<p>In <a href="https://economics.stackexchange.com/a/1728/61"><strong>this post</strong></a>, we find that the optimal monopoly price can be written as</p>

<p><span class="math-container">$$P^* =  \frac {|\eta|}{|\eta|-1} MC $$</span></p>

<p>where <span class="math-container">$\eta$</span> is the elasticity of demand with respect to price, and so optimal price will necessarily be at a point where <span class="math-container">$\eta$</span> is higher than unity in absolute terms.</p>

<p>From this one can deduce some unambiguous and some ambiguous scenarios when the demand schedule shifts outwards, e.g.</p>

<p><strong>SCENARIO A:</strong> constant price elasticity of demand, convex costs: <span class="math-container">$\implies$</span> Price and quantity will increase.</p>

<p><strong>SCENARIO B:</strong> constant price elasticity of demand, linear costs: <span class="math-container">$\implies$</span> Price will stay put, quantity will increase.</p>

<p>The floor is yours. </p>

<p><strong>PS:</strong> Note that to have constant price elasticity of demand, the demand function will necessarily be non-linear.</p>

CC BY-SA 4.0
2019-12-02T15:05:45.447Z
2019-12-02T17:27:36.723Z
2019-12-02T17:27:36.723Z
Alecos Papadopoulos
<p>Supposing that demand for a product in a monopolised market has grown, is it possible that equilibrium price will go down?</p>

<p>In most cases we simply draw curves D, MR, MC and make conclusions. I usually deal with linear demand and constant marginal costs, so nothing interesting. </p>

<p>It is naturally to say that the monopolist will increase the price to gain profit, even for inferior goods this seems true.</p>

CC BY-SA 4.0
2019-12-02T08:05:00.473Z
In the case of a nonlinear demand, indeed, the new marginal revenue can be below its former value, and total production and price can decrease.
Bertrand
<monopoly>
Will the monopolist inevitably increase the price if demand grows?
Dahn
# Will the monopolist inevitably increase the price if demand grows?

(Asked by: username_0 on 2019-12-02)

Supposing that demand for a product in a monopolised market has grown, is it possible that equilibrium price will go down?

In most cases we simply draw curves D, MR, MC and make conclusions. I usually deal with linear demand and constant marginal costs, so nothing interesting.

It is naturally to say that the monopolist will increase the price to gain profit, even for inferior goods this seems true.

**Tags:** monopoly
> **Comments:**
> **username_1**: In the case of a nonlinear demand, indeed, the new marginal revenue can be below its former value, and total production and price can decrease.  

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## 1 answers

### Answer by username_2 on 2019-12-02. Score: 3

In [**this post**](https://economics.stackexchange.com/a/1728/61), we find that the optimal monopoly price can be written as

$$P^\* = \frac {|\eta|}{|\eta|-1} MC $$

where $\eta$ is the elasticity of demand with respect to price, and so optimal price will necessarily be at a point where $\eta$ is higher than unity in absolute terms.

From this one can deduce some unambiguous and some ambiguous scenarios when the demand schedule shifts outwards, e.g.

**SCENARIO A:** constant price elasticity of demand, convex costs: $\implies$ Price and quantity will increase.

**SCENARIO B:** constant price elasticity of demand, linear costs: $\implies$ Price will stay put, quantity will increase.

The floor is yours.

**PS:** Note that to have constant price elasticity of demand, the demand function will necessarily be non-linear.


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