Download Monopoly

Monopoly
Overheads
A firm is a monopoly if it is the only supplier
of a product for which there is no close substitute
A monopoly sets the price of its product without
concern that the price might be undercut by rivals
A monopoly faces a downward sloping demand curve
Monopoly and substitutes
Being the only seller of a narrowly defined
product does not make one a monopoly
Cola products
Computer chips
Novels
Mountain bikes
Pure monopoly
One seller of a good with few substitutes
Impure Monopoly
Any firm with downward sloping demand
Creating and maintaining a monopoly
Monopolies exist because of barriers to entry
There are many different barriers to entry
Economies of scale
If marginal cost is decreasing as
production rises,
one firm will emerge as the only
survivor in an industry
When total production costs would rise if two
or more firms produced instead of one, the single
firm in the industry is called a natural monopoly
A natural monopoly exists when, due to economies
of scale, one firm can produce at a lower cost
per unit than can two or more firms
Natural monopolies and limit pricing
New firm (entrant) considers entry
Incumbent firm sets price just below
average cost of entrant
Why can the incumbent do so?
Entrant goes away!
Life is good!!
Local (natural) monopolies
service station
movie theatre
doctor
feed store
Control of scarce inputs
Alcoa
De Beers
Big Bear’s Burro Rides
Special knowledge prevents imitation
KFC
Slick 50
Bagel recipes
Special knowledge lowers cost
Robotics in automobile manufacturing
Chemical process for crushing soybeans
Legal protection
Intellectual property
literary works
paintings
musical compositions
scientific inventions
Intellectual property rights
- an incentive for innovation
Innovation is risky and costly
Profit incentives counteract risk and cost
Intellectual property rights create a monopoly
Government strikes a compromise
Creators of intellectual property get a monopoly
The monopoly has a limited time frame
Patents
Cover scientific discoveries and products
Provide protection for about 20 years
drugs
herbicides
computer chips
Copyrights
Cover literary, musical and artistic works
Provide protection for about 50 years
songs
books
plays
software
Government restrictions or franchise
When there is a natural monopoly,
society may be better off with monopoly
Government usually reserves right to regulate
taxi-cabs
electricity
cable television or local phone service
postal service
Single Price Monopoly
A monopoly is a price setter
A monopoly is a price maker
A monopoly is a price searcher
Price makers face downward sloping
demand curves and set price
Demand
The individual demand curve facing a firm tells us,
for different prices, the quantity of output that
customers will choose to purchase from the firm.
The demand curve facing the firm show us the
maximum price the firm can charge to sell
any given amount of output
A monopolist faces a downward sloping demand curve
Q = D(p)
p = D-1 (Q) = g(Q)
1
Q  18  p
14
p  25214 Q
Single-price monopoly
A firm which is limited to charging
the same price for each unit of the
product is called a single-price monopoly
Total Revenue
Revenue is the total income that comes from the
sale of the output (goods and services) of a given
firm or production process
Revenue  R (p , Q)  pQ
 p f (x1 , x2 , , xn )
 g (Q) Q
Linear inverse demand
p  A BQ
R  pQ
 g (Q) Q
R  ( A BQ)Q
 AQ BQ
2
Example
p  25214 Q
R  p Q  g(Q) Q
R  ( 252 14 Q) Q
 252 Q 14 Q 2
Marginal Revenue (MR)
Marginal revenue is the increment, or addition,
to revenue that results from producing
one more unit of output
Marginal revenue is the change in total revenue
from producing one more unit of output
change in revenue
ΔR(Q, p)
ΔTR(Q, p)
MR 


change in output
ΔQ
ΔQ
Demand /Price
Q
0
252
TR
0
MR 
MR
252
238
1
238
238
224
210
2
224
448
196
182
3
210
630
168
154
4
196
784
140
126
5
182
910
112
98
6
168
1008
84
70
7
154
1078
56
42
8
140
1120
28
Example
Increase output from 3 to 4 units
ΔTR(Q,p)
MR 
ΔQ
(784630 )

(4 3)
154

 154
1
Linear inverse demand
p  A BQ
R  pQ
 g (Q) Q
R  ( A BQ)Q
 AQ BQ 2
MR  A 2BQ
Marginal revenue has the same price
intercept as the inverse demand curve
Marginal revenue has twice the slope
as the inverse demand curve
Example computation (Q = 4)
p  A BQ  252 14Q
MR  A 2BQ
 252 (2)(14)Q
 252 (2)(14) (4)
 252 (8)(14)
 252 112
 140
A note on marginal revenue and price
Marginal revenue is always less
than or equal to price
WHY?
The firm must lower price in order to sell more units
Price taker
p
p0
1
2
q0
3
4
5
q
Price Searcher
p
p0
p1
B
Demand
A
Q
Q0
Q1
The lower price applies to all units and so
the revenue per unit will be less than the price
Marginal revenue is given by the area A-B since the firm now sells
Q1 units at a price of p1
The gain in revenue is given by (Q1 - Q0) p1
while the loss is given by (p1 - p0) Q0
MR  (Q1 Q0) p1  (p1 p0) Q0
 p1 Q1 p1 Q0 p1 Q0 p0 Q0
 p1 Q1 p0 Q0  TR1 TR0
p
p0
p1
B
Demand
A
Q0
Q1
Q
For the example in the table, note that when Q
increases from 3 to 4, that the firm gains
(Q1 Q0 )p1  (4 3) (196)  196
Demand /Price
Q
2
224
TR
448
MR 
MR
196
182
3
210
630
168
154
4
196
784
140
126
5
182
910
112
But the firm has a loss of
(p1 p0 )Q0  (196 210) (3)
 (
14)(3)  
42
Demand /Price
Q
2
224
TR
448
MR 
MR
196
182
3
210
630
168
154
4
196
784
140
The firm then has a net gain of 154 (196 - 42) as before
The monopolist will never produce at an
output level where MR < 0
Cost for the monopolist
C(Q, w1 ,w2 ,) 
n
min
x1 ,x2 , , x n
Σ wi xi such that Q  f (x1 ,x2 ,xn )
i 1
Cost  TC  C(x1 , x2 , , w1 , w2 ,  )
n
 Σ wi xi
i 1
 C(Q, w1 , w2 ,  )
Q FC VC C
MR Profit
0 100 0
100
AFC
AVC ATC
MC  MC
D
Price TR
252
0
120
1 100 120
220
100.00 120 220.00
320
50.00 110
109
160.00
238
238
406
33.33
92
102 135.33
224
448
484
25.00
81
96.0 121.00
210
630
560
76
20.00 92.0 112.00
196
784
640
77
16.67 90.0 106.67
182
910
730
84
14.29 90.0 104.29
168
1008
836
97
12.50 92.0 104.50
154
1078
964
116
11.11 96.0 107.11
140
1120
56
348
28
284
0
170
14
141
126
1134
156
10 1001020 1120 10.00 102 112.00
368
42
128
9 100864
84
70
106
8 100736
112 350
98
90
7 100630
140 300
126
80
6 100540
168 224
154
76
5 100460
196 128
182
78
4 100 384
224 18
210
86
3 100 306
252 -100
238
100
2 100 220
MR 
-14
172
112
1120
-28 0
Marginal cost (MC)
Marginal cost is the increment, or addition,
to cost that results from producing
one more unit of output
change in cost
MC 
change in quantity
ΔC(Q, w)
ΔTC(Q, w)


ΔQ
ΔQ
Q FC VC C
MR Profit
4 100 384 484
D
MC  MC Price TR
76
196
784
76
5 100 460 560
182
910
80
300
112
350
84
368
56
348
98
84
168
1008
90
7 100 630 730
140
126
77
6 100 540 640
MR 
70
97
154
1078
ΔC(Q, w)
MC 
ΔQ
(640
560)

( 6 5)
80

 80
1
Returns (Profit)
π  Revenue Costs
 R C
n
π  p QΣ wi xi
i 1
n
 g(Q) QΣ wi xi
i 1
 g(Q) Q C(Q, w)
The profit max problem
max g(Q)Q C(Q, w)
Q
max (252 14Q) Q C(Q, w)
Q
max 252Q 14Q 2 C(Q, w)
Q
Maximizing profit
Choose the level of output where
the difference between TR and TC
is the greatest
Profit Max Using MR and MC
An increase in output will always increase profit
if MR > MC
An increase in output will always decrease profit
if MR < MC
The rule is then
Increase output whenever MR > MC
Decrease output if MR < MC
Choose output where MR = MC
Q FC VC C
Profit
4 100 384 484
D
MC  MC Price TR
76
196
784
76
5 100 460 560
182
910
80
300
112
350
84
368
56
348
98
84
168
1008
90
7 100 630 730
140
126
77
6 100 540 640
MR  MR
70
97
154
1078
Should we increase output from 4 to 5?
Yes
Should we increase output from 5 to 6? Yes
Should we increase output from 6 to 7?
No !
Cost Curves, Demand and Marginal Revenue
300
$
Demand
MR
MC
250
200
150
100
50
0
0
2
4
6
8
10
12
14
16
Output
18
Cost Curves, Marginal Revenue and Optimal Price
300
$
Demand
MR
MC
250
200
Q Opt
P Opt
150
100
50
0
0
2
4
6
8
10
12
14
16
Output
18
Optimal Q = 6
Optimal p = $168
Measuring Total Profit
Profit is always given by
Profit  π  Total revenue Total cost
 pQ C ( Q, w1 , w2 , )
Graphically it is the distance between
total revenue and total cost
Cost Curves
2000
$ 1800
1600
1400
1200
1000
800
600
400
200
0
TR
C
0
2
4
6
8
10 12 14 16 18
Output
Profit, price, and average total cost
Profit per unit is given by
Profit per unit  π
Q
pQ C(Q, w1 , w2 ,  )

Q
pQ
TC


Q
Q
 p ATC
Cost Curves, Marginal Revenue and Profit
300
$
Profit per unit
Demand
MR
MC
ATC
Q Opt
P Opt
ATC Opt
250
200
150
100
50
0
0
2
4
6
8
10
12
14
16
18
Output
The distance between price and ATC at
the optimum output level is profit per unit
Total profit is given by the area of the box
bounded by
price,
the optimum quantity,
average total cost at the optimum quantity,
and the price axis
Cost Curves, Marginal Revenue and Profit
300
$
Profit
250
Demand
MR
MC
ATC
Q Opt
P Opt
ATC Opt
200
150
A
100
50
0
0
2
4
6
8
10
12
14
16
Output
18
Q
C
AVC
4
484 96.00
ATC
MC
121.00
MC
Price
TR
Profit
76
196
784
300
77
182
910
350
84
168
1008
368
97
154
1078
348
76
5
560 92.00 112.00
80
6
640 90.00 106.67
90
7
730 90.00 104.29
(168 - 106.666) = 61.333
(61.333) (6) = $368
The firm earns a profit whenever
p > ATC
A firm suffers a loss whenever p < ATC
at the optimum level of output
Let p = 165 - 14 Q
The optimum quantity is 3 units
The market price is $128
Profit = $-37
Q
0
C
100
AVC ATC
Demand
Price
165
TR
0
109
151
151
92
137
274
81
123
369
76
109
436
77
95
475
84
81
486
97
67
469
116
53
424
141
39
351
172
25
250
MC ) MC
120
1
220
120
220.00
100
2
320
110
160.00
86
3
406
102
135.33
78
4
484
96
121.00
76
5
560
92
112.00
80
6
640
90
106.67
90
7
730
90
104.29
106
8
836
92
104.50
128
9
964
96
107.11
156
10 1120 102
112.00
MR ) MR
165
151
137
123
109
95
81
67
53
39
25
11
-3
-17
-31
-45
-59
-73
-87
-101
-115
Profit
-100
-69
-46
-37
-48
-85
-154
-261
-412
-613
-870
Q
0
1
2
3
4
5
6
C
100
220
320
406
484
560
640
MC
132
109
92
81
76
77
84
Demand
Price
165
151
137
123
109
95
81
TR
0
151
274
369
436
475
486
MR
165
137
109
81
53
25
-3
Profit
-100
-69
-46
-37
-48
-85
-154
Cost Curves, Marginal Revenue and Optimal Price
300
$
Demand
MR
MC
ATC
Q Opt
P Opt
250
200
Loss
150
ATC Opt
100
50
0
0
2
4
6
8
10
12
14
16
Output
18
Monopoly in the Short Run
Does the monopoly keep producing
if it is losing money?
It depends
In the short-run, to maximize profit,
the single price monopolist should
Produce at a level where MR = MC
(and MC crosses MR from below)
Continue to produce if total revenue
exceeds total variable costs
or equivalently
price (p) is greater than average variable cost (AVC);
Otherwise, it should shut down
Cost Curves, Marginal Revenue and Loss
300
$
Don’t shut down!
Demand
MR
MC
ATC
Q Opt
P Opt
250
200
Loss
150
ATC Opt
AVC
AVC Opt
100
50
0
0
2
4
6
8
10
12
14
16
Output
Return above variable cost
18
The shutdown rule
In the short-run, the firm should continue to produce
if total revenue exceeds total variable costs;
otherwise, it should shut
down
Monopoly in the Long Run
Unlike perfectly competitive firms,
a monopoly may earn economic profit
in the long run
A privately owned monopoly suffering an
economic loss in the long run will exit the industry,
just as would any other business firm
Comparing Monopoly to Perfect Competition
Main result
All else equal, a monopoly market will have
higher prices and
lower output
than a purely competitive market
Example problem
100 competitive firms
Q = 100q
C(q, w) = 100 + 10q + q2
MC(q, w) = 10 + 2q
P = 70 - 0.04 QD
QD = 1750 - 25 P
For the individual firm we set P = MC
MC  10  2q  P
 2q  P 10
1
 q  P 5
2
For the industry
1
q  P 5
2
Q  100 q
1
 (100) ( P 5)
2
 50P 500
Now setting supply equal to demand
Q S  50P 500  1750 25P  Q D
 75P  2250
 P  30
 Q  1,000
Equilibrium for 1000 Competitive Firms
P = MC = 30, Q = 1000
70.00
$
Demand
60.00
Supply
50.00
Price
40.00
30.00
Q Opt
20.00
10.00
0.00
0
200
400
600
800
1000 1200 1400
Output
Optimum for the individual firm
1
q  P 5
2
1
q  (30) 5
2
 15 5
 10
This is a long run equilibrium; there are zero profits
R  (30)(10)  300
C  100  (10)(10)  10  300
2
Individual Firm
80.00
ATC
$
60.00
MC
40.00
Price
20.00
Q Opt
0.00
0.00
5.00
10.00
15.00
20.00
Output - q
Now consider a monopoly firm which buys all 100
competitive firms and operates them as previously
The marginal cost curve for the monopolist will be
the same as the supply curve for the 100 firms
Why?
The monopolist will produce such that each plant
has the same marginal cost
So, the cost of producing one more unit of the good is
the cost of producing one more unit at one of the plants
We need to find aggregate marginal cost
from the supply equation
Q S  50P 500
S
 50P  Q  500
1 S
P
Q  10
50
 MC  0.02 Q  10
S
Revenue = PQ = (70 - 0.04Q)Q
MR = 70 - 0.08Q
Setting marginal cost equal to marginal revenue
MC 0.02 Q  10  70 0.08Q MR
0.1 Q  60
 Q  600
How do we get price?
Substitute the quantity in the inverse demand
P = 70 - 0.04 QD
= 70 - 0.04 (600)
= 70 - 24
= 46
Profit Max for Monopolist
P = 46, MC = 20, Q = 600
80
$
Demand
70
MR
60
MC
50
40
Q Opt
30
Price
20
10
0
0
200
400
600
800
1000
1200
Output - Q
Competition
P = MC = 30, Q = 1000
Monopoly
P = 46, MC = 20, Q = 600
Do monopolies use the same technology
and have the same costs?
A monopoly may be able to specialize
and reduce costs or consolidate plants
and realize economies of scale
Why monopolies may have zero economic profit
Regulation
Rent seeking
Rent seeking is any costly action undertaken by a
firm to establish or maintain its monopoly status
Rent seeking may well reduce profits to zero
Why?
The End
Profit Max for Monopolist
22
$
20
18
16
Price
14
MR
12
MC
10
8
PU
6
QU
4
2
0
0
1
2
3
4
5
6
7
8
9
10
11
Output
12