Topic 3 : Lecture 17
Perfect competition and Consumer Surplus
p
S
pc
D
Xc
X
Consumer Surplus is given by? And Producer Surplus?
Robin Naylor, Department of
Economics, Warwick
1
Topic 3 : Lecture 17
Monopoly and Consumer Surplus: Suppose a monopolist takes over the
previously competitive industry.
p
MC
The Monopolist
faces the Market
Demand Curve.
We assume that
the Monopolist’s
Cost Curves are
simply the sum
of those of the
individual
competitive
firms.
AC
S
pc
D
Xc
X
Consumer Surplus under Monopoly is given by? And Producer Surplus under Monopoly?
Robin Naylor, Department of
Economics, Warwick
2
Topic 3 : Lecture 17
Monopoly and Consumer Surplus: Suppose a monopolist takes over the
previously competitive industry.
p
MC
AC
pm
S
pc
D
MR
Xm
Xc
X
Consumer Surplus under Monopoly is given by? And Producer Surplus under Monopoly?
Robin Naylor, Department of
Economics, Warwick
3
Topic 3 Lecture 17
• Monopoly welfare loss: recap
– A monopoly firm takes over. The Market Demand is now the same as
that for the individual firm: how much will it produce? Price?
p
LMC
LAC
Identify:
p, X, CS, PS under
monopoly.
S
MR
D
Compare PS and CS
under Monopoly and
under Perfect
Competition.
X
Robin Naylor, Department of
Economics, Warwick
4
Topic 3 : Lecture 17
Monopoly and Consumer Surplus: An alternative representation of the
Deadweight Loss of Monopoly (see also B&B p. 469):
p
MC
AC
pm
S
pc
D = MB
MR
Xm
Xc
Robin Naylor, Department of
Economics, Warwick
X
5
Topic 3 Lecture 17
• Algebra of monopoly (this is essentially the same analysis as that of
Lecture 12 Slide 13)
Assume market demand is given by p  a  bX .
Let the monopoly firm's costs be constant; AC  MC  c.
The monopoly firm's profit is:
  TR  TC  ( p  c) X  (a  bX  c) X .
The firm's profits are maximised when

 a  2bX  c  0, or X  (a  c)/2b.
X

 0. That is,
X
From this, one can work out the values of:
Price, (super-normal) Profit, Consumer Surplus and Welfare,
and compare these with the perfectly competitive levels.
Robin Naylor, Department of
Economics, Warwick
6
Topic 3 Lecture 17
• Monopolistic competition
– Like Perfect Competition, there are many firms
– Unlike Perfect Competition, each faces a downward-sloping demand
curve (why?)
– Industry equilibrium is when each just breaks even:
p
LMC
LAC
Here the industry is
not in equilibrium:
Why not?
D
What happens next?
MR
X
Robin Naylor, Department of
Economics, Warwick
7
Topic 3 Lecture 17
• Monopolistic competition
– Like Perfect Competition, there are many firms
– Unlike Perfect Competition, each faces a downward-sloping demand
curve (why?)
– Industry equilibrium is when each just breaks even:
p
LAC
LMC
Here the industry is in
equilibrium:
Why?
D
MR
X
Robin Naylor, Department of
Economics, Warwick
8
Topic 3 Lecture 17
• Oligopoly
– Few firms (in our models, we’ll typically assume 2 for simplicity)
– Interdependent (Why?)
– Various possible behaviours
• Collusive
• Cournot (quantity) Competition
Robin Naylor, Department of
Economics, Warwick
9
Topic 3 Lecture 17
• Collusive Oligopoly
– Here the firms simply act as if they were a single monopolist
– They determine profit-maximising output and each produce, say, half of
that output. The price is the monopoly price and the welfare loss,
compared to perfect competition, is the monopoly welfare loss.
– Example: if p=a – bX and MC=AC=c, then each firm produces:
x1  x2  X / 2  (a  c) / 4b
– So total output is (a – c)/2b, the same as under monopoly.
– It is not then difficult to work out market price, supernormal profits,
Consumer Surplus, and Welfare (Loss)
– Note, under Perfect Competition, output is (a – c)/b.
(Because c=p=a – bX)
Robin Naylor, Department of
Economics, Warwick
10
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
Each firm chooses its own profit-maximising output given what the other firm is producing.
Consider Firm 1 (of 2):
 1  ( p  c) x1.
Note that market price, p, is the same for both firms and depends on market output, p  a  bX ,
where X  x1  x2 .
Substituting,
 1   a  b  x1  x2   c  x1.
The first-order condition for profit maximisation by Firm 1 is:
 1
 a  c  bx2  2bx1  0, which implies that:
x1
x1  (a  c  bx2 ) / 2b.
This is called Firm 1's Best-Reply Function to Firm 2's chosen output level.
We can draw it.
Robin Naylor, Department of
Economics, Warwick
11
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
R1 : x1  (a  c  bx2 ) / 2b.
This is called Firm 1's Best-Reply Function to Firm 2's chosen output level.
x2
R1
x1
Robin Naylor, Department of
Economics, Warwick
12
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
Firm 1's Best-Reply Function to Firm 2's chosen output is given by:
x1  (a  c  bx2 ) / 2b.
Similarly, we can represent Firm 2's Best-Reply Function to Firm 1's chosen output:
x2  (a  c  bx1 ) / 2b.
We can draw both together:
Robin Naylor, Department of
Economics, Warwick
13
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
x2
R1
R2
x1
Robin Naylor, Department of
Economics, Warwick
14
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
Firm 1's Best-Reply Function:
x1  (a  c  bx2 ) / 2b.
Firm 2's Best-Reply Function:
x2  (a  c  bx1 ) / 2b.
The (oligopoly/duopoly) market is in equilibrium when each firm's output
is the best reply to that of the other: i.e., where the best reply functions
intersect. This is where the two best reply functions are satisfied simultaneously:
solving, and using symmetry, we obtain:
x1  (a  c  bx1 ) / 2b,
 2bx1  (a  c  bx1 )
 3bx1  (a  c)
 x1  (a  c) / 3b
Robin Naylor, Department of
Economics, Warwick
15
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
As x1  x2  (a  c) / 3b,
it follows that:
X  x1  x2  2(a  c) / 3b
How does this compare with output under monopoly (and hence
collusive oligopoly)?
How does it compare with output under perfect competition?
What can you conclude about the comparison of:
Price
Producer Surplus
Consumer Surplus
Total Welfare
under Cournot Oligopoly, Collusive Oligopoly, Monopoly and Perfect Competition?
Robin Naylor, Department of
Economics, Warwick
16
Topic 3 Lecture 17
• Oligopoly with Cournot Competition
It is straightforward to show that the 2 firms do better when colluding
than when competing (eg in the Cournot way).
So why don't they always collude?
1. Legality
2. Prisoners' Dilemma
If Firm 2 is producing the collusively-agreed output, (a-c)/4b,
what will Firm 1 want to produce?
Robin Naylor, Department of
Economics, Warwick
17
Topic 3:
Lecture 17
Now read B&B 4th Ed., pp. 370-377, 389-390, 469-471, 530-541, 558-560.
You might also consult:
• Frank, Chapters 11-13
• Estrin, Laidler and Dietrich, Chapters 11-13, 15, 16
Robin Naylor, Department of
Economics, Warwick
18