Cremer, Helmuth; De Donder, Philippe; Maldonado, Dario; … - 2006
our compact notation, the problem of the social planner is expressed as follows:
L =
X
j=M,R
π
j
{Eu[w(1−τ)null
j
−s
j
−v …(null
j
)]
+ Eu[s
j
+ τ (αwnull
j
+(1−α)Ewnull)]},
Differentiating this expression yields:
∂L
∂τ
= −
X
π
j
©
E
£
wnull
j
¡
u
0 …
(x
j
)−αu
0
(d
j
)
¢
−u
0
(d
j
)(1−α)Ewnull
¤ª
+π
M
ταE
∙
w
∂null
M
∂τ
u
0
(d
M
)
¸
+
X
π
j
Eu
0
(d
j
)τ (1−α)Ew
∂null
j …