microeconomics -- Bertrand’s duopoly game with fixed costs-solving- plz help!!?
1. (Bertrand’s duopoly game with fixed costs) Consider Bertrand’s game in which the cost function of each firm i is given by ci(qi)=f+cqi for q>0, and ci(0)=0., where F is positive and less than the maximum of (p-c)(a-p)with respect to p. Note that the demand function is p=a-q where q=q1+q2 is the total output and a>0. Denote by P* the price P that satisfies (p-c)(a-p)=f and is less than the maximizer of (p-c)(a-p) Show that if firm 1 gets all the demand when both firms charge the same price, then (P*,P*)is a Nash equilibrium. Show also that no other pair of prices is a Nash equilibrium. (Hint: first consider cases in which the firms charge the same price, then cases in which they charge different prices.)
1. (Bertrand’s duopoly game with fixed costs) Consider Bertrand’s game in which the cost function of each firm i is given by ci(qi)=f+cqi for q>0, and ci(0)=0., where F is positive and less than the maximum of (p-c)(a-p)with respect to p. Note that the demand function is p=a-q where q=q1+q2 is the total output and a>0. Denote by P* the price P that satisfies (p-c)(a-p)=f and is less than the maximizer of (p-c)(a-p) Show that if firm 1 gets all the demand when both firms charge the same price, then (P*,P*)is a Nash equilibrium. Show also that no other pair of prices is a Nash equilibrium. (Hint: first consider cases in which the firms charge the same price, then cases in which they charge different prices.)