1. Consider a duopoly market by two firms {1,2}. The market inverse demand function is given by 𝑃(𝑄) = 10 − 𝑄. Each firm

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1. Consider a duopoly market by two firms {1,2}. The marketinverse demand function is given by 𝑃(𝑄) = 10 − 𝑄. Eachfirm 𝑖 = 1,2 simultaneously determines itsquantity 𝑞𝑖. The marginal costs for firms are givenby 𝑐1 = 2 and 𝑐2 =4. (a) Consider monopoly markets of firm 𝑖 = 1,2.Derive the optimal quantity and the associated monopolist profitfor each firm. (b) Derive the Cournot Nash Equilibrium and theassociated profits. (c) Suppose that two firms need toconstruct a factory to produce. The fixed cost for construction isF=5. Consider the following game: at period 1, each firm determineswhether or not to construct decision of each other. At period 2,firms which constructed at period 1 determines the quantity(qi=0, if a firm does not construct). Derive the subgameperfect Nash Equilibrium and its outcome (equilibrium path) of thisgame.