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Section Notes Week 2
Outline
Key Concepts
Announcements
Externality
Numerical Example
Over or Under Production
Welfare Graphing
Regulation
Discussion
Internalization
Calculating Outcomes
Competition
Monopoly
Monopsony
Middleman
Social Planner
M. Benefit
MPB
MR
MPB
MR
MSB=MPB+MEB
M. Cost
MPC
MPC
MO
MO
MSC=MPC+MEC
Solution
MPB=MPC
MR=MPC
MPB=MO
MR=MO
MSB=MSC
Recall that: MR =
d
d
Q
Revenue =
d
d
Q
(Q
·
MPB(Q)) = MPB(Q) + Q
·
d
d
Q
MPB(Q)
MO =
d
d
Q
Outlay =
d
d
Q
(Q
·
MPC(Q)) = MPC(Q) + Q
·
d
d
Q
MPC(Q)
Putting numbers to it
Let marginal private benefit of output
Q
be given by
P
= 12

Q
, marginal private cost
by
P
= 2
Q
.
Suppose that production generates a negative externality, with marginal cost
as a function of output given by
MEC
= 1
.
5 + 0
.
5
Q
.
Let’s assume there are no positive
externalities. Find the equations for:
•
MR:
Revenue =
(12

Q
)
·
Q
=
12
Q

Q
2
. MR =
d
d
Q
(12
Q

Q
2
)
=
12

2
Q
•
MO:
Outlay =
(2
Q
)
·
Q
=
2
Q
2
. MO =
d
d
Q
(2
Q
2
)
=
4
Q
•
MSB:
MSB = MPB + MEB. MEB is zero, so MSB = MPB =
12

Q
•
MSC:
MSC = MPC + MEC =
(2
Q
) + (1
.
5 + 0
.
5
Q
)
=
1
.
5 + 2
.
5
Q
Now we’re going to go through the case of (perfect) competition. Solve out the competitive
case quantity and price (
Q
C
, P
C
).
Q
C
: Set MPB=MPC, so
12

Q
= 2
Q
, which can be arranged to find
Q
= 12
/
3
=
4
.
P
C
: This quantity is then plugged into demand to find price:
P
= 12

4
=
8
.
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2
Next find the socially optimal quantity and price (
Q
*
, P
*
).
Try solving out the other
outcomes if you have time.
Q
*
: Set MSB=MSC, so
12

Q
= 1
.
5 + 2
.
5
Q
, which results in
Q
= 10
.
5
/
3
.
5
=
3
.
P
*
: This quantity is then plugged into demand to find price:
P
= 12

3
=
9
.
Q
M
: Set MR=MPC, so
12

2
Q
= 2
Q
, which can be arranged to find
Q
= 12
/
4
=
3
.
P
M
: This quantity is then plugged into demand to find price:
P
= 12

3
=
9
.
Q
N
: Set MPB=MO, so
12

Q
= 4
Q
, which can be arranged to find
Q
= 12
/
5
=
2.4
.
P
N
: This quantity is then plugged into
supply
to find price:
P
= 2
·
(2
.
4)
=
4.8
.
Q
MM
: Set MR=MO, so
12

2
Q
= 4
Q
, which can be arranged to find
Q
= 12
/
6
=
2
.
Middleman has two prices, one to consumers,
P
C
MM
, and one to producers,
P
P
MM
...
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 Spring '09
 ZELBERMAN
 Monopoly, producer, Externality

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