Two firms, A and B, are engaged in a Cornet quantity competition game. They choo

Question

Two firms, A and B, are engaged in a Cornet quantity competition game. They choose their respective quantities, q_A for firm A and q_B for firm B, simultaneously and independently. It is known that firm A's reaction function is given by q_A = 20-q_B and firm B's reaction function is q_B = 16-q_A/2 Answer the following questions based on the above description: (a) If firm B produces at a level of 4, firm A's best response is (b) If firm A produces at a level of 8, firm B's best response is (c) The Nash equilibrium quantity choices are:

Explanation / Answer

(a) If firm B produces at a level of 4, firm A's best response is [(20 - 4) / 2] = 8

(b) If firm A produces at a level of 8, firm A's best response is [(16 - 8) / 2] = 4

(c) Nash Equilibrium quantity choices are defined as follows-

Substituting one equation in the other we obtain qA = [20 - {(16 - qA) / 2}] / 2 = 8.

Now substitute qA in qB we will get qB = (16 - 8) / 2 = 4.

So the Nash Equilibrium Choices are (qA , qB) = (8 , 4)

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