Consider a duopoly with a demand curve given by P = a -bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition).

a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent.

Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts.

Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved.

How would the graphical analysis in part a change if Firm A had a fixed cost of production?