies that the Kemp-MacDougall
246 A.K. Basu, N.H. Chau International Review of Economics and Finance 8 1999 239–252
solution to the foreign investment problem carries over to the case with multiple sources of capital inflow. In particular, with perfect information, each i-type firm can
be subject to a productivity specific tax, which is proportional to the elasticity of its capital supply schedule.
7
Proposition 3: s
i
5 2 M
K
i
m h
i
, 0 for all i.
4. Optimal Policy under imperfect information
