# Is It necessary for a monopoly firm to be profitable at the elastic region of the demand curve?

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?

• The question in the title is different from the question in the body. Commented Jul 29 at 6:28

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 <iostream>
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;
}

• Yes. Was thinking about a similar model but wasn't sure, Thanks Commented Jul 29 at 7:10