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PROBLEM SET 4
I. TRUE OR FALSE (No justification needed but again, you should think
of one for the exam)
1. The production set of a firm is the set of all products the firm can
produce.
FALSE
2. If there are constant returns to scale, then doubling the amount of
any input will exactly double the amount of output.
FALSE
3. If the production function is
f
(
x
,
y
) = min{2
x
+
y
,
x
+ 2
y
}, then
there are constant returns to scale.
TRUE
4. The production function
f
(
x
,
y
) =
x
2/3
+
y
2/3
has increasing returns to
scale.
FALSE
5. A firm’s production function is
f
(
x
1
,
x
2
) =
x
1
+ 2
x
2
. This means that
x
2
is twice as expensive as
x
1
.
FALSE
6. A fixed factor is a factor of production that is used in fixed
proportion to the level of output.
FALSE
8. If the production function is
f
(
x
1
,
x
2
) = min{
x
1
,
x
2
}, then the cost
function is
c
(
w
1
,
w
2
,
y
) = min{
w
1
,
w
2
}
y
.
FALSE
9. The cost function
c
(
w
1
,
w
2
,
y
) expresses the cost per unit of output
of producing
y
units of output if equal amounts of both factors are
used.
FALSE
10. A firm uses a single variable input
x
to produce outputs according
to the production function
f
(x) = 300
x
 6
x
2
. This firm has fixed costs
of $300. This firm’s shortrun marginal cost curve lies below its
shortrun average variable cost curve for all positive values of
x
.
FALSE
11. The average variable cost curve must always be Ushaped.
FALSE
12. The marginal cost curve passes through the minimum point of the
average fixed cost curve.
FALSE
II. MULTIPLE CHOICE
13. If a firm moves from one point on a production isoquant to another
point on the same isoquant, which of the following will certainly
not
happen?
a. A change in the level of output
b. A change in the ratio in which the inputs are combined
c. A change in the marginal products of the inputs
d. A change in the rate of technical substitution
e. A change in profitability
14. Which of the following production functions exhibit constant
returns to scale? In each case
y
is output and
K
and
L
are inputs. (1)
y
=
K
1/
2
L
2
/3
. (2)
y
= 3
K
1/2
L
1/2
. (3)
y
=
K
1/2
+
L
1/2
. (4)
y
= 2
K
+ 3
L
.
a. 1, 2, and 4
b. 2, 3, and 4
c. 1, 3, and 4
d. 2 and 3
e. 2 and 4
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View Full Document15. A firm uses only two inputs to produce its output. These inputs are
perfect substitutes. This firm
a. must have increasing returns to scale.
b. must have constant returns to scale.
c. could have increasing returns to scale, constant returns to
scale, or decreasing returns to scale.
d. must have decreasing returns to scale.
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 Fall '08
 Hansen
 Microeconomics

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