Question #31847

Given p=100-4q
Mc=4
1. socially optimal price
2. Monopoly price
3. Loss in consumer price
4. Deadweight loss

Expert's answer

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

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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