Public Economics: Taxation
. For this problem set, you can work with your classmates, but
everybody should hand in their own copy. Please indicate on your copy who you are working with.
I recommend working on it on your own and then compare results with your classmates.
When
you derive your answers, please make clear what the answer path is supposed to be.
Focus on the
questions marked in bold.
1 Capital Tax Competition
There is a unit mass of agents in the home country, endowed with assets
A
and one unit of labor,
which is supplied perfectly inelastically, and consume
c
. The government is benevolent and maxi-
mizes the utility of its citizens
u
(
c
) +
v
(
g
) by choosing government consumption
g
and linear capital
taxes

{ note that there are no labor taxes and that utility does not depend on labor. As usual,
households react to government policy optimally.
u
(
c
) and
v
(
g
) are both increasing and concave.
The government has to balance its budget, so that
rK
=
g
, where
r
is the rate of return on capital
and
K
is the capital employed at home. Production takes place according to a CRS production
function
F
(
K;L
), so that
r
=
F
K
and
w
=
F
L
due to perfect competition of rms (
w
are wages).
The household only receives income from capital and labor.
1
(a) In a closed economy, set up the government’s maximization problem, dening the choice vari-
ables.
Show that the optimal allocation satises
v
0
(
g
) =
u
0
(
c
)
. Brie
y explain.
(b) Now suppose that there are two identical countries, as described above. There is perfect capital
mobility and agents can choose in which country to allocate their assets. Set up the gov-
ernment’s maximization problem, dening the choice variables.
Show that
g
is provided
sub-optimally, i.e. at a lower level than in a closed economy. Brie
y explain.
1
Hint: For this question, it is easiest to substitute out
c
and
g
from the budget constraints and to use the rst-order
condition with respect to

to derive results.
1
(c) Now assume that the home country owns assets
A
+

and that the foreign country owns
A

Public Economics: Taxation
. For this problem set, you can work with your classmates, but
everybody should hand in their own copy. Please indicate on your copy who you are working with.
I recommend working on it on your own and then compare results with your classmates.
When
you derive your answers, please make clear what the answer path is supposed to be.
Focus on the
questions marked in bold.
1 Capital Tax Competition
There is a unit mass of agents in the home country, endowed with assets
A
and one unit of labor,
which is supplied perfectly inelastically, and consume
c
. The government is benevolent and maxi-
mizes the utility of its citizens
u
(
c
) +
v
(
g
) by choosing government consumption
g
and linear capital
taxes

{ note that there are no labor taxes and that utility does not depend on labor. As usual,
households react to government policy optimally.
u
(
c
) and
v
(
g
) are both increasing and concave.
The government has to balance its budget, so that
rK
=
g
, where
r
is the rate of return on capital
and
K
is the capital employed at home. Production takes place according to a CRS production
function
F
(
K;L
), so that
r
=
F
K
and
w
=
F
L
due to perfect competition of rms (
w
are wages).
The household only receives income from capital and labor.
1
(a) In a closed economy, set up the government’s maximization problem, dening the choice vari-
ables.
Show that the optimal allocation satises
v
0
(
g
) =
u
0
(
c
)
. Brie
y explain.
(b) Now suppose that there are two identical countries, as described above. There is perfect capital
mobility and agents can choose in which country to allocate their assets. Set up the gov-
ernment’s maximization problem, dening the choice variables.
Show that
g
is provided
sub-optimally, i.e. at a lower level than in a closed economy. Brie
y explain.
1
Hint: For this question, it is easiest to substitute out
c
and
g
from the budget constraints and to use the rst-order
condition with respect to

to derive results.
1
(c) Now assume that the home country owns assets
A
+

and that the foreign country owns
A