Monopolies
Mark Holmes
[email protected]
Definition of Monopoly
•
•
•
•
One firm in the industry
Unique good
No entry
Firm is price maker
Examples:
AT&T, Standard Oil, Microsoft (?), US Postal Service
[email protected]
Price Maker Means Downward
Sloping Demand
P
As firm sells more,
the price falls.
D
Q
[email protected]
New concept: Marginal Revenue
Suppose I sell aircraft carriers. There is a guy from the
Defense Dept in the room. I can sell one carrier for $1
PMR
billion, or 2 for $100 each.
P
10
9
8
7
6
Q
1
2
3
4
5
TR
10
18
24
28
30
MR
10
8
6
4
2
As sell more units,
have to discount all
the “previous” ones.
Example: Moving from Q=1 to Q=2:
Old: P=$10, sold 1
New:P=$9, sell 2
Lose $1 on the first unit (10-9) but make extra 9 (P) on the 2nd
MR = -1 + 9 = 8 [email protected]
MR, continued
Why is MR< P? As you go to sell more units, you have to
discount all the ones you sold so far. (It’s not an auction.)
P
10
9
8
7
6
Q
1
2
3
4
5
TR
10
18
24
28
30
MR
10
8
6
4
2
Q=2 to Q = 3:
Lose $1 * 2 units
Gain $8 on 3rd unit.
Net = + $6
TR
Formula: MR 
Q
[email protected]
Compare
I can sell 3 units for $8...
$8
+ $8
+ $8
….or 4 units for $7.
Marginal
$7
-1
+ $7
+ -1
Unit C
+ $7
+ -1
Unit D
+ $7
----$28
+ $7
----$4
Unit A
Unit B
[email protected]
Golden Rule
The best profit Q>0 is the largest Q where MR=MC.
How important is
something called the
“Golden Rule”?
[email protected]
Practice Problem: MR
For the following, compute TR and MR. Sketch D and MR.
Q
1
2
3
4
5
P
100
80
60
40
20
Q
10
20
30
40
50
P
10
9
8
7
6
More on webpage http://www.unc.edu/~gholmes/econ10
[email protected]
The Skinny on MR
Explain why MR<P
Explain why MR falls as Q increases
Know the formula for MR
Why do we care about MR versus P?
Consider the aircraft carrier story.
At P=$100, QD=1 ==>MR = $100, TR = $100, TP=$50
At P = $75, QD=2 ==>MR = $50, TR = $150, TP=$50
At P = $50, QD=3 ==>MR = $0, TR = $150, TP=$0
Suppose marginal cost = $50.
Are you better off at Q=2 or Q=3?
[email protected]
Graphs of D and MR
P
Given a linear demand
curve (the only kind in
this class), the MR
curve lies beneath D,
twice as steep, and
halfway between D
and the P axis.
D
MR
Q
[email protected]
Why? (for calculus folks)
Strictly for fostering intellectual climate
P  a  bQ
Linear demand
TR  P * Q  aQ  bQ 2
dTR
 a  2bQ
dQ
Same intercept, twice the slope (2b).
Algebra gives you halfway between.
[email protected]
Monopoly:
Generic Cost Curves
$
MC
ATC
AVC
[email protected]
Q
Monopoly:
Generic Demand and MR curves
$
D
MR
[email protected]
Q
Monopoly:
Condition I
Where does
MR=MC?
MC
$
ATC
AVC
What is
the price?
D
MR
q*
[email protected]
Q
Monopoly:
If the price is here...
..are we in eq?
Condition I
MC
$
ATC
AVC
What
if price
is
here?
D
MR
q*
[email protected]
Q
Lesson (an easy one to forget)
The firm goes up to D from the q* where MR=MC.
MC
$
ATC
AVC
D
MR
q*
[email protected]
Q
Monopoly:
Condition I
The rest is the same as Perfect Competition...
MC
$
ATC
Profit
AVC
TR
TC
D
MR
q*
[email protected]
Q
Monopoly:
Condition II
MC
$
ATC
AVC
Where does
MR=MC?
What is P?
D
MR
[email protected]
Q
Monopoly:
Condition II
MC
$
ATC
LOSS
TR
TC
AVC
D
MR
[email protected]
Q
Monopoly:
Condition II
MC
$
ATC
LOSS
AVC
TFC
TFC>loss
Don’t shut down
D
MR
[email protected]
Q
Monopoly:
Condition III
MC
$
ATC
LOSS
TC
AVC
TR
MR
D
[email protected]
Q
Monopoly:
Condition III
MC
$
ATC
LOSS
TFC
AVC
TFC<LOSS
Shut down
MR
D
[email protected]
Q
Tables
Q
100
200
300
400
500
P
50
40
35
30
25
N
50
75
85
110
150
TR
5000
8000
10500
12000
12500
MR
50
30
25
15
5
TVC
3000
4500
5100
6600
9000
TC
9000
10500
11100
12600
15000
AVC
30
22.5
17
16.5
18
ATC
90
52.5
37
31.5
30
MP
2
4
10
4
2.5
MC
30
15
6
15
24
wage= 60
TFC= 6000
Back to the tables. We can compute TVC, TC, etc. Now
we need to add TR and MR. Here, MR=MC at Q=400.
Profit = 12,000-12,600 = -600. This is a smaller loss than TFC, so
don’t shut down.
[email protected]
Monopoly:
Condition II
MC
$
ATC
LOSS
AVC
TC
TR
D
MR
[email protected]
Q
Let’s do one
Q
10
15
20
25
30
P
100
90
80
70
60
N
2
5
10
16
25
TR
1000
1350
1600
1750
1800
MR
100
70
50
30
10
TVC
100
250
500
800
1250
TC AVC ATC
MP
1100
10
110
5
1250 16.67 83.33 1.667
1500
25
75
1
1800
32
72 0.833
2250 41.67 75 0.556
wage= 50
TFC= 1000
[email protected]
MC
10
30
50
60
90
Graph
MC
$
ATC
AVC
D
MR
[email protected]
Q
Does this make sense?
MC
$
ATC
AVC
D
MR
[email protected]
Q
Your Turn
Q
10
15
20
25
30
P
100
95
90
80
70
wage= 100
TFC= 1000
N
5
7
8
10
15
Compute
best profit Q>0
Profit/loss
Does firm want to shut down?
Sketch
Also:
Sketch a monopolist
- with zero profits.
- indifferent about shutting down.
[email protected]