Updated: 21 Feb. 2007
MICRO ECONOMICS
(ECON 601)
Lecture 6
Topics to be covered:
a- Pricing under homogeneous oligopoly
b- Quasi-competitive model
c- Cartel model
d- Cournot solution
e- Conjectural variation models
f- Price leadership model
g- Cournot’s natural spring duopoly
h- Product differentiation
i- Entry and monopolistic competition
j- Contestable markets and industry structure
Traditional Models of Imperfect Competition
Nicholson Chapter 14
These models fall between the extremes of perfect competition and monopoly.
Three types of market situations to be studied:
(1)
Pricing of homogeneous goods in markets in which there are relatively few firms
(2)
Product differentiation and advertising in such markets
(3)
The effect that entry and exit possibilities have on long-run outcomes in imperfectly
competitive markets.
In the analysis we use the competitive model as a useful benchmark.
Criteria
(1)
Are prices under imperfect competition equal to marginal costs?
(2)
In the long-run does production occur at minimum average costs.
Pricing under homogeneous oligopoly
Output of each firm in the model is denoted by qi (i = 1,...,n)
Firms are all identical; hence output of each firm is the same.
Inverse demand function:
P = f (Q) = f (q1 + q2 + ...+ qn)
Total cost of each firm is TCi (qi)
i
= Pqi – TCi (qi) = f (Q) qi – TCi (qi)
i
= f (q1 + q2 + ...+ qn) qi – TCi (qi)
Central question is how firms make profit maximizing output choice. Key issue is how firm
assumes other firms react to its decisions.
Four of the many possible models are examined here:
1.
Quasi-competitive model: Assumes price-taking behavior by all firms (P is treated as fixed).
2.
Cartel model: Assumes firms can collude perfectly in choosing industry output.
3.
Cournot model: Assumes that firm i treats firm j’s output as fixed in its decision can
(∂qj/ ∂qi) = 0.
4.
Conjectural variations model: Assumes that firm j’s output will respond to variations in
firm i’s output (∂qj/ ∂qi  0).
1
Quasi-Competitive Model
Each firm assumes that it is a price taker and that its decisions will not affect the market.
First order conditions for a maximum from profit function i = Pqi – TCi (qi)
or,
∂Пi/∂qi = P – ∂ [TCi (qi)]/∂qi= 0
P = MCi (qi) (i = 1,...,n)
These n supply equations together with the market clearing demand equation,
P = f (Q) = f (q1 + q2 + ...+ qn)
will ensure that market arrives at the short-run competitive solution, with constant marginal costs
of MC. The condition that each firm as a price taker gives us the competitive equilibrium of C
below with Pc and Qc.
D
C
PC
MC
D
MR
QC
Cartel Model
Alternative assumption is that each firm recognizes that its decisions have an effect on price. The
firms as a group recognize that they can affect price and coordinate their decisions to achieve
monopoly profits.
The cartel operates as a multi plant monopoly.
2

= PQ – [TC1 (q1) + TC2 (q2) +... + TCn (qn)]

= f (q1 + q2 + ...+ qn) (q1 + q2 + ...+ qn) –
n

TCi (qi)
i 1
∂Пi/∂qi = P + (q1 + q2 + .......+ qn) – ∂P/∂qi - MCi (qi) = 0
= MR (Q) – MCi (qi) = 0
MR can be written as a function of the combined output of all firms, since its value is the same no
matter which firm’s output level is changed. If MC’s are equal and constant for all firms, the
output choice is indicated by point M in figure below.
Price
D
Pm
M
MC
PC
D
MR
Qm
Quantity by per period
This coordinated plan requires a specific output level for each firm. Aggregate profits will be as
large as possible given market demand and the industry's cost structure. Profits will be shared
according to the output level of each firm.
1.
2.
Cartel solution requires a considerable amount of information available to directors of the
cartel. (a) market demand function and (b) each firm’s marginal cost function.
Cartel solution is fundamentally unstable since each cartel member will produce an output
level for which P>MCi. Hence, each will have an incentive to expand output. If director's
of cartel can not stop such over production, the monopolistic situation will collapse eq.
OPEC in 1980’s.
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Cournot Solution
Assumes that firm recognizes its own decisions about qi affecting the price in the market
∂P/∂qi 0 but assumes,
q j
q i
= 0, for j  i.
(1)
∂Пi/∂qi = P +qi*∂P/∂qi-MCi (qi) = 0
(for all i = (1,...,n)
The n equations of the form of (1) together with market clearing demand equation
P = f(Q) will give an equilibrium solutions for q1, q2,...,qn.
As long as marginal costs are increasing, each firm’s output in the Cournot solution will
exceed the cartel output, since the “firm-specific” marginal revenue is larger than the
market marginal revenue shown in the cartel situation i.e. P + qi (∂P/∂qi)>P + Qm (∂P/∂qi)
because qi < Q. The greater the number of firms in the industry the closer the equilibrium
points will be to the competitive case.
Price
D
P*
MC
D
MR
Q*
Quantity by per period
Conjectural Variations Models
Need to allow for strategic interactions among firms. This is important when number of firms is
small. One approach relies on game theory to examine strategic choices.
4
We introduce into the model assumptions that might be made by one firm about another firms
behavior for each firm i we are concerned with the assumed value of the derivative
q j
q i
for all
firms j other than firm i itself.
Because value of derivative is speculative, models based on various assumptions are termed
“conjectural variations” models.
To this point in our discussion of oligopoly, we have assumed
q j
q i
= 0 for all j  i, once we relax
this assumption then first order condition for profit maximization becomes.
∂∏i/∂qi = P + qi [∂P/∂qi +
n

j i
∂P/∂qj
q j
] – MCi (qi) = 0
q i
Firm must now consider how variations in its own output will affect the market price
through their effect on the other firms’ output decisions.
Price Leadership Model
Market is composed of a single price leader and a fringe of quasi – competitive competitors.
The price leader has lower cost than that of the competitive suppliers, e.g. Saudi Arabia in OPEC.
D
Supply of quasi-competitive firms
P1
D’
Excess demand curve
PL
D’
P2
MCL
MR
O
Qc
QL
QT
QL set by MR = MCL
5
D
QT = QL + QC
At the price set by price leader, the competitive firms all together will supply Qc.
At prices above P1 the market will be supplied by competitive fringe. At prices below P2 there is
no competitive Fringe.
The price leader considers the excess demand function it faces D’D1, and equals its Marginal
Revenue with its own MC curve.
Consider a number of types of market organization using:
Cournot’s Natural Spring Duopoly
Two firms, no production costs, MC = 0
Demand Curve,
Q = q1 + q2 = 120 – P
P = 120 – Q
Quasi Competitive Solution:
Total output = 120 with price zero, and allocation between two firms indeterminate.
Cartel Solution
P
= 120 – Q

= P. Q – TC
= 120 Q – Q2 – 0
∂∏/∂Q = 120 – 2Q = 0
Q
= 60
P
= 60

= 3600
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120
M
60
O
60
MR
120
Q
Cournot Solution
P=120-q1-q2
1 = P q1 = (120 – q1 – q2) q1 = 120q1 – q12 – q1q2 (where P = 120 – q1 – q2)
2 = P q2 = (120 – q1 – q2) q2 = 120q2 – q1q2 –q22
(1)
(2)
Assume,
∂q1/ ∂q2= ∂q2/ ∂q1 = 0
∂∏1/∂q1 = 120 – 2q1 – q2 = 0
∂∏2/∂q2 = 120 – 2q2 – q1 = 0
Solving for q1 and q2,
From (2) q1=120-2q2
Solution (1) q2=120-2(120-2q2)
q2=120-240+4q2
3q2=120
q2=40
q1 = q2 = 40
P = 120 – (q1 + q2) = 40
1 = (40) (40) = 1600
2 = (40) (40) = 1600
 = 3200
Given that one spring owner’s output is 40 in the Cournot model why can’t the other one gain by
lowering its price to sell more?
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Stackelberg Leadership Model
What are the consequences if firm 1 knows that firm 2 chooses q2 so that q2 = (120-q1)/2
The amount that firm 2 sells is equal to half of the difference between the max. amount demanded
and the quantity supplied by firm 1.
Demand:
Q = q1 + q2 = 120 – P, P=120-q1-q2
Profit, 2 = (120 – q1 – q2) q2 – TC
Where TC and MC is assumed = 0
2 = 120q2 – q1q2 – q22
For profit maximization,
∂∏2/∂q2= 120 – q1 – 2q2 = 0
 q2 = (120-q1)/2
Hence, ∂q2/∂q1 = – ½ is firm 1`s conjectural variation of the response of firm 2 to a change in q i`s
output.
Firm 2 reduces its output by ½ unit for each unit increase in output of firm 1, (q1)
Firm 1 knows that Firm 2 reduces its output by ½ unit for every unit increase by q1.
Profit maximization by firm 1 is now:
1 = P q1 = 120q1 – q12 – q1q2
∂∏1/∂q1= 120 – 2q1 – q1 (∂q2/∂q1) – q2 = 0
As (∂q2/∂q1) = – 1/2
= 120 – 2q1 + ½ q1– q2 = 0
(1)
=120 – (3/2)q1– q2 = 0
Solving (1) with q2 = (120-q1)/2
120 – (3/2) q1 – (120-q1)/2 = 0
60 – 3/2 q1 + q1/2 = 0
Gives, q1 = 60 and q2 = 30.
P = 120 – (q1 + q2) = 30
1 = P q1 = 60 * 30 = 1800
2 = P q2 = 30 * 30 = 900
Problem to determine which firm is chosen as the leader. If each firm assumes that the other is a
follower each will produce 60 and profits will fall to zero. If both acts as a follower than the
Cournot solution is the result.
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Product Differentiation
Product Group
The outputs of a set of firms constitute a product group if the substitutability in demand among
the products (as measurable the cross-price elasticity) is very high relative to the substitutability
between those firms` outputs and other goods generally.
If there are n firms competing in a particular product groups. Each firm can choose the amount it
spends (z) to differentiate its product from those of the competitors.
Total Costs = TCi (qi, zi)
Pi = g (qi, Pj, zi, zj)
Presumably,
∂g/∂qi < 0
∂g/∂Pj > 0
∂g/∂zi > 0
∂g/∂zj < 0
i = Pi qi – TCi (qi, zi)
If,
∂zj/∂qi; ∂zj/∂zi ; ∂Pj/∂qi ; ∂Pj/∂zi are all assumed to be equal to zero.
Then, (1)
(2)
∂∏i/∂qi = Pi + qi ∂Pi/∂qi – ∂TCi/∂qi = 0
∂∏i/∂zi = qi ∂Pi/∂zi – ∂TCi/∂zi = 0
This is saying from (1) that output should be produced up to the point where MR = MC. From (2)
and additional differentiation will be pursued up to the point where the additional revenues they
generate will be equal to their marginal costs.
Entry and Monopolistic Competition
Possibility of new firms entering the industry will lower prices and reduce profits.
Zero profit equilibrium will take place in a competitive industry with free entry when
P = MR = MC and P = AC. If entry is allowed this will also cause a monopolistic industry to
have its profits reduced to zero.
If firms can differentiate their product hence they will face a downward sloping demand curve.
Before entry profits maximized at P0*Q0* where MC = MR0 (see figure).
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Excess Capacity of Qm – Q1
MC
AC
A
P*0
B
C
P1
D0
MR0
MR1
O
Q1
Q*0
D1
Qm
At the same time entry into the industry will cause the demand curve to shift to the left until it is
just tangent to its average cost curve. At this point there will be zero profits but P > MC and
MR1=MC. At P1, Q1 there will be zero profits but excess capacity.
This zero-profit equilibrium was first described by Edward Chamberlin as monopolistic
competition.
In the equilibrium each firm has P1 = AC but P1 > MC. Each firm has diminishing average costs
at its final equilibrium point. As there are zero profits the final equilibrium will be sustainable.
What happened if price set by regulation and at the same time free entry?
For example- Taxi cabs prices set by regulation but no restrictions in taxi cab licences.
- The rate of “take” of casinos set by regulation but no restriction on entry of casinos.
Contestable Markets and Industry Structure
Monopolistic competition neglects the effects of potential entry on market equilibrium by
focusing only on the behavior of actual entrants. Competition for the market provides a more
appropriate perspective for analyzing the free entry assumption.
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Perfectly Contestable Market
A market is perfectly contestable if entry and exit are absolutely free. Equivalently, a perfectly
contestable market is one in which no outside potential competitor can enter by cutting price and
still make profits. Hence, even if the number of firms operating in a market is relatively small but
the perfectly contestable assumption will ensure competitive behavior. The ability of potential
entrants to seize any possible opportunities for profit constrains the types of behavior that are
possible.
Price
MC1
MC2
AC1
MC3
AC2
MC4
AC3
AC4
D
q*
2q*
3q*
number of firms, n = Q*/q*
Q* = total market demand, when P = min AC
q* = size of firm at min AC.
A Contestable Natural Monopoly
Total cost of producing electric power:
Q = megawatts of electricity
Total Cost:
TC = 100 Q + 8000
∂TC/∂Q = MC = 100
Demand:
QD=1,000-5P
P = 1000/5 – QD/5
Total Revenue
TR = PQ = 200 Q – QD2/5
∂PQ/∂Q = MR = 200 – (2/5)Q
MR = 200 – (2/5)Q = MC = 100
11
Q*=4q*
Output
Qm = 100 * (5/2) = 250
250 = 1000 – 5P
5P = 750
P = 750/5 = 150
Profits will be TR – TC = (150)(250)-[100(250)+8000]=37,500 – 33,000 = 4,500
A. Contestable Solution
The only viable price under the threat of potential entry is average cost.
The monopoly will set price when its profits =0
Q = 1000 – 5P = 1000 – 5 (AC)
AC = TC/Q = 100 + 8000/Q
AC=P
QD=1000-5(100+8000/Q)
QD=500-40000/Q
Q2 – 500 Q + 40,000 = 0
(Q – 400) (Q – 100) = 0
P
AC
MC
100
400
Q = 400 solution is a sustainable entry deterrent.
Therefore the market equilibrium is Q = 400. Therefore, with QD=1000-5P
400 = 1000 – 5P
P = 600/5 = 120
Contestable solution is precisely what might be chosen by a regulatory commission interested in
average cost pricing.
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Price
D
150
120
AC
100
MC
D
MR
250
400
Quantity
Price is set by regulation with free entry
Firm
Market
Efficiency loss in
production
Price
Price
s
s
P
P
q1
q0
Q1 Q0
Quantity
P set competitively
Q
n0= 0
q0
At q0 P=Min AC=MC
s set by regulation
At q1 s=AC≠ MC
n1=
WC=[AC(q1)-AC(q0)]Q1+ ½(Q0-Q1)(AC(q1)-AC(q0))
13
Q1
q1
Quantity
Efficiency loss in
consumption
Barriers to entry
Product differentiation may raise entry barriers so that no room remains for would be entrants.
Strategic pricing may deter entry some types of capital investments that may not be reversible.
The End
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