EC201, Fall 2007, Prof. Jordi Jaumandreu
Solutions to Problem set #4
Costs
1. Call
H
the number of hours, then the expression for cost is
C
=
wH
= 8
H.
The implicit production function is
q
= 4
H
, where
q
is the number of o
ﬃ
ces.
This implies
H
=
q
4
,
expression that substituted for
H
in the expression of cost
gives the cost function
C
= 2
q.
This (linear) cost function implies the same
constant average and marginal cost:
MC
=
AC
= 2
.
If a franchise lumpsum
tax of 30 is imposed we have a new cost function
C
= 30 + 2
q,
which gives an
average cost
AC
=
C
q
=
30
q
+
q
while
MC
=
∆
C
∆
q
= 2
2. This is a case of increasing returns to scale by purely technological reasons.
A crate of 1 cubicfoot needs 6 sides of a squarefoot and this implies a total cost
of $6. A 8 cubicfoot needs 6 sides of 2 squarefoot, each side of 2 squarefoot
needs 4 squarefoot and this implies a total cost of $24. In general, calling
V
to
the volume, we have
C
= 6(
3
√
V
)
2
= 6
V
2
3
. AC
(1) =
C
(
1
)
1
= 6
, AC
(8) =
C
(8)
8
=
24
8
= 3
and, in general,
AC
(
V
) =
C
(
V
)
V
= 6
V
−
1
3
.
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 Fall '08
 Idson
 Economics, Microeconomics, Average cost

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