Consider duopoly firms which produce homogeneous products and maximize its profits where demand function is linear and each firm has zero marginal cost.

Market demand is given by p=a-bq, total market output is q=q₁+q2,

cost function is ci=ai^.qi+d

(1)Solve outputs and profits under Bertrand, Cournot, and Stackelberg competitions, respectively.

(2)Consider a timing game where market structure is determined by the firms. That is, each firm chooses whether to produce outputs in period 1 or 2 at the same time. That is, if both firms choose either the same period or different period, then each firm can be either leader or follower in the game. Solve the equilibrium in this timing game of output productions.