# How do I find the optimal uniform price for a monopoly?

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?

• You define the profit of the firm as a function of either prices and quantities. Then you maximize that function. Oct 31, 2022 at 15:12
• Another hint: Add the two profits and use the condition that $P_\text{UK}=P_\text{EU}$ (uniform price across UK and EU). Nov 1, 2022 at 2:37
• Note that if you get this right with these hints, you can answer your own question.
– BKay
Nov 3, 2022 at 19:52
• 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) Nov 14, 2022 at 19:11