7. Bertrand duopolists, Firm 1
7. Bertrand duopolists, Firm 1 and Firm 2, face inverse marketdemand P= 50-Q. and both have marginal cost, MC=$20. Theequilibrium output this market will be: a) 15 b) 20 c) 30 d) 40
Answer:
As they are Bertrand duopolists, this means that both willcompete in setting a price.
Now, If Firm 1 charges price > 20, then Firm 2 will chargeprice just lesser than 20 and thus will take all the market demand.Firm 1 will not charge price lesser than 20 as it will result in aloss as (MC = 20 and MC cannot be greater than P).
Now If Firm 1 charges price= 20, then Firm 2 will also chargeprice = 20 and thus both will get equal share of market.
Now, If Firm 2 charges price > 20, then Firm 1 will chargeprice just lesser than 20 and thus will take all the market demand.Firm 2 will not charge price lesser than 20 as it will result in aloss as (MC = 20 and MC cannot be greater than P).
Now If Firm 2 charges price= 20, then Firm 1 will also chargeprice = 20 and thus both will get equal share of market.
Hence, Both Firm will charge price = 40(This is what we calledBertrand Nash equilibrium).
So we have P = 20 => 20 = 50 – Q
=> Q = 30
Hence, the correct answer is (c) 30
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