Consider a market for a homogenous good where the relationship between price and sales is indicated by p = 14 - q. There are no fixed costs of production, but there is a variable cost of 2 per unit produced.
(i) Find the equilibrium outcome under monopoly.
(ii) Find the Nash equilibrium under Cournot duopoly competition (i.e., quantity is the strategic variable).
(iii) Find the Nash equilibrium under Bertrand duopoly competition (i.e., price is the strategic variable).
(iv) Stay with the game you analyzed in the previous problem (iii). What strategies in that game are weakly dominated?
(v) Stay with the game you analyzed in the previous problems (iii) and (iv), but now suppose that game is the stage game of a infinitely repeated game where each firm's discount factor is δ such that 0<δ<1. Assuming an appropriate value of δ, describe a subgame perfect equilibrium in trigger-strategies such that along the path of play both players always choose the monopoly price. Derive an exact bound on δ for such an equilibrium to exist.