The inverse market demand for a homogeneous good is given by p = 1 – Q,...

The inverse market demand for a homogeneous good is given by p = 1 – Q, where p denotes the price and Q denotes the total quantity of the good. The good is supplied by three quantity-setting firms (Firm 1, Firm 2, and Firm 3) competing à la Cournot, each producing at a constant marginal cost equal to c > 0. a) Derive the best reply of Firm 1. b) Compute the Cournot-Nash equilibrium quantity and profits of Firm 1. c) Show that the Cournot-Nash equilibrium price increases as c increases. Assume now that Firm 1 is given a cost advantage. Its cost of production is half of that of its competitors. d) Show that Firm 1 makes higher profits than its competitors.

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Expert Solution

(a) The best reply of Firm1,look at its payoff as a function of its output,given output of firm 2 . Any price greater than p2 is a best reply to p2:B1(p2)= {p1:p1>p2}. A price between p2 and c is a best reply

(b) The Cournot model of oligopoly assumes that rival firm produce a homogeneous product,and each attempts to maximize profits by choosing how much to produce.all firm choose output simultaneously. The resulting equilibrium is a Nash equilibrium in quantities, called a Cournot (Nash) equilibrium.

Rahul Sunny answered 1 year ago

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