Question

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 1

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