Question

The demand for cigarettes is given by P = 100−0.2Q. Cigarettes are manufactured at a constant marginal cost of 10 and sold in a competitive market. If cigarettes generate a marginal external cost of 0.1Q, what is the socially optimal level of cigarettes?

Answer 1

Social optimal level of quantity is the quantity at which MSB = MSC

MSB = Marginal Social benefit and as here there is no positive externality so, MSB = Marginal Private Benefit(MPB).

As, MPB = P => MSB = P = 100 - 0.2Q

MSC = MPC + MEC where MSC = Marginal Social cost, MPC = Marginal Private cost(or Marginal Cost) and MEC = Marginal External cost => MSC = 10 + 0.1Q

So, MSB = MSC => 100 - 0.2Q = 10 + 0.1Q => Q = 300

Hence, the socially optimal level of cigarettes(Q) = 300