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Fun with Monopoly and Games
A.
Simplified Monopoly Model
1.
Start with a simplified version of the monopoly model.
Assume that the market demand curve is linear
and that marginal cost is a constant (instead of increasing with output as suggested by the law of
diminishing returns).
In class, I use demand equations p = 10 – q or p = 100 – q or p
= 30 – q.
In general,
the corresponding marginal revenue curve is formed by doubling the slope coefficient. To use the model,
you need to understand the basics thoroughly, particularly the difference between price (on the demand
curve) and marginal revenue.
W = 1800
Competitive Equilibrium: Example
Competitive Equilibrium: Example
$/Q
D
MR
MC
Q
c
= 60
100
Q
C
P
c
= 40
100
.
.
Figure 2
MONOPOLY
v.
COMPETITION
MONOPOLY
v.
$/Q
D
MR
MC
P
m
Q
m
Q
c
Q
M
.
C
c =
P
c
S
L
π
a
π
=
W/2
S
=
W/4
L
=
W/4
.
.
Figure 1
2.
The first exercise is to compare equilibrium positions under monopoly and competition.
Under
competition, equilibrium lies at point C in Figure 1, where MC (competitive supply) intersects demand.
In
the problem set, demand is p = 100 – q, marginal cost is c = 40, so the competitive equilibrium price and
quantity would be P
c
= 40 and Q
c
= 60.
The entire potential surplus goes to the consumer.
That’s the
triangle formed between D and MC in Figure 2.
Call that W (for “welfare”).
In this particular example, the
area of that triangle is W = 1800.
I just do the competitive equilibrium in the example because, once you
have it, all of the monopoly numbers follow logically from inspection of the graphs.
Caution: these
numbers are valid only because we have assumed linear D and constant MC.
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This note was uploaded on 05/09/2008 for the course ECN 212 taught by Professor Nancy during the Fall '07 term at ASU.
 Fall '07
 nancy
 Monopoly

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