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
We now turn to the case where the government cannot perfectly decipher the true quality of foreign firms. Denote G
I
as the expectation of national welfare under imperfect information,
8
G
I
5 N
o
n i
5
1
[a
i
wL
i
2 msK
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
. 9
Therefore [Eq. 10], dG
I
ds 5 N
o
n i
5
1
a
j
M
K
i
2 m 2 C9
i
2 C ″
i
K
i
] K
i
] s
5 2N
o
n i
5
1
a
i
ms 1 C ″
i
K
i
] K
i
] s
. 10
From proposition 2, both the absolute and the relative levels of K
1
rise upon an increase in the uniform subsidy, s. K
j
, on the other hand, may fall as a result of an increase in s, as long as j . 1 and if the labor intensity of firm type j is sufficiently
large, which, in turn, once again gives rise to the possibility of a welfare improvement upon an increase in the uniform subsidy. We have the following result,
Proposition 4: The optimal foreign investment policy under asymmetric informa- tion is a uniform subsidy on the import of foreign capital if and only if
mS
n i
5
1
a
i
K
i
wS
n i
5
1
a
i
L
i
; mk
M
w+
M
, e
w
. Hence, in the presence of imperfect information and the adverse selection problem
discussed above, the normative ordering of the optimal foreign investment policy can be reversed, with a strictly positive foreign investment subsidy, as long as the labor
income response to the subsidy, as measured by elasticity e
w
, is no less than the increase in subsidy expenditure. Note, in particular, the same condition which guarantees an
optimal foreign investment subsidy coincides with that which governs the extent of adverse selection as stated in proposition 2, 3.
A.K. Basu, N.H. Chau International Review of Economics and Finance 8 1999 239–252 247
To see this, not that if mk
M
+
M
, e
w
, then, while K
1
is strictly increasing in s, there must be some foreign capital type j, such that for i j, mk
i
w , e
w
. Thus, K
i
is strictly decreasing in s due to adverse selection and relatively high quality capital
inflow decreases upon an increase in the uniform subsidy. In addition, making use of Eq. 14 in Appendix B, it can be readily verified that ]k
M
]s , 0 if and only if mk
M
w+
M
, e
w
. In other words, the domestic wage increase impact of the uniform subsidy is large enough to force a sufficiently large amount of high quality foreign capital out
of the home country, so that the aggregate supply of foreign capital bears an inverse relationship with s.
As such, adverse selection reverses the slope of the aggregate foreign capital supply curve with respect to the uniform subsidy s, and drives a positive wedge between
the average and marginal cost of subsidizing foreign capital inflows. It follows, there- fore, that the appropriate policy response in the face of an undersupply of foreign
capital when s 5 0, is to impose a capital import subsidy.
5. Conclusion
