Question

Suppose the demand for electricity in some large community is given by the following demand function P = 1200 – 0.4Q. If the supply function is given by P = 400 + 0.6Q. These are both private market valuations. Electricity generation is given for both functions in thousands of kilowatts, and involves the emission of sulfur dioxide into the atmosphere which has been linked to the prevalence of acid rain in the area. The marginal external damage associated with the harmful effects to the community from acid rain is $50 per thousand kilowatts generated.

Assume a Pigovian tax is implemented to resolve this problem, discuss the amount of the tax and how it will correct the externality. (2 points)

Demonstrate using the analytics of consumer, producer and total surplus, why the market allocation is inefficient and how the correct policy implemented achieves efficiency (i.e. provide a welfare economics numerical explanation for why the correctly computed solution is efficient) (4 points)

Answer 1

Solution:-

(a)Demand: P = 1,200 - 0.4Q

Supply: P = 400 + 0.6Q

Marginal external cost (MEC) = 50Q

In private equilibrium, Demand price equals Supply price.

1,200 - 0.4Q = 400 + 0.6Q

Q = 800

P = 1,200 - (0.4 x 800) = 1,200 - 320 = $880

The acid rain, being a negative externality, will increase marginal cost and supply curve will shift leftward. New supply function becomes:

P - 50 = 400 + 0.6Q

P = 450 + 0.6Q

Equating with demand,

1,200 - 0.4Q = 450 + 0.6Q

Q = 750

P = 1,200 - (0.4 x 750) = 1,200 - 300 = $900

When Q = 750 (Socially efficient quantity), Private supply: P = 400 + (0.6 x 750) = 400 + 450 = $850

Therefore, Pigouvian tax per unit = $(900 - 850) = $50

Total tax = $50 x 750 = $37,500

The Pigouvian tax will internalize the negative externality by lowering market quantity and increasing market price.

(b).Market allocation in this case will lead to a negative externality equal to E as depicted in the diagram. Thus, pigouvian taxes should be imposed to eliminate such negative externality. This will decrease the amount of output of output produced to 762 units . The taxes will decrease the consumer surplus, producer surplus and will lead to revenue generation for the government and also benefit to the external agents.

The net impact of all this will lead to gain of E. Thus, a negative effect of externality can be eliminated by imposing taxes.