On the Optimal Taxation of Capital Income

106 JONES, MANUELLI, AND ROSSI
income in the limit. One example of this, discussed below, occurs when
pure rents appear in the consumer's budget constraint. Secondly, if the
planner faces different constraints than the household which involve the
capital stock, again capital is taxed in the limit. This is the focus of our
second example in which there are two types of labor and the planner must
tax them equally. Finally, to gauge the quantitative importance of these
deviations, we solve for the optimal tax system in a parameterized version
of the second example.
To keep the presentation as simple as possible, from now on we restrict
attention to a one capital good growth model.
Consider a pseudo planner's problem given by
max :
t=0
; t [W(c t, n t, k t, *)]&m(c 0, n 0, k 0, *, b 0)
c t+x t+g t
k t+1
F(k t, n t)
(1&$) k t+x t
, i(c t, n t, k t, c t+1, n t+1, k t+1) 0 i=1, 2, ..., I,
(P.4)
where the interpretations of all of the variables are as in Section 2, except
that in this section, we will consider an example in which n is a vector.
This problem is general enough so that one special case is the one capital
good version of (P.3). More precisely, consider a standard one sector
growth model where preferences are given by
:
t=0
and the resource constraints are
c t+g t+x t
k t+1
; t u(c t,1&n t)
F(k t, n t)
(1&$)k t+x t.
Then, following the steps described in the previous section, it is possible
to show that the Ramsey problem for this economy when the planner can
choose { k
t and {n
t , t=1, 2, ..., can be found as the solution to (P.4) where
W(c, n, k; *)#u(c, 1&n)+*[u cc&u ln],
m(c 0, n 0, k 0; *)#*u c(c 0,1&n 0)[F k(k 0, n 0)(1&{ k
0 )+1&$ k+b 0],
and the constraints, , i(t) correspond, for example, to bounds on the
feasible tax rates.