<p>A1. This assumption is not &quot;intuitively deducible&quot; 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.</p>
<p>A2. This is plain wrong. The reference given on Wikipedia does not actually say this.</p>
<p>Generally, Wikipedia is not an authoritative source for economic theory.</p>

CC BY-SA 4.0
2023-10-30T08:04:06.547Z
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
CC BY-SA 4.0
2023-10-30T08:11:51.727Z
In that case (with symmetric costs), it does not matter. The assumption is harmless there.
Michael Greinecker
CC BY-SA 4.0
2023-10-30T12:10:08.763Z
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
CC BY-SA 4.0
2023-10-30T18:44:43.003Z
We don't. But neither the consumers (who get the samegood for the same price) or the fitms (who make zero profit) care.
Michael Greinecker
CC BY-SA 4.0
2023-10-29T22:00:21.947Z
2023-10-29T22:00:21.947Z
Michael Greinecker
<p>Q1. Under the lists of <a href="https://en.wikipedia.org/wiki/Bertrand_competition#Underlying_assumptions_of_Bertrand_competition" rel="nofollow noreferrer">assumptions</a> 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:<br />
<strong>If the price set by the firms is the same,
<span class="math-container">$p_1=p_2=...=p$</span>, they will serve the market equally, <span class="math-container">$\frac{p}{n}$</span>.</strong></p>
<p>What's the intuition behind it, is there something that is stopping the consumers to buy (or firm to supply) <span class="math-container">$1/4^{th}$</span> from firm 1 and <span class="math-container">$3/4^{th}$</span> from firm 2 (in case of duopoly). Is there a formal proof of the above or some source to understand it.</p>
<p>Q2: The <span class="math-container">$2^{nd}$</span> assumption is : <strong>the market demand function <span class="math-container">$Q=D(p)$</span>, where Q is the summation of quantity produced by firms, is continuous and downward sloping with <span class="math-container">$D'(p)=0$</span>.</strong><br />
In this how did derivative of Demand function became <span class="math-container">$0$</span>.</p>

<oligopoly>
Underlying assumptions of Bertrand competition
hr08
# Underlying assumptions of Bertrand competition

(Asked by: username_0 on 2023-10-29)

Q1. Under the lists of [assumptions](https://en.wikipedia.org/wiki/Bertrand_competition#Underlying_assumptions_of_Bertrand_competition) 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 $0$.

**Tags:** oligopoly


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## 1 answers

### Answer by username_1 on 2023-10-29. Score: 4 | Accepted answer

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.

> **Comments:**
> **username_0**: 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.  
> **username_1**: In that case (with symmetric costs), it does not matter. The assumption is harmless there.  
> **username_0**: 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.  
> **username_1**: We don't. But neither the consumers (who get the samegood for the same price) or the fitms (who make zero profit) care.  

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