L19 - Cournot Competition Flashcards
Who are Cournot and Bertrand?
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)
What are the Assumptions of Oligopolies?
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)
What is the Market Structure of Oligopolies?
(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)
What are Specific Assumptions for Cournot’s Model of Oligopoly?
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
How do we find the Cournot-Nash Equilibrium?
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!
What is the Residual Demand Curve?
- 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
What does the Residual Demand and Market Demand curve look like on a graph?
- 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
How is the residual demand curve and total revenue related?
- 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)
How do you derive Cournot’s best response function from a Firms Demand Function?
- 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
What does Firm A’s best response curve look like?
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
What is the Cournot-Nash Equilibrium?
- 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
How does Cournot model compare to a Monopoly?
- 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
How does Cournot’s model compare to Perfect Competition?
- 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
