Suppose that demand for a product is Q = 1200 - 4P and supply is Q = - 240 + 2P. Furthermore, suppose that the marginal external damage of this product is $12 per unit. How many more units of this product will the free market produce than is socially optimal? Calculate the deadweight loss associated with the externality.

Answer: 16 units more than social optimum.

DWL = dead weight loss = (1/2) * (Q * - Q°) 12 = 96

Explanation:

Q=1200 - 4P and Q=-240 + 2P

In a free market quantity demand = quantity supplied

1200 - 4P = - 240 + 2P

P = 240

Sub P

Q * = 240

Socially optimal quantity is

Marginal social benefit (MSC) = marginal social cost (MSC), including external damage = MEC

MPC = marginal private cost = inverse of supply function

MPC = (1/2) * Q + 120

MEC=12

MSC = (MPC + MEC) = (1/2) Q + 120 + 12

MSC = MPB where MPB is marginal private benefit = inverse of demand functn

MPB = 300 - (1/4) Q

(1/2) Q + 132 = 300 - (1/4) Q

Q° = 224

Difference btw Q * & Q° = 16 units more than social optimum.

DWL = dead weight loss = (1/2) * (Q * - Q°) 12 = 96