# 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? Commented Apr 19, 2015 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. Commented Apr 19, 2015 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). Commented Apr 19, 2015 at 13:17
• You are very welcome. If you have any questions regarding my "answer" just ask :-) Commented Apr 19, 2015 at 13:42

Try to think about what the the optimal level of production is supposed to be. What should it maximize? The revenue?

What you have calculated is the revenue maximizing level of production but maybe you wanted to find a level of production that maximizes something different?