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Question #31847
Given p=100-4q
Mc=4
1. socially optimal price
2. Monopoly price
3. Loss in consumer price
If P = 100 - 4Q, Qd = 25 - 0.25P.
1. Social optimal price will be in point, where MC = D, so P = 100 - 4Q = $4, Q = 25 - 0.25*4 = 24 units. 2. Monopoly price will be higher and will be in point with quantity where MR = MC. MR = TR&#039; = (P*Q)&#039; = (100 - 4Q)*Q)&#039; = (100Q - 4Q^2)&#039; = 100 - 8Q MR = MC 100 - 8Q = 4 8Q = 96 Q = 12 units So, the monopoly price = 100 - 4*12 =$52
3. Loss in price will be: 52 - 4 = $48 4. The deadweight loss will be 0.5*48*(24 - 12) =$288

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