Please answer me in detail. Thank you.
P = 120 - 2Q
(a)
Total revenue (TR) = P x Q = 120Q - 2Q^{2}
Marginal revenue (MR) = dTR/dQ = 120 - 4Q
MC1 = 20 + 2Q1, therefore Q1 = (MC1 - 20) / 2 = 0.5MC1 - 10
MC2 = 10 + 5Q2, therefore Q2 = (MC2 - 10) / 5 = 0.2MC2 - 2
As Q = Q1 + Q2,
Q = 0.5MC1 - 10 + 0.2MC2 - 2
Q = 0.5MC1 + 0.2MC2 - 12
Equating MC1 and MC2 as MC,
Q = 0.5MC + 0.2MC - 12
Q = 0.7MC - 12
0.7MC = Q + 12
MC = (Q + 12) / 0.7
Profit-maximizing condition is: MR = MC.
120 - 4Q = (Q + 12) / 0.7
84 - 2.8Q = Q + 12
3.8Q = 72
Q = 18.95
P = 120 - (2 x 18.95) = 120 - 37.9 = 82.1
(b)
MC = (Q + 12) / 0.7 = (18.95 + 12) / 0.7 = 30.95 / 0.7 = 44.21
Q1 = 0.5MC - 10 = (0.5 x 44.21) - 10 = 22.11 - 10 = 12.11
Q2 = 0.2MC - 2 = (0.2 x 44.21) - 2 = 8.84 - 2 = 6.84
Please answer me in detail. Thank you. Question 9 Suppose that a monopolist faces a demand curve given by P 120-2Q. A m...
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