# Why is AC = MC in the monopoly?

Using the Microeconomic Theory Basic Principles and Extensions, Nicholson, W. and Snyder, C., I've reached to the point where Monopoly and Imperfect Competition is discussed (Chapter 14 and 15 to be more specific).

It's kind of easy to deduce that Marginal Cost equals Marginal Revenue at the point of profit maximization. In the imperfect competition in the long-run (or in the perfect competition) no one can surpass the point where price equals marginal cost equals average cost, because above this point firms will have negative economic profit.

The main question is why (and not only the graphic explanation please) the firm will choose AC (average cost) = MC (marginal cost)?

Graphically, it looks like the slope of the Demand Curve makes this choice the best one, but why in imperfect competition is this choice not pursued by the firm instead of the Supply Curve?

• AC = MC is not generally true in monopoly. Are you looking at a special case? – Pburg Jun 26 '15 at 13:58
• For the long run isn't true? And also for Natural Monopoly – dekio Jun 26 '15 at 14:33

Suppose the marginal cost is constant and equal to $c$, that fixed costs are $K>0$, and that revenue is $R(q)$. You seem to understand that MR=MC must be true for profits to be maximized: $R'(q)=c$. We also know that average costs are given by $AC=(K+qc)/q$. But note that $AC=(K+qc)/q>c=MC$. Thus, when profits are maximized we have $AC>MC=R'(q)$. So it is not true that $AC=MC$ when profits are maximized in this example. We can conclude that $AC=MC=R'(q)$ holds only in certain special cases.