L19 - Cournot Competition Flashcards

1
Q

Who are Cournot and Bertrand?

A

Theories of such oligopolies either follow the work of Cournot or Bertrand:
- In 1838, Antoine Augustin Cournot assumed that firms
choose how much output to produce
- In 1883, Joseph Bertrand criticised Cournot’s model, because oligopolists
will use their price as the strategic variable in some markets
- Thus, contemporary models of oligopoly are either:
quantity-setting (Cournot) or price-setting (Bertrand)

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2
Q

What are the Assumptions of Oligopolies?

A

We retain A(1) and A(2) from lecture 1, slide 9:

  • buyers are price takers
  • buyers and sellers have complete information

A(3): SELLERS ARE PRICE MAKERS
- A price maker can influence the price which it sells its output.
- (a) A seller sells more when its price is lower: its demand curve slopes
downwards
- (b) the seller’s output choice does trigger a reaction its rivals

A(4): ENTRY IS BLOCKED
- A potential seller cannot enter the market. Not even in the long-run.

  • These are similar to monopoly and monopolistic competition, apart from A(3) (b)
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3
Q

What is the Market Structure of Oligopolies?

A

(a) SIZE & NUMBER OF SELLERS –> Few, Large
- Each seller must be large enough to affect price: they are price makers
- Each seller’s rivals must also be large, because their rivals respond strategically to the seller’s output choice

(b) BARRIERS TO ENTRY –> High
- Firms must be unable to enter the market

  • (c) PRODUCT SUBSTITUTABILITY - > Undifferentiated and Differentiated
  • Products can be identical or differentiated under oligopoly
  • Sellers’ market power stems from few firms and high entry barriers
  • Common for models to assume that products are homogeneous (identical)
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4
Q

What are Specific Assumptions for Cournot’s Model of Oligopoly?

A

A(1) –> There are two sellers (A & B) in the market (they are “duopolists”)

  • They choose the level of output to produce (i.e. they compete in quantities)
  • They make their output decisions simultaneously

A(2) –> Further entry into the market is completely blocked
- This ensures that we only have to consider the firms in the market already

A(3) –> Firms produce homogeneous products
- This simplifies the model compared to differentiated products

A(4) –> The market’s (inverse) demand is –> P =a-Q

  • where a > 0 and Q is the total output in the market
  • So if Firm A produces Q{A} and Firm B produces Q{B}, then Q = Q{A} + Q{B} and P=a-Q{A}-Q{B}
  • if price is above a –> this is the choke point and nothing would be sold in the market
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5
Q

How do we find the Cournot-Nash Equilibrium?

A

In this case, there is a Nash equilibrium when:
- no firm wants to change its output level, holding the other firm’s output level constant

PRECISE:
A Nash equilibrium consists of two output levels, Q{A}* and Q{B}* such that:
1) Given that Firm B produces Q{B}*
, Firm A’s profit is maximised by producing Q{A}*
2) Given that Firm A produces Q{A}* , Firm B’s profit is maximised by producing Q{B}*

To solve for the Nash equilibrium, we must find the firms’ best responses!

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6
Q

What is the Residual Demand Curve?

A
  • The residual demand curve is a firm’s demand curve, given the output of its rivals Effectively it is the market demand that its rival has not supplied
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7
Q

What does the Residual Demand and Market Demand curve look like on a graph?

A
  • With Price (P) on the y-axis and Quantity(Q) on the x-axis
  • on the market demand curve the downwards demand line is given with the equation D{M}= a -Q{A} - Q{B}
  • To construct Firm’s A Residual Demand Curve –> first we assume that Firm B will produce Q{B1} at P{B} –> this would mean if A produced 0 the Price would be P{B}
  • next say the quantity produced in the market is Q{1} at the Price P{1} –> then A produces Q{1}-Q{B} at the market price level of P{1}
  • repeat this for various levels of Price and Quantity of Firm B and connect all these points to create Firm A’s Residual Demand Curve
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8
Q

How is the residual demand curve and total revenue related?

A
  • IMPORTANT: Firm A’s residual demand curve depends on Firm B’s output
    The more Firm B produces, the closer Firm A’s residual demand curve is to the origin If Firm B produces nothing, the residual demand curve is the market demand curve
  • Firm’s A residual demand curve shows what the market price will be for different levels of output, given Firm B’s output level
  • Thus, we can work out what Firm A’s total revenue will be: –> e.g. if firm A produced Q{1}-Q{B}, the TR{A}=P{1}(Q{1}-Q{B})
    -Given we know what total revenue is, we can find marginal revenue
  • This enables us to apply the marginal output rule
  • Marginal revenue is downward sloping and below the residual demand curve
  • (for the same reasons as for monopoly and monopolistic competition)
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9
Q

How do you derive Cournot’s best response function from a Firms Demand Function?

A
  • Looking at the the graph of Firms A Demand curve
  • With Price (P) on the y-axis and Quantity (Q) on the x-axis
  • Upwards sloping curve or MC{A} and the negative gradient line of the market demand
  • to the left of it is Firm A’s demand curve –> they distance it is from the market demand curve is the quantity Firm B is producing
  • From this specific demand curve we can figure out the Marginal Revenue line –> from this using the marginal output rule for a monopoly we can figure out the level of output and price A will be charging
  • We repeat this exercise for various outputs of Firm B to figure out the best response curve
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10
Q

What does Firm A’s best response curve look like?

A

With Firm B’s Output on the y-axis and Firm A’s Output of the x-axis

  • If Firm B Produces nothing Firm A will produce the monopoly amount
  • for now increasing amounts of output of Firm B we plot the corresponding lessen output of Firm A
  • At the point where Firm B produces everything A obviously produces nothing
  • By connecting these points we create a negative gradient curve passing through the maximum market output of Firm B on the y-axis and the monopoly output of Firm A on the x-axis
  • This Shows that Firm A’s profit increases as its output tends towards the monopoly level
  • To get Firm B’s best response function you repeat the step for Firm B instead
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11
Q

What is the Cournot-Nash Equilibrium?

A
  • Recall that there is a Nash equilibrium in this model when no firm wants to change its output level, holding the other firm’s output level constant
  • Occurs a the level of output where both firms best response curves intersect
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12
Q

How does Cournot model compare to a Monopoly?

A
  • in the cournot model the market price will be lower than a monopolist price
  • as because firm B produces some quantity in the market firm A’s residual demand line and thus their marginal revenue line is less than if they were to have total monopoly
  • therefor they produce less at a lower price under Cournot’s model
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13
Q

How does Cournot’s model compare to Perfect Competition?

A
  • In the Cournot model, the market price is above marginal cost whereas under perfect competition price=marginal cost
  • If Marginal Cost is not increasing too much, the duopolists together produce less than under perfect competition
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