Now consider a Bertrand game with two firms: Firm A and Firm B.

The market demand is equal to P=280-Q, where Q is number of units demanded. Consumers will purchase the good from the firm who offers the lower price. If the firms offer the same price, each firm will sell half of the units that are demanded.

The marginal cost is constant and equal to $40 for both firms. The firms have zero fixed costs.

What is the equilibrium price in this market?

Question

Now consider a Bertrand game with two firms: Firm A and Firm B.

The market demand is equal to P=280-Q, where Q is number of units demanded. Consumers will purchase the good from the firm who offers the lower price. If the firms offer the same price, each firm will sell half of the units that are demanded.

The marginal cost is constant and equal to $40 for both firms. The firms have zero fixed costs.

What is the equilibrium price in this market?

BlackTom AI · Accepted Answer

We are analyzing a Bertrand competition with two identical firms, A and B, facing the demand P = 280 − Q and constant marginal cost MC = 40 for both.

First, recall the standard result: when firms have identical marginal costs and compete on price with the possibility of undercutting, the Bertrand-Nash outcome drives the price down to the common marginal cost, provided there is no capacity constraint and there are no fixed costs or other frictions. In this setup, there are zero fixed costs and continuous pricing, so the usual logic applies.

Consider any price above marginal cost, say P > 40. The firm offering the lower price would capture the entire market demand at that price, since consumers buy from the cheaper seller (and if prices are equal, market is split). If one firm undercuts the other by a tiny amount (P = 40 + ε for the high-price firm and the other at P = 40), the undercutting firm would capture Q = 280 − P units at price P, yielding profit per unit of (P − MC) = ε and total profit ε × Q. However, as ε approaches 0, profits approach zero, and there is an incentive for the undercutting firm to keep dropping price toward MC to secure the entire market, making any price above MC unstable in a simultaneous-move game.

Now, at P = MC = 40, consider profits: each unit sold yields zero margin, so if both firms price at 40, the total market quantity Q = 280 − 40 = 240 is split evenly, giving each firm 120 units and profits of zero. This is consistent with zero fixed costs and zero profits at the Bertrand equilibrium with identical costs.

If either firm tries to price below 40, it would sell at a loss on every unit, which cannot be a best response given the other firm can price at 40 and capture the market at zero or positive profits. Thus P < 40 cannot be an equilibrium.

Therefore, the only stable Bertrand equilibrium in this setup is at P = 40, with each firm earning zero profit and sharing the market when prices are equal, or with one firm capturing the market if it undercuts by a negligible amount—which is prevented in equilibrium by the incentive structure at MC.

Putting these ideas together, the equilibrium price in this market is driven down to the common marginal cost, which is 40.

ECON_104B_001_25S Lecture Quiz #6

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