1. (6 points). Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods. Total market demand for the good is: Q(P)=35,10045P The inverse demand function is therefore P(QM)=780451Q=7800.02222QM QM is total market production (i.e., combined production of firm's A and B. That is: QM=QA+QB As a result, the inverse demand curve for each firm is: P(QA,QB)=780451QA451QB=7800.02222QA0.02222QB Unlike the example in class, the two firms have different costs. TCA(QA)=400QATCB(QB)=260QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces QB, calculate what firm A's best response is to firm B's decision to produce QB. Note: Firm A's best response should be a function of QB c. Using the demand function and the cost functions above, what is firm B's profit function d. Using the profit function above and assuming that firm A produces QA, calculate what firm B's best response is to firm A's decision to produce QA. Note: Firm B's best response should be a function of QA 2. (6 points). Nash Equilibrium in a Cournot Oligopoly a. Using the best response functions you calculated in the previous question, calculate how much each firm produces at the Nash Equilibrium for this game. b. Using the QA and QB you calculated in part a, calculate the market price. 3. (6 points). Nash Equilibrium in a Cournot Oligopoly a. Does firm A or firm B produce more in this case? Does this result make sense to you? Why do you think this is (in words!)? EXPLAIN 4. (6 points). Nash Equilibrium in a Cournot Oligopoly a. Use the profit functions you calculated earlier to calculate profits for both firms in this example? Which firm has higher profits? Why do you think this is? EXPLAIN 1. (6 points). Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods. Total market demand for the good is: Q(P)=35,10045P The inverse demand function is therefore P(QM)=780451Q=7800.02222QM QM is total market production (i.e., combined production of firm's A and B. That is: QM=QA+QB As a result, the inverse demand curve for each firm is: P(QA,QB)=780451QA451QB=7800.02222QA0.02222QB Unlike the example in class, the two firms have different costs. TCA(QA)=400QATCB(QB)=260QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces QB, calculate what firm A's best response is to firm B's decision to produce QB. Note: Firm A's best response should be a function of QB c. Using the demand function and the cost functions above, what is firm B's profit function d. Using the profit function above and assuming that firm A produces QA, calculate what firm B's best response is to firm A's decision to produce QA. Note: Firm B's best response should be a function of QA 2. (6 points). Nash Equilibrium in a Cournot Oligopoly a. Using the best response functions you calculated in the previous question, calculate how much each firm produces at the Nash Equilibrium for this game. b. Using the QA and QB you calculated in part a, calculate the market price. 3. (6 points). Nash Equilibrium in a Cournot Oligopoly a. Does firm A or firm B produce more in this case? Does this result make sense to you? Why do you think this is (in words!)? EXPLAIN 4. (6 points). Nash Equilibrium in a Cournot Oligopoly a. Use the profit functions you calculated earlier to calculate profits for both firms in this example? Which firm has higher profits? Why do you think this is? EXPLAIN
