#19. Questions 18-21 rely on the following prompt: Firm A and Firm B compete in

Question

#19. Questions 18-21 rely on the following prompt: Firm A and Firm B compete in the sale of a product with market inverse demand given by P(Q) = 150-Q, where Q is market output, and Q-qA + qB (qA-Firm A's output, q,-Firm B's output). Firm A's Total Cost function is given by TCAGa) = 104a and Firm B's is given by TCB(qb) = 104a. 18. Find the value of Q when Firms A and B Cournot compete to maximize profits (i.e. when they simultaneously determine profit maximizing output). 19. At what price will Firms A and B sell their output?

Explanation / Answer

18 -

let K1 be the profit of firm A, also p(q1+q2) = 150-(Qa+Qb)

now K1 = (150-Qa-Qb)(Qa)-10Qa

now d(K1)/dQa = 150-2qa-qb-10 = 0

so 2qa+qb = 140

symmetrically

qa+2qb = 140

solving the two equations together

qa = qb = 140/3 = 46.67 approx

19- now price is 150-(280/3) = 170/3 = 56.67

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