Will a monopoly firm ever operate on the inelastic portion of its demand curve?

We had this question for homework. So my answer was:

"A monopoly would never operate on the inelastic portion of its demand curve." That so far is correct. However, the next part of the question explaining why is apparently wrong. I don't know why.

I said: "The reason is because if it did operate on the inelastic portion of its demand curve, then increasing price would increase revenue while decreasing quantity. Decreasing quantity would reduce costs. As a result, revenue go up and costs go down and the firm must not be profit maximizing."
Please can anyone explain to me why this is wrong? It makes perfect sense to me, but my teacher diagrees and says it's wrong. What would be the correct answer?
Thanks in advace

Hi there!

Okay erms firstly, its not that a monopoly would never produce on the inelastic portion of its demand curve. It is that a profit maximizing monopoly would not produce on the inelastic portion.

THis is because, when the demand curve is inelastic, a rise in quantity will lead to a relatively larger fall in price, and hence total revenue will actually fall.

I don't quite understand your answer, but it seems confused because for one, decreasing quantity will not necessarily reduce costs. You do not know how the cost curve is positioned.

Hope this helped. Quote me if you want clarification

The reason monopolies always operate where demand is elastic is because when demand is inelastic the firms will just continue to increase prices as their revenue will increase. So therefore it will only stop increasing prices where demand becomes elastic.

thanks (:, but you said: (italics)
why? I mean I don't get it. Quantity increases so prices decrease by a LARGE amount?

I thought an increase in price does not mean revenue increases, as revenue= price x quantity, so an increase in price would just lead to a fall in quantity... maybe im wrong

heya. You've got to get back to your demand-supply basics. When the demand curve is inelastic, a rise in quantity means a proportionally larger fall in price. THus revenue falls. THis is opposed to an elastic demand curve where a large rise in quantity means a small fall in price. Thus revenue rises.

Does that help any? Hope it does!

woops! guess after one year you forget simple things like that.
Okay let's take an inelastic good like salt for example.
NO MATTER what the PRICE is, people would still BUY it because it is a necessasity!
So my question is, WHY would producers LOWER the price, and as you said "larger fall in price" when they can charge it at a higer price? I mean quantity demanded would stay the same since it is an inelastic good!
thank you in advance

The reason monopolies always operate where demand is elastic is because when demand is inelastic the firms will just continue to increase prices as their revenue will increase. So therefore it will only stop increasing prices where demand becomes elastic.

It all depends on the elasticity of the good and the degree of elasticity. In your example of a necessary good such as salt, the elasticity will be 0 (considering people HAVE to buy the product whatever the price) which means that any change in price will not lead to any change in quantity demanded. This would mean that the producer can increase the price infinitely without having a decrease or increase in the quantity demanded. But in real life, no good is PERFECTLY INELASTIC in nature and thus there will always be a decrease in the quantity demanded (even if by a very minute amount) and thus there will be a point when the firm will reach 0 amount of quantity demanded after continually increasing the price. If quantity demanded becomes 0 then the revenue earned will become 0 as (TR=P×Q where P=price and Q=quantity demanded and TR=total revenue earned by the firm). Thus a firm will not want to operate in such a situation and to maximize it's profit, it will want to operate on a market where it's produced good has an elastic nature which will lead to a greater degree of responsiveness of the quantity demanded with respect to price.

You're 9 years late, but thank you