I know that Bertrand Oligopolies will charge a price equal to marginal cost. But if marginal cost is, say,
2Q or 4Q^2
(i.e. not constant) then how does one determine where, on the MC curve, the equilibrium lies?
If there are 5 Bertrand firms, then do I just find where MC intersects the Demand Curve and divide the quantity by 5, and then set price equal to MC at that quantity?
Conceptually this sounds reasonable, but I'm not sure that this is correct. If these firms charge this price then it seems to me that one of them will under produce to charge a lower price until (if MC is 2Q for instance) price and quantity = 0. So that no firms will produce because if they do then someone will charge a cent less till we reach 0 again.