<p>This is not a Bertrand equilibrium. Altough both firms set prices and they do so simultaneously, the products are not perfect substitutes because the travel distance differs for most consumers.</p>

<p>What this seems to be is the second stage of a <a href="https://www.jstor.org/stable/2224214" rel="nofollow noreferrer">Hotelling model</a>. The usual assumptions are that a continuum of buyers are spread out uniformly along the line and that every buyer's reservation price is very high compared to the transportation cost, so in equilibrium all buyers will be served. The total quantity of buyers may be scaled to one for simplicity.</p>

<p>Given these assumptions you can derive the demand function each firm faces.</p>

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2018-05-09T12:33:09.923Z
2018-05-09T12:33:09.923Z
Giskard
<p>Two cell phone companies A and V are located at the extremes of a line of
length <strong>one</strong> and transportation cost <strong>t = 4</strong>. Consider an initial situation where both firms offer a generic phone that consumers value the same (except obviously
for the transportation cost.) Marginal cost is <strong>zero</strong>.</p>

<p><strong>*N = 800</strong> denote the total population,
show that profits for each firm will be <strong>1600</strong></p>

<p>How do I interpret the demand function for this example?</p>

<microeconomics><game-theory>
Finding Bertrand equilibrium with no demand function explicitly given
EconDude
# Finding Bertrand equilibrium with no demand function explicitly given

(Asked by: username_0 on 2018-05-09)

Two cell phone companies A and V are located at the extremes of a line of
length **one** and transportation cost **t = 4**. Consider an initial situation where both firms offer a generic phone that consumers value the same (except obviously
for the transportation cost.) Marginal cost is **zero**.

**\*N = 800** denote the total population,
show that profits for each firm will be **1600**

How do I interpret the demand function for this example?

**Tags:** microeconomics, game-theory

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## 1 answers

### Answer by username_1 on 2018-05-09. Score: 1

This is not a Bertrand equilibrium. Altough both firms set prices and they do so simultaneously, the products are not perfect substitutes because the travel distance differs for most consumers.

What this seems to be is the second stage of a [Hotelling model](https://www.jstor.org/stable/2224214). The usual assumptions are that a continuum of buyers are spread out uniformly along the line and that every buyer's reservation price is very high compared to the transportation cost, so in equilibrium all buyers will be served. The total quantity of buyers may be scaled to one for simplicity.

Given these assumptions you can derive the demand function each firm faces.


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