Question

7. Bertrand duopolists, Firm 1 and Firm 2, face inverse market demand P= 50-Q. and both have marginal cost, MC=$20. The equilibrium output this market will be: a) 15 b) 20 c) 30 d) 40

Answer 1

As they are Bertrand duopolists, this means that both will compete in setting a price.

Now, If Firm 1 charges price > 20, then Firm 2 will charge price 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 a loss as (MC = 20 and MC cannot be greater than P).

Now If Firm 1 charges price= 20, then Firm 2 will also charge price = 20 and thus both will get equal share of market.

Now, If Firm 2 charges price > 20, then Firm 1 will charge price 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 a loss as (MC = 20 and MC cannot be greater than P).

Now If Firm 2 charges price= 20, then Firm 1 will also charge price = 20 and thus both will get equal share of market.

Hence, Both Firm will charge price = 40(This is what we called Bertrand Nash equilibrium).

So we have P = 20 => 20 = 50 - Q

=> Q = 30

Hence, the correct answer is (c) 30