L20 - Price Setting Oligopolists Flashcards
What was Bertrand’s reasoning for making his model?
To say that economics should not be studied with maths because you can get paradoxical results sometimes.
What are the assumptions for Bertrand’s model of Oligopoly?
1) Two firms in the market (Duopolists)
- Choose the level of price
- Make their pricing
decisions simultaneously
2) Further entry into market completely blocked
3) Firms have same constant marginal costs (c) and no fixed costs.
- Implies firm A’s costs:
- TCa = CxQa + F= CQa
- Mca= c
- ACa= c + F/Qa = c
Difference between constant marginal costs and increasing on notes.
4) Firms produce homogeneous products
- Implies buyers purchase
good from cheapest seller
5) Market’s Demand is: Q= a -P
-Where Q is total demand.
- P is the lowest price of
Firm A and Firm B
When is there a Nash Equilibrium in this model?
When no firm wants to change its price holding the other firm’s price constant.
1) Given that Firm B charges Pb, Firm A’s profit maximised charging Pa
2) Given that Firm A charges Pa, Firm B’s profit maximised by charging Pb
In order to find the Bertrand-Nash Equilibrium need to find firms best response function.
First, start on firm-specific Demand Curve.
From there, construct best response function.
Diagrams on Notes
What is the Bertrand Paradox?
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. Seems extreme.
How do you break the Bertrand 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
Comparison with Monopoly
Diagram on notes
Comparison with Perfect Competition
Diagram on notes
Comparison with Cournot
Diagram on notes
How to construct best response function?
Diagram on notes
