Why is AC = MC in the monopoly?
Suppose the marginal cost is constant and equal to $c$, that fixed costs are $K&gt;0$, 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 $AC=(K+qc)/q&gt;c=MC$. Thus, when profits are maximized we have $AC&gt;MC=R'(q)$. 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.