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?
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?
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
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?
- 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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