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Econ 301 – F07
Answers to PROBLEM SET 5  due in class on Thursday Nov 1
Wissink
1.
Critically evaluate the following statements and explain in what way or ways they are true, false, or
uncertain.
a.
Constant returns to scale is incompatible with the law of diminishing marginal productivity.
[Answer]
False
.
Constant returns to scale implies that if you scale all inputs by the same factor,
say t, then output is scales by that same factor, t.
On the other hand, the law of diminishing
returns deals with shortrun production situations where at least one factor of production is fixed.
For example, x=L
1/2
K
1/2
exhibits constant returns to scale, but also satisfies the law of
diminishing marginal productivity with respect to each input.
b.
If an input’s marginal product curve is falling, so must its average product curve.
[Answer]
False
.
When marginal product of an input is less than its average product, its average
product curve should be falling.
See the graph below (left).
MP
L
AP
L
L
X
MC
AC
X
$
c.
If marginal cost is rising, then average variable cost must also be rising.
[Answer]
False
.
When marginal cost is grater than average cost, the marginal cost is pulling
average cost up.
When marginal cost if rising, average cost can be falling or rising. See the
graph above (right).
d.
When average total cost is rising, then so is marginal cost and average variable cost.
[Answer]
True.
Average total cost can only rise if avc is rising and if avc is rising then so must
mc.
e.
To cost minimize, the firm should juggle the use of variable inputs until the marginal products of
all the variable inputs are equal to each other.
[Answer]
False
.
To cost minimize, a firm should juggle the use of variable inputs until there is
equal bang per buck, or equivalently, where MRTS=ERTS, i.e., MP
L
/MP
K
=w/r.
However, if
w=r, then that would be a special case where then you would get equal marginal products at the
cost minimizing solution.
.
2.
x = L
1/2
K
1/2
and that w=$2 and r=$2.
a.
Find the 3 long run cost curves and graph them.
b.
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 Fall '07
 WISSINK
 Microeconomics

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