Answers
I. True of false
1. FALSE. An element in the production set is a pair
(
x;y
)
where
0
y
f
(
x
)
. For each input level, the second coordinate of the pair is the set
of all possible production levels
for that input level
. It is not possible to
determine if a point is an element of the production set without specifying
the input level.
2. FALSE. If there are constant returns to scale, the output is doubled if
all
inputs are doubled at the same time.
3. TRUE
f
(
tx;ty
)
=
min
f
2
tx
+
ty;tx
+ 2
ty
g
=
min
f
t
(2
x
+
y
)
;t
(
x
+ 2
y
)
g
=
t
min
f
2
x
+
y;x
+ 2
y
g
=
tf
(
x;y
)
4. FALSE.
f
(
tx;ty
)
=
(
tx
)
2
3
+ (
ty
)
2
3
=
t
2
3
x
2
3
+
t
2
3
y
2
3
=
t
2
3
(
x
2
3
+
y
2
3
)
=
t
2
3
f
(
x;y
)
< tf
(
x;y
)
5. FALSE. For this production function,
x
2
is twice as
productive
as
x
1
.
To know which one is more expensive, the input prices are needed. That
information is not provided here.
the output level increases.
7. FALSE. If the production function is
f
(
x
1
;x
2
) = min
f
x
1
;x
2
g
, the con
ditional input demands are
x
1
=
x
2
=
y
. Therefore the cost function
is
c
(
w
1
;w
2
;y
)
=
w
1
y
+
w
2
y
=
(
w
1
+
w
2
)
y
8. FALSE. The cost function
c
(
w
1
;w
2
;y
)
expresses the total cost of produc
ing
y
units of output when the input prices are
w
1
and
w
2
and the cost
minimizing combination of inputs given these prices is used.
1
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 Fall '08
 Hansen
 Microeconomics, 2k, 3L, 2L

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