Consider two firms competing a la Cournot, and facing linear inverse demand p(Q) = 100 - Q, where Q = q1 + 92 denotes aggregate output. For simplicity, assume that firms face a common marginal cost of production c = 10.a) b) d) Unrepeated game. Find the equilibrium output each rm produces when competing a la Cournot (that is, when they simultaneously and independently choose their output levels) in the unrepeated version of the game (that is, when rms interact only once). In addition, nd the prots that each rm earns in equilibrium. Repeated game - Collusion. Assume now that the CEOs from both companies meet to discuss a collusive agreement that would increase their prots. Set up the maximization problem that rms solve when maximizing their joint prots (that is, the sum of prots for both rms). Find the output level that each rm should select to maximize joint prots. In addition, nd the prots that each rm obtains in this collusive agreement. Repeated game Permanent punishment. Consider a grim-trigger strategy in which every rm starts colluding in period 1, and it keeps doing so as long as both rms colluded in the past. Otherwise, every rm deviates to the Cournot equilibrium thereafter (that is, every rm produces the Nash equilibrium of the unrepeated game found in part a forever). In words, this says that the punishment of deviating from the collusive agreement is permanent, since rms never return to the collusive outcome. For which discount factors this grim-trigger strategy can be sustained as the SPNE of the inf'mitely-repeated game? Repeated game Temporary punishment. Consider now a \"modied\" grim-trigger strategy. Like in the grim-trigger strategy of part (0), every rm starts colluding in period 1, and it keeps doing so as long as both rms colluded in the past. However, if a deviation is detected by either rm, every rm deviates to the Cournot equilibrium during only 1 period, and then every rm returns to cooperation (producing the collusive output). Intuitively, this implies that the punishment of deviating from the collusive agreement is now temporary (rather than permanent) since it lasts only one period. For which discount factors this \"modied\" grim-trigger strategy can be sustained as the SPNE of the innitely-repeated game? Consider again the temporary punishment in part (d), but assume now that it lasts for two periods. How are your results from part (d) affected? Interpret. Consider again the temporary punishment in part ((1), but assume now that it lasts for three periods. How are your results 'om part (d) affected? Interpret