Consider 2 airplane manufacturers that compete as Cournot duopolists in the market for commercial aircraft. Arrowing (firm A} has a cost function given by C(q) = EqA, whereas SkyTrain (firm 5) has a cost function given by C(qs) = qsz. The market demand function for commercial airliners is given by: Q = 240 3P where Q is the sum of the quantity of planes available for purchase. If we were to solve each firm's profit-maximization problem, treating the other firm's output level as fixed, we would nd the following best response (BR) functions: 1 312.1015) = 'Ll = 119 ills 1 33501.4) = '15 = 30 Ella a) If the two companies choose the quantities of trips supplied simultaneously, nd the Cournot equilibrium quantities supplied for each firm and the equilibrium price. What are each firm's profits earned? b) Suppose thatrm A has the opportunity to choose their quantity of trips first, so that they are a Stackelberg leader. Find the Nash Equilibrium to this game and calculate the prots that each firm would receive. 1:) Com pare prots from part (a) and part (b). Would firm A benet from moving rst? Does firm B benet from moving last? 2. Answer the following, assuming the firms in Question 2 above compete as Bertrand duopolists. a) What would you expect to be the price that would prevail in this market? Who will produce how much for the market? Explain intuitively. b) Would rm 2 want to initiate Bertrand competition? In other words, reect back on your answers in Question 2 and ask if rm 2 would want to leave the world of Cournot duopolv by initiating a price war? 3. Consider the market shares for the top 10 firms in each of the following three markets: bl Market 1: 11%, 9%, 8%, 8%, 6.5%, 5%, 5%, 4%, 4%, 3% Market 2: 46%, 43%, 4%, 2%, 2%, 1%, 0.5%, 0.5%, 0.5%, 0.5% Market 3: 91%, 1.5%, 1.5%, 1%, 1%, 1%, 1%, 1%, 0.5%, 0.5% Calculate the 1 rm, 4 rm, and 8 firm concentration ratios for each of the three markets. Calculate the HHI using the market shares of the top 10 firms in each ofthe three markets. Using your answers to part (a) and (b), characterize each market's structure. Explain which of the following tools you would need to think about optimal production in each setting: optimization, the analysis of market power, and game theory