Consider a homogeneous good Cournot duopoly with linear inverse demand curve P(Q) = a - bQ. Suppose each firm i has constant marginal and average cost of production, ci.
(a) Derive the (Cournot) Nash equilibrium for all possible configurations of c1 and c2.
(b) Display a diagram in (c1,c2) space that indicates the cost combinations for which firm 2 will choose not to compete. Interpret the equation describing the boundary between the regions where firm 2 does and does not compete.