# what is the optimum level of production?

The demand function of a monopolist is $q = 12 - p$ where $p$ is the price. Using the total cost and total revenue I was trying to calculate the optimal (short term) level of production.

I tried to solve it using the total revenue $r = p x$. Then I calculated the marginal revenue (the derivative of total revenue) and set it to $0$. Then I got $p = 6$ and $x = 6$.

However, I never used the cost function, what did I do wrong?

• To get an answer you should explain a little bit what you have done. How did you get the price and quantity? – The Almighty Bob Apr 19 '15 at 13:00
• I calculated the marginal revenue (the derivative of total revenue) and I have given 0 to it and I found x = 6. and then I replaced x in the price function and I found p = 6. The function of revenue is r = p*x. P is the price and the x is the quantity. – Lioneds Apr 19 '15 at 13:08
• @user2437789 OK, that explains it. I edited the question so everyone understands what you did there, I hope you don't mind (and I captured the essence of your question). – The Almighty Bob Apr 19 '15 at 13:17
• You are very welcome. If you have any questions regarding my "answer" just ask :-) – The Almighty Bob Apr 19 '15 at 13:42