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Dynamic Optimal Taxation
• Follows Kocherlakota, N. (2005) “Advances in Dynamic Optimal Taxa-
tion” http:/ /www.econ.umn.edu/˜nkocher/london3.pdf
1 Environment
• T periods.
• E ff ective labor units given by n
t
= θ
t
c
t
where θ
t
is skill and c
t
is e ff ort
• θ
t
is an iid shock across agents. At the beginning of the period θ
t
is
revealed. Let μ denote the prob distn over history θ
t
.
• ( θ
t
, c
t
) are private info but n
t
is observable.
• CRS technology F ( K
t
,
R
θ
t
n
t
( θ
t
) dμ ) with initial capital given by K
0
.
• Preferences:
E
"
T X
t =1
β
t − 1
{ u ( c
t
) − v ( c
t
) }
#
• Govt purchases G
t
2 Equilibrium
• Defn. An allocation is resource feasible if
Z
θ t
c
t
( θ
t
) dμ + K
t +1
+ G
t
≤ F ( K
t
,
Z
θ t
n
t
( θ
t
) dμ ) + (1 − δ ) K
t
• Defn. An allocation is incentive compatible if
T X
t =1
β
t − 1
Z
θ t
©
u ( c
t
( σ
T T
)) − v ( n
t
( σ
TT
) /θ
t
)
ª
dμ ≥
T X
t =1
β
t − 1
Z
θ t
{ u ( c
t
( σ )) − v ( n
t
( σ ) /θ
t
) } dμ
where σ
TT
denotes the truthtelling reporting strategy and σ denotes any
other report.
• Defn. An allocation which is incentive compatible and resource feasible is
called incentive feasible .