# Bertrand.pdf - Oligopoly the Bertrand Model Laura Lasio...

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1/23 Oligopoly: the Bertrand Model Laura Lasio ECON 305
2/23 Oligopoly and Strategic Interaction Monopoly and perfect competition display NO strategic interaction: independent decision making
2/23 Oligopoly and Strategic Interaction Monopoly and perfect competition display NO strategic interaction: independent decision making Usually few firms on the market: strategic interdependence
2/23 Oligopoly and Strategic Interaction Monopoly and perfect competition display NO strategic interaction: independent decision making Usually few firms on the market: strategic interdependence 1. decisions taken by one firm may affect its own payoff and the payoff of its rivals 2. the payoff of one firm depends on its own decisions and the decisions of its rivals
2/23 Oligopoly and Strategic Interaction Monopoly and perfect competition display NO strategic interaction: independent decision making Usually few firms on the market: strategic interdependence 1. decisions taken by one firm may affect its own payoff and the payoff of its rivals 2. the payoff of one firm depends on its own decisions and the decisions of its rivals for example: 1. demand depends on own price and on rivals’ prices 2. profits depend on share of demand a firm gains on the market
3/23 Oligopoly: Bertrand model Assumptions 1. 2 firms (duopoly): I = 1, 2 2. homogeneous product: perfect substitution 3. symmetric costs: C i ( q i ) = c i q i + F i i I I F i = fixed costs (may be zero) I c i = marginal cost c (may be constant, same for both) 4. demand Q = f ( P ) example: Q = a - bP (linear, convenient to use direct) 5. simultaneous pricing decision
4/23 Demand for firm i How does individual demand respond to both prices ?
4/23 Demand for firm i How does individual demand respond to both prices ? q i ( p i , p - i ) = Q ( p i ) if p i < p - i Q ( p i , p - i ) /2 if p i = p - i 0 if p i > p - i
4/23 Demand for firm i How does individual demand respond to both prices ? q i ( p i , p - i ) = Q ( p i ) if p i < p - i Q ( p i , p - i ) /2 if p i = p - i 0 if p i > p - i In words: I if firm i sets a price lower than its rival, it gets all demand I if firm i sets a price higher than its rival, it gets no demand I if firm i sets a price equal to its rival, they share demand (equally)
5/23 Demand for firm i P a p =p Q p 1 =p 2 Q(p 1 ,p 2 )/2
6/23 Profit for firm i π i ( p i , p - i ) = ( p i - c ) Q ( p i ) if c p i p - i - e ( p i - c ) Q ( p i ) /2 if p i = p - i 0 if p i p - i + e
6/23 Profit for firm i π i ( p i , p - i ) = ( p i - c ) Q ( p i ) if c p i p - i - e ( p i - c ) Q ( p i ) /2 if p i = p - i 0 if p i p - i + e In words: I if firm i sets a price lower than its rival (even by a very small amount e ) and above marginal cost, it gets monopoly profits I if firm i sets a price equal to its rival, it shares profits with its rival I if firm i sets a price higher than its rival (even by a very small amount e ), it gets no profit I Assume here that fixed costs are zero
7/23 Profit for firm i π i p i p i =p -i p i <p -i p i >p -i c
8/23 Best Response / Reaction Function What price p i should firm i choose?
8/23 Best Response / Reaction Function What price p i should firm i choose?
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