Econ 100A
December 10, 2008
NonComprehensive Review of Competition
Michael Schihl
Note the
caveat utilitor
.
1
Characteristics of a Perfectly Competitive Market
According to the textbook, the model of a perfectly competitive market rests on three assumptions.
1. Price taking
2. Product homogeneity
3. Free entry and exit
2
Profit Maximization
All firms, by assumption, maximize profits. One can express profit as
π
i
(
q
i
)
=
TR
i
(
q
i
)

TC
i
(
q
i
)
(1)
=
p
(
Q

i
, q
i
)
q
i

TC
i
(
q
i
)
(2)
Q

i
represents the output of all firms except firm
i
.
When we optimize, i.e., find the extrema of, a function, we typically set the first derivative equal to zero. For a
firm maximizing profit, we’ll take the derivative of profit and set it equal to zero.
d
dq
i
π
i
(
q
i
)
=
0
(3)
d
dq
i
[
p
(
Q

i
, q
i
)
q
i

TC
i
(
q
i
)]
=
0
(4)
dp
(
Q

i
, q
i
)
dq
i
q
i
+
p
(
Q

i
, q
i
)

{z
}
MR
i
(
q
i
)

MC
i
(
q
i
)
=
0
(5)
MR
i
(
q
i
)

MC
i
(
q
i
)
=
0
(6)
MR
i
(
q
i
)
=
MC
i
(
q
i
)
(7)
This gives us the familiar result that marginal revenue equals marginal cost. Note that, for a perfectly competitive
firm,
p
(
Q

i
, q
i
) is a constant determined by the market equilibrium, thus its derivative is zero. So marginal revenue
for a firm in a perfectly competitive market is simply price.
MR
i
(
q
i
)
=
dp
(
Q

i
, q
i
)
dq
i
q
i
+
p
(
Q

i
, q
i
)
(8)
=
0
×
q
i
+
p
(
Q

i
, q
i
) since
dp
(
Q

i
, q
i
)
dq
i
= 0 for a firm in a perfectly competitive market
(9)
=
p
since
p
(
Q

i
, q
i
) is a constant in a perfectly competitive market
(10)
This gives us the result that is specific to a firm in a perfectly competitive market: the firm produces
q
such that
p
=
MC
(
q
).
This is the perfectly competitive firm’s profitmaximizing condition (i.e., it is the condition that
characterizes the output choice when the firm solves its profitmaximization problem).
3
Simple Example
Suppose that a firm has a total cost curve given by
TC
(
q
) = 100 + 20
q
+
q
2
, where the total fixed cost is 100 and
the total variable cost is
V C
(
q
) = 20
q
+
q
2
. The corresponding marginal cost function is
MC
(
q
) = 20 + 2
q
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
(a) What is the equation for average variable cost (
AV C
(
q
))?
Answer:
AV C
(
q
) =
V C
(
q
)
q
= 20 +
q
.
(b) What is the minimum level of average variable cost?
Answer:
We know that the minimum level of
AV C
occurs where
AV C
=
MC
.
20 +
q
=
20 + 2
q
(11)
q
=
2
q
(12)
This is satisfied when
q
= 0. The minimum
level
of
AV C
is the level of
AV C
when
q
= 0.
AV C
(0) = 20, thus
the minimum level of
AV C
is 20.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Kasa
 Supply And Demand, producer, perfectly competitive market

Click to edit the document details