2. More on Bertrand There are two firms in the market, A and B, producing the same output. Market demand is given by y = 17 – p for p < 17 and 0 otherwise. Each firm faces a cost function c(y) = y. The firms get to simultaneously choose their prices, pA and pB. Whichever firm, say i, sets the lower price faces the entire market demand, 17 – pi while the firm with the higher price faces 0 demand. If the two prices are equal PA = PB = q then each firm faces half the market demand, namely 17-9. a) Given that each firm wishes to maximize their profit, what would be the Nash Equilibrium profile of prices of this game? Now suppose, much to the delight of the consumers, Firm A announces that if Firm B charges a price of q, which is lower than firm A's price then it would beat that price by charging max{q, 1}. Firm B announces that if Firm A charges a price of s, which is lower than firm B's price then Firm B would charge max{s, 1}. The laws of the land force the firms to act according to their announcements. So for a given set of initial prices (pA, PB) the firms end up charging prices (PA, PB) according to their announced price beating schemes. The cost functions and market demand is the same as before. Only now the firm with the lower pi gets the entire market demand. If both the effective prices are the same then the demand gets divided as before. b) Find a Nash Equilibrium price profile for this game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Transcribed Image Text:2. More on Bertrand There are two firms in the market, A and B, producing the same output. Market demand is given by y = 17 – p for p < 17 and 0 otherwise. Each firm faces a cost function c(y) simultaneously choose their prices, pA and pB. Whichever firm, say i, sets the lower price faces the entire = y. The firms get to market demand, 17 – p; while the firm with the higher price faces 0 demand. If the two prices are equal PA = PB = q then each firm faces half the market demand, namely 9. a) Given that each firm wishes to maximize their profit, what would be the Nash Equilibrium profile of prices of this game? Now suppose, much to the delight of the consumers, Firm A announces that if Firm B charges a price of q, which is lower than firm A's price then it would beat that price by charging max{q, 1}. Firm B announces that if Firm A charges a price of which is lower than firm B's price then Firm B would charge max{s, 1}. The laws of the land force the firms to act according to their announcements. So for a given set of initial prices (pA, PB) the firms end up charging prices (PA, PB) according to their announced price beating schemes. The cost functions and market demand is the same as before. Only now the firm with the lower p; gets the entire market demand. If both the effective prices are the same then the demand gets divided as before. b) Find a Nash Equilibrium price profile for this game.

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