# Underlying assumptions of Bertrand competition

Q1. Under the lists of assumptions for Bertrand model it is mentioned in last that the following are intuitively deducible when considering the law of demand of firms' competition in the market:
If the price set by the firms is the same, $$p_1=p_2=...=p$$, they will serve the market equally, $$\frac{p}{n}$$.

What's the intuition behind it, is there something that is stopping the consumers to buy (or firm to supply) $$1/4^{th}$$ from firm 1 and $$3/4^{th}$$ from firm 2 (in case of duopoly). Is there a formal proof of the above or some source to understand it.

Q2: The $$2^{nd}$$ assumption is : the market demand function $$Q=D(p)$$, where Q is the summation of quantity produced by firms, is continuous and downward sloping with $$D'(p)=0$$.
In this how did derivative of Demand function became $$0$$.

A1. This assumption is not "intuitively deducible" and does not hold in versions of the model in which (a continuum of) consumers are explicit players. Indeed, if you allow different firms to have different (constant) marginal costs, there will be no equilibrium in pure strategies when the market is split as under this assumption.

A2. This is plain wrong. The reference given on Wikipedia does not actually say this.

Generally, Wikipedia is not an authoritative source for economic theory.

• So in classic Bertrand modelling (Duopoly market) it is fair to assume that the expectation of each firm's market share is half of the full market share and nothing else.
– hr08
Commented Oct 30, 2023 at 8:04
• In that case (with symmetric costs), it does not matter. The assumption is harmless there. Commented Oct 30, 2023 at 8:11
• So is it safe to remove that assumption, If we do not make the assumption in classic model (with symmetric cost) then how do we know what portion of market share each firm will serve at same price.
– hr08
Commented Oct 30, 2023 at 12:10
• We don't. But neither the consumers (who get the samegood for the same price) or the fitms (who make zero profit) care. Commented Oct 30, 2023 at 18:44