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(QM) = 10,000-10QM 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) = 10,000-10QA-10QB 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: TCA(QA) = 5000QA TCB(QB) = 5000QB 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 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?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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(QM) = 10,000-10QM

Qis 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) = 10,000-10QA-10QB

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:

TCA(QA) = 5000QA

TCB(QB) = 5000QB

  1. Using the demand function and the cost functions above, what is firm A’s profit function?
  1. 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)

 

  1. Using the demand function and the cost functions above, what is firm B’s profit function?
  1. 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)

 

  1. Using the best response functions you calculated in the previous question, calculate the Nash Equilibrium in this game.
  2. 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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