In Bertrand equilibrium, firms independently set prices equal to their constant marginal costs (c1 and c2). In a competitive equilibrium, prices are market-driven, reaching the lowest marginal cost (min(c1, c2)).
In a Bertrand competition model with two firms, each firm simultaneously sets its price to maximize profits, assuming that the other firm's price remains constant. In this scenario, if both firms have constant marginal costs (c1 and c2), the Bertrand equilibrium occurs when both firms set their prices equal to their respective marginal costs.
Mathematically:
- Firm 1's price (P1) equals marginal cost (c1).
- Firm 2's price (P2) equals marginal cost (c2).
In contrast, in a competitive equilibrium, prices are determined by the market demand and supply. In a perfectly competitive market, prices are driven down to the level of marginal cost.
Comparing the two equilibria:
- In the Bertrand equilibrium, prices are set at marginal cost by each firm independently.
- In the competitive equilibrium, prices are determined by market forces and driven down to the level of the lowest marginal cost (min(c1, c2)).
The key difference lies in how prices are determined: Bertrand equilibrium results in prices equal to individual marginal costs, while competitive equilibrium leads to prices equal to the lowest marginal cost in the market.