Question

Calculations on Externalities

1. The demand for (or marginal benefit of) travel on a road is given by MB = 300 - V, where V is traffic volume, measured by the number of vehicles entering the road per hour (there are no internal entrances or exits). The marginal private (or average) cost of travel on the road is MPC = V, while the marginal external cost of travel on the road is MEC = 0.5 x V.

(a) From the society's point of view, the optimum number of cars on this road is:__________

(b) The deadweight loss due to congestion externalities, i.e. excessive car driving, is calculated as:________

Answer 1

a)

The optimal number of car on this road is where,

Marginal social cost = Marginal benefit (1)

Marginal benefit = 300 - V

Marginal social cost = Marginal private cost + Marginal external cost = V + 0.5 V = 1.5V

From (1)

300 - V = 1.5V

300 = 2.5V

V = 120

The optimal number of cars on this road is 120.

b)

The point C represents the market equilibrium where the marginal private benefit is equal to marginal cost.

So the deadweight loss is the area ABC, which is the area of the triangle ABC

= 1/2 x height x base

The height is the gap between marginal social cost and marginal private cost which is marginal external cost at 150.

Height = 0.5 x V = 0.5 X 150 = 75

Base = 150 - 120 = 30

Dead weight loss = 1/2 x 30 x 75 = 1125.