# Will there always be excess profit in the Cournot model equilibrium/monopoly

So I'm studying market structures for the end of term, and I'm a bit confused about excess profits.

From what I can see, excess profits occur when the demand curve intersects the AC curve - the MR=MC quantity leads to a price which is above AC, and thus the firm earns excess/economic profits (as in monopoly). If the demand curve were tangent to the AC curve (as in long-run monopolistic competition), there are no excess profits, because the firm produces at AC.

My question is: is there any reason why the demand curve faced by a monopolist isn't just tangent to the AC curve? Or is it that this is the only situation where the monopolist doesn't earn economic profits? See the diagrams below.

Finally, what does this mean for a firm in a Cournot duopoly equilibrium, with no collusion? Does the competition from its rival leave it with a similar result as the firm in monopolistic competition with the demand curve tangent to the AC curve, or does it enjoy excess profits?

• Hi Evan! Can you please define more precisely what you mean by "excess profits"? Positive profits? Dec 7, 2021 at 15:02
• "is there any reason why the demand curve faced by a monopolist isn't just tangent to the AC curve?" ... is there any reason why it should generally be tangential to the AC curve? Dec 7, 2021 at 15:04
• @Giskard Thanks, I mean supernoral or economic profits - as in, any profit earned by the firm above the minimum level of profit it would require to stay in business. Also, I don't see any reason why the demand curve should generally be tangential to the AC curve - my question is essentially whether this means it's possible to have a monopolist who doesn't earn excess profits
– Evan
Dec 7, 2021 at 15:07
• Is this different from positive economic profit? Dec 7, 2021 at 15:07
• No, that's not different - I mean positive economic profit
– Evan
Dec 7, 2021 at 15:10

## 1 Answer

If the AC curve is assumed convex and demand is assumed linear, as in the figure, then an AC curve tangent to the demand line means that AC > P at all quantities but one (where AC = P). Thus the monopolist makes zero profits in his optimum. However, for cost and demand parameters drawn from a continuous distribution this is a probability-zero event. You'd rather expect that either AC > P everywhere (and the monopolist would have left the market) or AC < P somewhere (the standard example). Analogous considerations hold for a Cournot duopoly.

• Yes, when the number of firms is an integer, $AC=P$ is unlikely to hold, and the long-run equilibrium is characterized by $AC(y_N)<p_N$ for all active firms (of the economy with $N$ firms), and $AC(y_{N+1})>p_{N+1}$ if $N+1$ firms were active, Dec 9, 2021 at 11:50
• Thanks for your answer! I'm just a bit confused by what you mean by "cost and demand parameters drawn from a continuous distribution".
– Evan
Dec 10, 2021 at 15:58
• @Evan, I just meant that for "randomly chosen" parameter values this case will "never" happen, sort of. Dec 10, 2021 at 18:40