Chapter 22
NAME
Firm Supply
Introduction.
The shortrun supply curve of a competitive Frm is the
portion of its shortrun marginal cost curve that is upward sloping and
lies above its average variable cost curve. The longrun supply curve of a
competitive Frm is the portion of its shortrun marginal cost curve that
is upwardsloping and lies above its longrun average cost curve.
Example:
A Frm has the longrun cost function
c
(
y
)=2
y
2
+ 200 for
y>
0and
c
(0) = 0. Let us Fnd its longrun supply curve. The Frm’s
marginal cost when its output is
y
is
MC
(
y
)=4
y
. If we graph output on
the horizontal axis and dollars on the vertical axis, then we Fnd that the
longrun marginal cost curve is an upwardsloping straight line through
the origin with slope 4. The longrun supply curve is the portion of this
curve that lies above the longrun average cost curve. When output is
y
,
longrun average costs of this Frm are
AC
(
y
y
+ 200
/y
.Th
i
si
sa
U
shaped
curve. As
y
gets close to zero,
AC
(
y
) becomes very large because
200
/y
becomes very large. When
y
is very large,
AC
(
y
) becomes very
large because 2
y
is very large. When is it true that
AC
(
y
)
<MC
(
y
)?
This happens when 2
y
+ 200
/y <
4
y
. Simplify this inequality to Fnd that
AC
(
y
)
(
y
)when
10. Therefore the longrun supply curve is
the piece of the longrun marginal cost curve for which
10. So the
longrun supply curve has the equation
p
=4
y
for
10. If we want to
Fnd quantity supplied as a function of price, we just solve this expression
for
y
as a function of
p
.Thenw
ehav
e
y
=
p/
4 whenever
p>
40.
Suppose that
p<
40. ±or example, what if
p
= 20, how much will
the Frm supply? At a price of 20, if the Frm produces where price equals
longrun marginal cost, it will produce 5 = 20
/
4 units of output. When
the Frm produces only 5 units, its average costs are 2
×
5 + 200
/
5 = 50.
Therefore when the price is 20, the best the Frm can do if it produces a
positive amount is to produce 5 units. But then it will have total costs of
5
×
50 = 250 and total revenue of 5
×
20 = 100. It will be losing money. It
would be better o² producing nothing at all. In fact, for any price
40,
the Frm will choose to produce zero output.
22.1 (0)
Remember Otto’s brother Dent Carr, who is in the auto repair
business? Dent found that the total cost of repairing
s
cars is
c
(
s
)=
2
s
2
+ 100.
(a)
This implies that Dent’s average cost is equal to
2
s
+ 100
/s
,
his average variable cost is equal to
2
s
, and his marginal cost is
equal to
4
s
.
On the graph below, plot the above curves, and also plot
Dent’s supply curve.
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FIRM SUPPLY
(Ch. 22)
0
5
10
15
20
20
40
60
Output
Dollars
80
Supply
mc
ac
avc
Revenue
Costs
Profit
(b)
If the market price is $20, how many cars will Dent be willing to
repair?
5.
If the market price is $40, how many cars will Dent
repair?
10.
(c)
Suppose the market price is $40 and Dent maximizes his proFts. On
the above graph, shade in and label the following areas: total costs, total
revenue, and total proFts.
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 Fall '10
 no
 molehills, Stanley Ford

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