Firm A and Firm B sell identical goodsThe total market demand is:Q(P) = 1,000-1.0PThe inverse demand function is therefore: P(QM) = 10,000-10QMQM is total market production (i.e., combined production of firm’s A and B). That is: QM = QA + QBAs a result, the inverse demand curve for each firm is: P(QA,QB) = 10,000-10QA-10QBThe difference between this example and the example in class is that the two firms have different costs. Firm A has the same cost as in class, but firm B has a different cost function:TCA(QA) = 5000QATCB(QB) = 5000QBUsing the demand function and the cost functions above, what is firm A’s profit function?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) Using the demand function and the cost functions above, what is firm B’s profit function?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) Using the best response functions you calculated in the previous question, calculate the Nash Equilibrium in this game.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

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Answered: Firm A and Firm B sell identical goods…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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Firm A and Firm B sell identical goods

The total market demand is:Q(P) = 1,000-1.0P

The inverse demand function is therefore: P(Q_M) = 10,000-10Q_M

Q_Mis total market production (i.e., combined production of firm’s A and B). That is: Q_M = Q_A + Q_B

As a result, the inverse demand curve for each firm is: P(Q_A,Q_B) = 10,000-10Q_A-10Q_B

The difference between this example and the example in class is that the two firms have different costs. Firm A has the same cost as in class, but firm B has a different cost function:

TC_A(Q_A) = 5000Q_A

TC_B(Q_B) = 5000Q_B

Using the demand function and the cost functions above, what is firm A’s profit function?

Using the profit function above and assuming that firm B produces Q_B, calculate what firm A’s best response is to firm B’s decision to produce Q_B. (Note: Firm A’s best response should be a function of Q_B)

Using the demand function and the cost functions above, what is firm B’s profit function?

Using the profit function above and assuming that firm A produces Q_A, calculate what firm B’s best response is to firm A’s decision to produce Q_A. (Note: Firm B’s best response should be a function of Q_A)

Using the best response functions you calculated in the previous question, calculate the Nash Equilibrium in this game.
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

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