Assume that two companies $($A and B$)$ are duopolists who produce identical products. Demand for the products is given by the following linear demand function:

$P=200-Q_A-Q_B$

where $Q_A$ and $Q_B$ are the quantities sold by the respective firms and $P$ is the selling price. Total cost functions for the two companies are

Assume that the firms form a cartel to act as a monopolist and maximize total industry profits $($sum of Firm A and Firm B profits$).$ In such a case, Company A will produce units and sell at

Similarly, Company B will produce units and sell at

At the optimum output levels, Company A earns total profits of and Company B earns total profits of $-$ Therefore, the total industry profits are

At the optimum output levels, the marginal cost of Company $A$ is and the marginal cost of Company $B$ is

The following table shows the long$-$run equilibrium if the firms act independently, as in the Cournot model $($i$.$e$.,$ each firm assumes that the other firm's output will not change$).$