Lyon
Econ 7140
February 27, 2004
Second Exam
1.
We analyze the welfare loss of placing sales taxes on the commodities
x
1
,
and
x
2
. The
representative consumer has utility function and transformation function:
u(x
1
, x
2
)u
,
C
2
,
u
strictly quasiconcave
G(x
1
, x
2
) = 0
with
G
C
2
,
G
strictly concave,
!
G
1
(x
1
, x
2
)
G
2
(x
1
, x
2
)
ÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉÉ
< 0
G
is identified from the problem:
Max:
p
1
x
1
+ p
2
x
2
Subj to:
f
1
(a
11
, a
21
)
!
x
1
= 0
f
i
C
2
and strictly concave
f
2
(a
12
, a
22
)
x
2
= 0
f
i
have positive marginal products
a
11
+ a
12
a
1
= 0
a
1
given
a
21
+ a
22
 a
2
= 0
a
2
given
a.
We place a excise tax of
J
on both commodities, and redistribute the tax revenues
in a neutral way. That is, a consumer pays
(1+
)p
1
x
1
+ (1+
)p
2
x
2
but the seller
receives only
p
1
x
1
+ p
2
x
2
.
The government then redistributes the tax revenue with
random lump sum payments to the consumers. Using the information that we
developed in class identify the welfare loss of this taxing scheme.
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 Spring '10
 Kutler
 Economics, Microeconomics, Utility, tax revenues, lump sum payments, positive marginal products, random lump sum, endogenous variable Jacobian

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