Question

A monopolist's inverse demand function is P= 150 – 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2: a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q1 + Q2 = Q.) MR(Q) = 150-C6 Q4-06 Q2 b. Determine the profit-maximizing level of output for each facility. Output for facility 1: C * Output for facility 2: * c. Determine the profit-maximizing price. $ Explanation

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Answer 1

Pago no a) MR = IR do TR = PA Q = (150-3Q) Q 150Q - 302 MR: d (1999 - 30%) = 150- 3(2) de MR = 150-6Q where MR = 150-6Q,-6Qq Q = Q,+ Qz, so MR = MC. Profit max. level is where For firm 1 :- MR = 150-6Q, - 6Q2 22 MC = EQ, 150 -69, -6Q₂ = 6Q, 150-60,- 6Q, z 6Q2 150- 12Q1 = 692- Qg > 150 - 1201 - 25 - 207 - Q. for firm 2i) ou 150-6Q,- 6Q₂ = 202 150 -6Q2-20₂ 6Q, (25-8 Q2 = Q, Now Put Q, in Q., we get DELTA DELTA My NoteBook

Q2 = 25-100 49 30, - - 25 +8Q 25 = 89, -3Q, Q = 25-2(5) = 15 - Q2 =15 a p = 150-3Q P = 150-3/5+15) = 150-3(20)