L20 - Price-Setting Oligopolists Flashcards
What are the specific assumptions of Bertrand’s Model of Oligopoly?
A(1) –> There are two firms (A & B) in the market (they are “duopolists”)
- Sellers choose the level of price (i.e. they compete in prices)
- They make their pricing 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 have the same constant marginal costs, , and no fixed costs
EXAMPLE: This implies that firm A’s costs have the following properties
- Total Costs –> TC{A} = cq{A} + F = cq{A}
- Marginal Costs –> MC{A} = c
- Average Cost –> AC{A} = c + F/q{A} = c
What is the difference between increasing and constant marginal costs?
- While in the previous model we would have positive curves of MC and AC which are increasing marginal cost –> where the marginal cost curve would intersect the Average cost curve at its minimum
- in Bertrand’s model of Oligopoly we have constant MC which is a horizontal line where MC=AC
- this simplifies things alot as once we have put of the demand curves on (supposing they were a monopolist ) we can use the marginal output rule to find out what they would sell at what price –> this would allow the monopolist to make supernormal profits which is also a producer surplus
- Firm is never going to set a price below marginal cost –> as a firm makes normal profits at p=MC
What are two further Specific Assumption of Bertrand’s Model of Oligopoly?
A(4) –> Firms produce homogeneous (identical) products
- They sell products with that are not (horizontally or vertically) differentiated
- This implies that buyers will purchase the good from the cheapest seller
- If Firm A’s price is below Firm B’s, Firm A sells to all buyers & Firm B sells to none
- If they set the same price, they both supply half of the buyers
A(5) –>The market’s demand is: Q=a -P
- where Q is the total demand when the lowest price of Firm A and Firm B is P where a > 0 (at any price above a , nothing is demanded)
PRECISE:
- If Firm A sets P{A} below Firm B’s price of P{B} then Q = a- P{A}
- If Firm A sets P{A}above Firm B’s price of P{B} then Q = a- P{B}
When is there a Nash equilibrium in the Bertrand model of Oligopoly?
- no firm wants to change its price, holding the other firm’s price constant
PRECISE: a Nash equilibrium in prices consists of two prices, P{A}*
and P{B}, such that:
1) Given that Firm B charges P{B}, Firm A’s profit is maximised by charging P{A}*
2) Given that Firm A charges P{A}* , Firm B’s profit is maximised by charging P{B}*
To solve for the Nash equilibrium, we must find the firms’ best responses!
How do you create the firm-specific demand curve?
- suppose firm A believe that Firm B will set a Price at P{1} and A sets is price at any higher level –> Firm A will receive no demand which will all go to Firm B –> creating a straight line on the y-axis at above P{1}
- Suppose both Firm A and Firm B both set the same price –> both firm split the demand 50/50 –> creating a flat line across to total market demand at that price
- If Firm A sets a price below Firm B –> all the consumers are going. to come to Firm A instead –> therefore Firm A will supply all the demand in the market –> creates a downwards diagonal line of demand like normal
How to find Firm A’s best response to Firm B’s price?
- Using the marginal output rule we can find Firm A’s best response to a given price of Firm B
- If Firm A believe that Firm B will set a Price of P{1} overlap their residual demand curve of Firm A at this price and put on the marginal revenue curve –> which usually has a dotted line down below the level Firm A receives all demand
- Also at the horizontal Marginal Cost line
- time find Firm A response Price will be at the point on the demand curve directly above the point where MC=MR
How to Construct Firm A’s best response function?
- With Firm B’s Price on the y-axis and Firm A’s Price on the x-axis and a 45 degree line where both prices are equal
- set this next to Firm A’s profit maximising diagram
- if Firm B sets a Price very high above the Monopoly Price Firm A’s best response would be to set the price a monopolist would set –> this create the top vertical line of the best response function
- If Firm B sets a price below the Monopoly Level most like the MR curve will Intercept the MC curve at the discontinuity point
- at any point the MC line cross the dotted vertical line of MR Firm A will charge the price which is the smallest margin possible below firm B price
- To represent this on the diagram –> at Firm B’s price go across to the 45 degree line and move on increment to the left and plot the point of Firm A’s best response
- Finally suppose Firm B sets its price below Firm A’s marginal cost –> as Firm A would make no profit it will set it price only at the point of Marginal cost –> this creates the vertical line at the bottom of the best response function
- to finish on the best response function simply connect the top of the bottom vertical line with the bottom on the top vertical line and just repeat this with Firm A’s price to get Firm B’s best reponse
How do we find the Bertrand-Nash equilibrium?
- there is a Nash equilibrium when no firm wants to change its price,holding the other firm’s price constant
- The Bertrand-Nash Equilibrium is where the two firms’ best response functions intersect –> where both firms are selling at Marginal Cost
What is the Bertrand Paradox?
- The result of the Bertrand model is known as the Bertrand paradox -Why?
Consider the implications of the Bertrand model:
- 1) Suppose there was only one firm in the market:
this firm would be a monopolist and would charge a high price
- 2) Suppose another firm enters the market that sells an identical product:
the firms set the price that would be set under perfect competition…
- The paradox is that, by adding only one firm, we go from:
- the extreme of monopoly to the other extreme of perfect competition!
- In reality, we do not observe this, so there must be something wrong - but what?
What are the 4 flaws of Bertrand’s Paradox?
- (1) Product differentiation
Seller doesn’t lose all of their customers when their prices are higher than rivals’ - (2) Capacity constraints
A firm has market power over the residual demand if a rival cannot supply the
whole market (even if firms sell identical products) - (3) Incomplete information about prices and search costs
Lower prices cannot attract consumers who are not aware of them - (4) Repeated interaction
Firms may not compete as intensely as the Bertrand model predicts, if they
interact repeatedly
How does Bertrand’s Model compare with a monopoly?
- The duopolists set a lower price than the monopoly level (and Cournot level) –> - this occurs as both companies set their prices at marginal cost
How does Bertrand’s Model compare with perfect competition?
The duopolists set the same price as the market price of perfect competition
There is no deadweight loss (total welfare is maximised)
- Total welfare therefore is equal to consumer surplus
How does Bertrand’s model compare to Cournot’s model?
- Cournot’s model has downward arcing lines –> if Firm A increases its output Firm B would decrease theirs –> this indicates they are strategic substitutes
- Bertrand’s model has upwards sloping lines –> if Firm A increases their price so will Firm B –> this indicates they are strategic complements
