Simultaneous vs. Sequential 1\\-'Iove Quantity Setting Games Consider a market with inverse aggregate delnand "U 2 'f 3" PfQ] = I Q 1 Q ( o 0 if Q 2 35 All sellers can produce at a constant marginal cost of M'C'm} = 1|] for all :1 } 0. (:1 . If the market is perfectly competitive, what is the equilibrium price and quantity? . If the market is controlled by a monopolist, what is the equilibrium price and quantity? Compute the Consumers\" Surplus, Producer's Surplus, and Deadweight Loss. . Now suppose two rms compete as \"CournotFNash Duopolists", simultaneously and independently choosing their output quantities. What is the cournot Equilibrium price, quantity, surplus, and dead weight loss? [HINT: Follow these steps: (1) Write down the payoff functions, i.e. the rms" prots as functions of output quantities :11 and em, (2} Find the best responses for both players, (3} Solve for all Nash Equili bria] . Suppose the same two rms act as \"Stackelberg\" (leaderfollower) quantitysetters. That is, they choose their output quantities sequentially with rm 1 choosing an output level rst. Then rm 2 observes rm 1's output choice :1; before choosing its own output level q. Use Backward Induction to nd the subgaJneperfect Nash Equilibrium of the Stackelberg game. What is the equilibrium price and quantity? Compute the Consumers' surplus, the producer's surplus for each rm, and the deadweight loss. Is there a \"rstpmover advantage\" in this game? . Illustrate the various equilibria (pricequantity pairs} in one gure with the (inverse) demand and marginal cost curves