Question

Consider a market for electricity, where there is one electricity providor. Suppose demand (in megawatt hours) is given by Q=50−P and that the marginal private cost of generating electricity is $10 per megawatt hour ( P is in the same units). Suppose further that smoke is generated in the production of electricity in direct proportion to the amount of electricity generated. The health damage from the smoke is $15 per megawatt hour generated. a) On a graph, draw the demand and marginal revenue for this monopolist. Add in the marginal private cost of producing electricity, and the marginal social cost that incorporates the damage from pollution. b) If the monopolist was allowed to produce and set prices with no regulation, what would be the quantity and price? Label this quantity in the figure in a. c) What is the efficient quantity of electricity, taking into account pollution? Label this quantity in the figure in a. d) What would the output and price be if regulators imposed a Pigovian tax? Label this quantity in the figure in a. e) What is the change in deadweight loss when the regulator imposes the Pigovian tax? Make sure to take pollution into account when calculating the deadweight loss.

Answer 1

The graph should show the demand curve intersecting the marginal social cost curve to determine the socially efficient quantity of electricity. A monopolist would produce where marginal revenue equals marginal private cost, leading to a higher price and lower quantity than the socially efficient outcome. Imposing a Pigovian tax aligns the monopolist's production choice with the social optimum, reducing the deadweight loss.

Step-by-step explanation:

The question involves analyzing a market for electricity with a single provider, taking into account both the private costs and social costs associated with production, including pollution. To draw the necessary curves on a graph, we begin by plotting the demand curve, which is given by Q = 50 - P, and the marginal private cost, which is constant at $10 per megawatt hour. We also consider the marginal social cost, which is the sum of the marginal private cost and the external cost from pollution, totaling $25 per megawatt hour.

If the monopolist operates without regulation, it would produce where marginal revenue equals marginal private cost. The monopolist would set the price higher than the marginal cost to maximize profit, leading to quantity Qm and price Pm. The socially efficient quantity, quantity Qe, is determined where the marginal social cost equals demand, considering the external cost of pollution, which is lower than Qm.

If a Pigovian tax of $15 is imposed, equal to the external cost of pollution, it will shift the supply curve vertically upwards by the amount of the tax. This would lead to a new equilibrium, where the quantity produced and the price reflect the true social cost, resulting in quantity Qr with the Pigovian tax. Deadweight loss with the Pigovian tax is smaller compared to the unregulated scenario, as it corrects for the negative externality of pollution.