# A Cournot question

I am confused that If the marginal costs of the two firms are different, is it still a Cournot model? I saw many examples that give a fixed marginal cost of the products.

Two firms with marginal costs of $$c_1$$ and $$c_2$$ competing in quantities where inverse demand is $$p=A-b(q_1+q_2)$$. Firms are maximizing: $$\max_{q_i} \; (A-b(q_1 + q_2))q_i - c_i q_i$$ Taking a derivative and solving you can find unique quantities, e.g. $$q_1 = \frac{A+2b(c_1 -A) - c_2}{4b^2 -1}$$