<blockquote>
<p>the monopolist only produces at the elastic region ... But ...  the monopolist may incur losses even at the elastic region</p>
</blockquote>
<p>There is no contradiction here. If I like chocolate cake it does not mean that I like all cake; if the profit maximizing quantity is in the elastic region it does not mean that all quantities in the elastic region are profit maximizing or even profitable.</p>
<p><strong>An example</strong></p>
<p>Let <span class="math-container">$D(p) = 3 - p$</span> so <span class="math-container">$MR(q) = 3 - 2q$</span>, and let
<span class="math-container">$$
C(q) = \frac{q^{100}}{100}
$$</span>
so <span class="math-container">$MC(q) = q^{99}$</span>.</p>
<p>The profit maximizing quantity is <span class="math-container">$q = 1$</span>, at this point <span class="math-container">$MR(1) = MC(1)$</span>. The elastic region is <span class="math-container">$[0,1.5]$</span>, but at <span class="math-container">$q=1.1$</span> the monopolist is already making heavy losses, around <span class="math-container">$-135.716$</span> according to this C++ program.</p>
<pre><code>#include &lt;iostream&gt;
using namespace std;
int main() 
{
  float q = 1.1;
  double result = 1;
  for (int i = 0; i&lt;100; i++)
  {
     result *= q;
  }
  result = (3-q)*q - result/100;
  cout &lt;&lt; result;
  return 0;
}
</code></pre>

CC BY-SA 4.0
2024-07-29T07:10:30.603Z
Yes. Was thinking about a similar model but wasn't sure, Thanks
rhyme
CC BY-SA 4.0
2024-07-29T06:41:21.550Z
2024-07-29T06:41:21.550Z
Giskard
<p>Considering a linear demand curve, we conclude that the monopolist only produces at the elastic region of the demand curve (given, he doesn't discriminate prices). But if the cost is a function of quantity produced and increases rapidly due to increase in Q, then the monopolist may incur losses even at the elastic region, wouldn't he?</p>

CC BY-SA 4.0
2024-07-29T06:28:50.950Z
The question in the title is different from the question in the body.
Giskard
<microeconomics><monopoly><profit-maximization>
Is It necessary for a monopoly firm to be profitable at the elastic region of the demand curve?
rhyme
# Is It necessary for a monopoly firm to be profitable at the elastic region of the demand curve?

(Asked by: username_0 on 2024-07-29)

Considering a linear demand curve, we conclude that the monopolist only produces at the elastic region of the demand curve (given, he doesn't discriminate prices). But if the cost is a function of quantity produced and increases rapidly due to increase in Q, then the monopolist may incur losses even at the elastic region, wouldn't he?

**Tags:** microeconomics, monopoly, profit-maximization
> **Comments:**
> **username_1**: The question in the title is different from the question in the body.  

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## 1 answers

### Answer by username_1 on 2024-07-29. Score: 1 | Accepted answer

the monopolist only produces at the elastic region ... But ...  the monopolist may incur losses even at the elastic region

There is no contradiction here. If I like chocolate cake it does not mean that I like all cake; if the profit maximizing quantity is in the elastic region it does not mean that all quantities in the elastic region are profit maximizing or even profitable.
An example
Let $D(p) = 3 - p$ so $MR(q) = 3 - 2q$, and let
$$
C(q) = \frac{q^{100}}{100}
$$
so $MC(q) = q^{99}$.
The profit maximizing quantity is $q = 1$, at this point $MR(1) = MC(1)$. The elastic region is $[0,1.5]$, but at $q=1.1$ the monopolist is already making heavy losses, around $-135.716$ according to this C++ program.
#include 
using namespace std;
int main() 
{
  float q = 1.1;
  double result = 1;
  for (int i = 0; i<100; i++)
  {
     result *= q;
  }
  result = (3-q)*q - result/100;
  cout << result;
  return 0;
}

> **Comments:**
> **username_0**: Yes. Was thinking about a similar model but wasn't sure, Thanks  

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