Answer to Question #31847 in Microeconomics for mulugeta adane

Question #31847
Given p=100-4q Mc=4 1. socially optimal price 2. Monopoly price 3. Loss in consumer price 4. Deadweight loss
1
Expert's answer
2013-06-17T09:19:05-0400
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' = (P*Q)' = (100 - 4Q)*Q)' = (100Q - 4Q^2)' = 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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