1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). a. Assume firm A chooses quantity first. Frim B observes this choice and then chooses its own quantity. What is Frim B's profit as a function of QA and QB? b. Firm B has MRB = 220 – 2QB – QA. What is firm B’s best response to an arbitrary QA selected by firm A? c. Given that firm A expects firm B’s best response, what is firm A’s profit as a function of QA? (Hint: the only unknown variable in the profit function should be QA)
1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB).
a. Assume firm A chooses quantity first. Frim B observes this choice and then chooses its own quantity. What is Frim B's profit as a function of QA and QB?
b. Firm B has MRB = 220 – 2QB – QA. What is firm B’s best response to an arbitrary QA selected by firm A?
c. Given that firm A expects firm B’s best response, what is firm A’s profit as a function of QA? (Hint: the only unknown variable in the profit function should be QA)
d. Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game?
e. What is the
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