samlet årgang - Økonomisk Institut - Københavns Universitet

TAXATION OF SHAREHOLDER INCOME AND THE COST OF CAPITAL IN AN OPEN ECONOMY 441
versified. For this purpose, it is useful to move from the level of the individual investor
to the macro level. If K j is the aggregate capital stock invested in an unquoted company
of type j at the start of the period; j is the rate of profit on this capital stock (after
payment of corporation tax), and q j is the ratio of the initial market value to the
replacement value of the capital stock (Tobin’s average q for unquoted companies),
we have
j
e j
rj = , re q j = , j = 1, 2 (24)
j qj ~2 j
2 j E (r j –r e j )2 = , ~2 j E ( j – e j )2 , j = 1, 2 (25)
q 2 j
~ j3
j3 E (r j –r e j )(r 3 –re 3 ) = , ~ j3 E ( j – e j )(r 3 –re 3 ) , j = 1, 2 (26)
q j
~ 12
12 E (r 1 –r e 1 )(r 2 –re 2 ) = , ~ 12 E ( 1 – e 1 )( 2 – e 2 ) (27)
q 1 q 2
where e j is the expected profit rate. At the macro level v 1 q 1 K 1 /V 0 , v 2 q 2 K 2 /V 0
and v 3 S 3 /V 0 , where S 3 denotes the aggregate stock of quoted shares held by domestic
residents. Using these definitions along with (24) through (27), and remembering
that ˆV 0 , we may rewrite (19) through (21) as
e 1 = iq 1 + ˆ (1–t) (K 1 ~ 2 1 + K 2 ~ 12 + S 3 ~ 13
e 2 = iq 2 + ˆ (1 –t) (K 2 ~ 2 2 + K 1 ~ 12 + S 3 ~ 23
r e 3 = i + ˆ (1–t) (S 3 2 3 + K 1 ~ 13 + K 2 ~ 23
) (28)
) (29)
) (30)
In the short run considered here, the initial capital stocks in unquoted companies
are predetermined. Moreover, e 1 and e2 are given by the state of expectations, and i
and r e 3 are exogenously given from abroad. However, even in the short run investors
can adjust their aggregate holding of quoted shares by buying or selling on the international
stock market. Equation (30) then determines the equilibrium value of S3 which