Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand...

 

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Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand is Q(p). Firm with the lowest price serves the entire market. They split the demand equally if prices are equal. Each firm i = 1, 2 has constant unit of production (i.e., marginal cost) ci > 0 where cl > c2,and so the firms marginal costs are different. a) Show that pl = p2 = cl is not a Nash equilibrium. b) Show that there is no Nash equilibrium where the firms pick the same price (i.e., pl = p2). c) Is there a Nash equilibrium of this game? d) Suppose now that the prices are discrete, and so firm is price must be a multiple of a cent: That is, pi e {0.01, 0.02, 0.03, ., 0.01n, .} where n is some positive integer. What is the Nash equilibrium now? Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand is Q(p). Firm with the lowest price serves the entire market. They split the demand equally if prices are equal. Each firm i = 1, 2 has constant unit of production (i.e., marginal cost) ci > 0 where cl > c2,and so the firms marginal costs are different. a) Show that pl = p2 = cl is not a Nash equilibrium. b) Show that there is no Nash equilibrium where the firms pick the same price (i.e., pl = p2). c) Is there a Nash equilibrium of this game? d) Suppose now that the prices are discrete, and so firm is price must be a multiple of a cent: That is, pi e {0.01, 0.02, 0.03, ., 0.01n, .} where n is some positive integer. What is the Nash equilibrium now?

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A C1C2 is not a Nash equilibrium because if firm2 reduces price by a sm... View the full answer