Bertrand duopolists, Firm 1 and Firm 2, face inverse market demand . Both have marginal cost, . The equilibrium price in the market will be

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First, note the core setup: two Bertrand competitors with homogeneous goods face the market demand P = 50 − Q and have marginal cost MC = 20. In a standard Bertrand duopoly with identical products and constant marginal cost, undercutting the rival’s price by any positive amount drives the market winner to capture the entire demand at a price that minimizes the other firm’s profitable undercutting opportunities, which collapses the price to the common marginal cost.

Option by option analysis:
- Option $10: If the price were $10, it would be well below MC. At such a price, both firms would incur losses on every unit. Rational firms would not set P below MC, since they could instead raise price above $10 and still earn nonnegative profits or avoid losses. This makes P = $10 inconsistent with standard Bertrand incentives.
- Option $20: This matches the marginal cost. At P = MC, neither firm can profitably sustain a price above MC without the other undercutting; pricing at MC is the equilibrium outcome in homogeneous-good Bertrand markets with identical costs. Consumers capture surplus, and total profit is driven to zero in the simple setup, but price equals MC is the stable equilibrium under these assumptions.
- Option $30: A price of $30 would exceed MC by $10. In a Bertrand competition with identical products, one firm could undercut to a price slightly below $30 and capture the entire demand, driving the price downward rather than upward to $30. Hence $30 cannot be sustained as the equilibrium.
- Option $40: Similar to $30, $40 lies above MC and would be undercut by the rival. The Bertrand logic implies continuous undercutting until price falls to MC. Therefore $40 is not the equilibrium price.

Connecting to the demand: with P = 50 − Q and MC = 20, the competitive price outcome in this Bertrand setting is P = 20, which clears the market at Q = 30. The equilibrium price aligns with the marginal cost and is consistent with the standard Bertrand result for identical products with no capacity constraints.

ECON_104B_001_25S Chapter 13 Practice Problems -- Multiple-Choice

Bertrand duopolists, Firm 1 and Firm 2, face inverse market demand . Both have marginal cost, . The equilibrium price in the market will be

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