Consider a market with demand P (Q) = 100 Q. Sup- pose that firms compete by set

Question

Consider a market with demand P (Q) = 100 Q. Sup- pose that firms compete by setting prices in a Bertrand duopoly. Assume the following:

firms can only set prices in full dollars.

if you are indifferent between more than one price,

you always set the lowest price.

(a) Write out the reaction function for each firm (this should tell what price one firm should set for all prices that the other firm could set between 0 and ).

(b) If MC1 = 50 and MC2 = 50, what price does each firm set in the Bertrand equilibrium.

4. Consider a market with demand P(Q) = 100 – Q. Sup- pose that firms compete by setting prices in a Bertrand duopoly. Assume the following: • firms can only set prices in full dollars. • if you are indifferent between more than one price, you always set the lowest price. (a) Write out the reaction function for each firm (this should tell what price one firm should set for all prices that the other firm could set between 0 and w). (b) If MCG = 50 and MC2 = 50, what price does each firm set in the Bertrand equilibrium. (C) If MC = 50 and MC2 = 40, what price does each firm set in the Bertrand equilibrium.

Explanation / Answer

A) price of any firm should be 1 less than its rival price and price shoyld be atleast MC

B) P=50 will be the bertrand solution

C)firm 1 will set price =50 whereas firm 2 will set the price=49 and gets the profit of 9*51=459

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