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Cournot Competition Suppose there are two identical firms engaged in quantity

Cournot Competition Suppose there are two identical firms engaged in quantity competition. Every period each firm decides how much to produce, and the game is repeated forever Demand is P = 1 - Q where Q 2 and marginal cast of production is zero. Suppose firms use the same discount factor 6, (a) Compute the Cournot STATIC equilibrium first (ie., quantities, price, and profits). (b) Find the Monopoly equilibrium (Le., quant ity, price, and profit). (c) Suppose now that firms collude and each of them uses the following strategy: In the first period produces the monopoly quantity for each i 1,2. In subsequent periods, if the previous period equilibrium was (q )Le. if there is cooperation, then produce the monopoly quantity; otherwise punish the other firm by producing the Cournot quantity forever This temporal strategy characterizes the "DYNAMIC" aspect of the oligopoly model Show that if the discount rate is large enough, collusion can be an equilibrium in the infinitely repeated game. Hint: you need to find the minimum discount rate that makes collusion possible. (d) Suppose the two firms merge and form a monopoly. Compute the price, quantity, and profit of the monopoly. Hint: you can start by writing the monopoly's profit, derive the first order condition, solve for the optimal monopoly quantity,, and then find the monopoly's price and profit. (e) Suppose now that firms collude and each of them uses the following strategy In the first period each firm sets p50 for each i 1,2. (so both can make profit) In subsequent periods, if the previous period equilibrium was (p =50. p2 = 50) then they set p =50, p2 =50 again otherwise they set the Bertrand equilibrium price. Show that when the discount rate is large enough, the collusion agreement above can be an equilibeium in the infinitely repeated Bertrand game. Hint: you need to find the minimum discount rate that makes the above collusion possible.

Feb 01 2020 View more View Less

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