1. Firm A and Firm B sell identical goods As in the example in the mini-lecture, total market demand for the book is: Q(P) = 1,000 - 0.1P The inverse demand function is therefore P(QM) = 10,000 - 100M OM 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(QAQ=) = 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) = 3000QBe. Using the best response functions you calculated in the previous question, calculate the Nash Equilibrium in this game. f. 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 g. 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 h. Does firm B produce more or less than when both had the same costs? Why do you think this is? EXPLAIN 1 . Does firm A produce more or less than it did when both had the same higher costs Note that firm A's costs have not changed between the two cases. Why do you think this is? EXPLAINa. (3 points) Using the demand function and the cost functions above, what is firm A's profit function. Profits=total revenue-total cost PQ-TC Qa(10()-10Qa-10Qb)-5000Qa =10000Qa-10Qa*-10QaQb-5000Qa =5000Qa-10Qa3-10QQb ......this is firm A profit function b. (3 points) Using the profit function above and assuming that firm B produces Q, calculate what firm A's best response is to firm B's decision to produce Q. Note: Firm A's best response should be a function of QB FOC with respect to Qa: =5000-20Qa-10Qb=0 -5000-10Qb=20Qa divide both sides by 20 5000/20-10Qb/20=Qa 250-0.5Qb=Qa.......... .best reaction function c. (3 points) Using the demand function and the cost functions above, what is firm B's profit function Firm B profit function= revenue-costs =Qb(10000-10Qa-10Qb)-3000Qb =10000Qb-10QaQb-10Qb'-3000Qb =7000Qb-10QaQb-10Qb' this is the profit function d. (3 points) 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 FOC=7000-10Qa-20Qb=0 7000-10Qa=20Qb divide all through by 20 7000/20-10Qa/20=Qk 350-0.5Qa=Qk .this is the best reaction function for B