Answer: See explanation
Explanation:
The magnitude of the deadweight loss resulting from the externality is shown below:
MC = 500 + 2Q
MEC = 40 + 2Q
Therefore, the Marginal social cost (MSC) will be:
= MC + MEC
= 500 + 2Q + 40 + 2Q
= 540 + 4Q
Since Demand: Q = 150,000 - 100P, we have to get a function for P which will be:
Q = 150,000 - 100P
100P = 150,000 - Q
P = (150,000 - Q)/100
P = 1,500 - 0.01Q
Total revenue, TR = P x Q
= (1,500 - 0.01Q) × Q
= 1500Q - 0.01Q²
Marginal revenue, MR will be:
= dTR / dQ
= 1,500 - 0.02Q
It should be noted that for when there's no externality, Equilibrium, MC must be equal to MR. Therefore,
1,500 - 0.02Q = 500 + 2Q
2Q + 0.02Q = 1500 - 500
2.02Q = 1,000
Q = 1000/2.02
Q = 495
P = 1,500 - (0.01 x 495)
= 1,500 - 4.95
= 1,495.05
When there's externality, Equilibrium will be:
MR = MSC
1,500 - 0.02Q = 540 + 4Q
4.02Q = 960
Q= 960/4.02
Q = 239
Therefore, P = 1,500 - (0.01 x 239)
= 1,500 - 2.39
= 1,497.61
Then, we will calculate the deadweight loss which will be:
= 1/2 x Difference in price x Difference in quantity
= 1/2 x (1,497.61 - 1,495.05) x (495 - 239)
= 1/2 x 2.56 x 256
= 327.68
