<p>A monopolist is selling its products in the UK and the EU. The demand for the monopolist's product is Q(UK) = 42 - P and Q(EU) = 16-4P. The cost function of the monopolist is C(Q) = Q^2 where Q = Q(UK) = Q(EU). Monopolist cannot discriminate between markets and must choose a uniform price. What is the optimal uniform price for the monopolist?</p>
<p>I have written the price function as the demand function. P(UK) = -Q + 42 and P(EU) = -0.25Q + 4.</p>
<p>I get that we have to maximise the profit function but since there are two profit functions to maximise here how I do find the <strong>universal</strong> optimal price?</p>

CC BY-SA 4.0
2022-10-31T15:12:58.873Z
You define the profit of the firm as a function of either prices and quantities. Then you maximize that function.
Michael Greinecker
CC BY-SA 4.0
2022-11-01T02:37:48.507Z
Another hint: Add the two profits and use the condition that $P_\text{UK}=P_\text{EU}$ (uniform price across UK and EU).
Herr K.
CC BY-SA 4.0
2022-11-03T19:52:39.953Z
Note that if you get this right with these hints, you can answer your own question.
BKay
CC BY-SA 4.0
2022-11-14T19:11:36.077Z
I was trying to answer your question but I don't know if what you mean is that the EU and UK prices have to both be equal, while the EU and UK quantites both have to be equal at the same time. Also, in the Cost function, is that Q equal to both EU and UK market quantites or the total quantity (which would be = 2Q(EU) = 2Q(UK) if both quantities have to be equal)
Nicolas Torres
<microeconomics><monopoly>
How do I find the optimal uniform price for a monopoly?
econnoob
# How do I find the optimal uniform price for a monopoly?

(Asked by: username_0 on 2022-10-31)

A monopolist is selling its products in the UK and the EU. The demand for the monopolist's product is Q(UK) = 42 - P and Q(EU) = 16-4P. The cost function of the monopolist is C(Q) = Q^2 where Q = Q(UK) = Q(EU). Monopolist cannot discriminate between markets and must choose a uniform price. What is the optimal uniform price for the monopolist?

I have written the price function as the demand function. P(UK) = -Q + 42 and P(EU) = -0.25Q + 4.

I get that we have to maximise the profit function but since there are two profit functions to maximise here how I do find the **universal** optimal price?

**Tags:** microeconomics, monopoly

> **Comments:**
> **username_1**: You define the profit of the firm as a function of either prices and quantities. Then you maximize that function.  
> **username_2**: Another hint: Add the two profits and use the condition that $P_\text{UK}=P_\text{EU}$ (uniform price across UK and EU).  
> **username_3**: Note that if you get this right with these hints, you can answer your own question.  
> **username_4**: I was trying to answer your question but I don't know if what you mean is that the EU and UK prices have to both be equal, while the EU and UK quantites both have to be equal at the same time. Also, in the Cost function, is that Q equal to both EU and UK market quantites or the total quantity (which would be = 2Q(EU) = 2Q(UK) if both quantities have to be equal)  

---

## 0 answers

