-
Utility
function
Utility calculation
methods
Notation
Calculation methods
1.
m
in
v
(
p
,
m
)
st
:
?
p
i
x
i
?
m
2.
v
(
p
m
p
i
m
?
D
i
(
x
,1
)
?
1
U
(<
/p>
x
)
,
1),
w
here
1.
m
ax
U
(
x
)
st
:
?
p<
/p>
i
x
i
?
m
Indirect utility
function
v
(
p
,
m
)
< br>
2.
U
(
< br>D
(
p
,
m
))
3. the
inverse function of
e
(
p
,
u
)
< br>
Expenditure
function
1.
?
i
n
?
1
p
i
h
i
(
p
< br>,
u
)
e
(
p
,
u
)
2. the inverse
function of
v
(
p
,
m
)
1.
e
(
p
,
v
(
q
,
m
))
Money
metric
Indirect utility
function
u
(
p
,
q
,
< br>m
)
2.
< br>?
u
(
p
,
q
,
m
)
?
p
i
?
x
i
(
p
,
u
(
p
,
q
,
m
< br>)),
i
?
1,
2...
n
u
(
q
,
q
,
m<
/p>
)
?
m
1.
m
ax
U
(<
/p>
x
)
s
t
:
?
p
i<
/p>
x
i
?
m
?
v
(
p
,
m
)
?
m
n
Mashallian
demand
function
2.
x
i
?
?
x
i
?
D
i
(
p
m
)
?
v
(
p
< br>,
m
)
?
p
i
/
3.
x
i
?
m
?
v
(
p
,
m
)
?
p
i
/
?
i
?
1
< br>?
v
(
p
,
m
)
?
p
i
p
i
4.
x
i
?
h
i
(
p
,
e
(
p
,
u
))
1.
m
in
v
(
p
,
m
)
st
:
?
p
i
x
i
?
m
?
v
(
x
,
m
)
?
x
i
Inverse
demand
function
p
i
?
D
i
(
x
m
)
?
1
2.
p
i
?
m
?
u
(
x
m
)
?
x
i
/
?
i
< br>?
1
n
x
i
3. The inverse functions
of
x
?
D
(
p
,
m
)
1.
m
in{
?
p
i
x
i
}
st
:
U
(
x
)
?
u
Hicksian
demand
function
x
i
?
h
i
(
p
u
)
2.
x
i
?
?
e
(
p
,
u
)
?
p
i
3.
x
i
?
D
i
< br>(
p
,
e
(
p
,
u
))
Utility
function
Indirect utility
function
u
?
Cobb Douglas utility function
Formula
U
?
Ax
y
< br>?
1
?
?
Formula
x
?
m
Mashallian
demand function
Inverse demand
function
?
m
p
x
,
y
?
(1
?
?
)
m
p
y
A
?
(1
?
?
)
p
x
p
?
1
?
?
y
?
1
?
?
p
x
?
?
< br>m
x
,
p
y
?
(1
?
?
)
m
y
]<
/p>
1
?
?
Expenditure
function
Money metric
Indirect
utility
function
e
?
p
x
p
y
u
A
?
(1<
/p>
?
?
)
?
1
?
?
?
1
?
?
Hicksian demand
function
x
?
[
y
?
[
?
p
y
(1
?
?
)
p
x
(1
?
?
)
< br>p
x
u
A
?
p
y
]
?
u
A
u
?
p
x
p
y
m
q
x
q
y
?
1
< br>?
?
?
1
?
?
Utility
function
Leontief utility function
Formula
U
?
min{
x
,
y
}
Formula
x
?
y
?
m
p
x
?
p
y
Mashallian
demand function
p
x
?
m
x
,
p
y
?
0
x
?
y
m
x
x
?
y
m
y
< br>x
?
y
Indirect
utility
function
u
?
m
p
x
?
p
y
Inverse demand
function
p
x
?
p
y
?
p
< br>x
?
0,
p
y
?
Expenditure
function
Money metric
Indirect utility
function
e
?
(
p
x
?
p
y
)
u
u
?
< br>(
p
x
?
p
y
)
m
(
q
x
?
q
y
)
Hicksian demand
function
x
?
y
?
u
< br>
Linear utility function
Formula
x
?
m
p
x
Formula
,
y
?
0
p<
/p>
x
?
p
y
m
p
x
p
x
?
p
y
m
p
y
m
x
?
y
m
y
m
< br>x
Utility
function
U
?
x
?
y
Mashallian
demand
function
x
?
y
?
x
?
0,
y
?
p
x
?<
/p>
p
y
p
x
?
p
x
?
x
?
0,
y
?
0
Indirec
t utility
function
u
< br>?
m
m
in{
< br>p
x
,
p
y
}
Inverse
demand
function
p
x
?
p
y
?<
/p>
p
y
?
p
x
?
x
?
0,
y
?
0
x
?
0,
y
?
0
Expenditure
function
e
?
m
in{
p
x
,
p
y
}
< br>u
Hicksian
demand
function
x
?
u
,
y
?
0
p
x
?
p
y
x
?
y
?
u
,
p
x
?
p
y
x
?
0,
y
?
u
p
x
?
p
y
Money metric
m
in{
p
x
,
p
y
}
m
u
?
Indirect
utility
m
in{
q
x
,
q
y
}
function
Utility
function
CES utility function
Formula
U
?
(
?
x
i
)
??
?
?
?
1
?
1/
?
Formula
m
(<
/p>
x
i
?
[
?
n
j
?
1
1
p
i
(
1
Mashallian
demand function
)
1
?
?
1
p<
/p>
j
?
]
)
1
?
?
Indirect utility
function
u
?
m
[
?
n
j
?
1
(
1
p
j<
/p>
?
1
?
?
)
1
?
?
]
?
Inverse
demand
function
p
i
?
m
x
i<
/p>
?
?
?
1
n
j
?
1
x
j
?
Expenditure
function
e
?
[
?
n
j
?
1
u
(
1
p
j<
/p>
1
q
j
)
?
1
?
?
)
1
?
?
]
?
Hicksian
demand
x
?
i
function
u<
/p>
(
[
?
n
j
?
1
1
p
i
1
1
)
1
?
?
?
1
(
p
j
)
1
?<
/p>
?
]
?
?
1
?
?
Money
metric
Indirect utility
function
m
[
?
u
?
[
< br>?
n
j
?
1
(
)
1
?
?
]
?
?
n
j
?
1
(
1
p
j
?
1
?
< br>?
1
?
?
]
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