Question

Suppose we have a pulp mill that releasing effluent into an adjacent river. A property owner subdivides and builds waterfront homes on land downstream from the pulp mill. The people who purchased the new homes soon realize they are being negatively affected by pollution from the mill. The new home owners band together and decide to take the pulp mill to court. The pulp mill's marginal cost of production is MCp=0.5Q, where Q is the amount of output the mill produces. The damage from the effluent released from a unit of production is given by MCE=5. The pulp mill sells its output for the prevailing market price of $20 a unit.

a) Suppose the court refuses the request for an injunction. At what level does the pulp mill produce at? Show that this level of production is not economically efficient.
b) Assuming an agreement is possible between the two groups, demonstrate that an agreement will make both groups better off. Show in a graph and calculate the range of possible total payments from the home owners to the mill that would achieve the economically efficient level of production by the pulp mill.

Answer 1

The pulp mill will produce 40 units if the court refuses an injunction, which is not economically efficient due to the pollution externality. An agreement to pay the mill for reducing its output could achieve the socially optimal level of 30 units. The total payments range that benefits both parties is between $0 and $150.

Step-by-step explanation:

When discussing the economic efficiency of a pulp mill's production in relation to pollution and its impact on downstream homeowners, we must consider both marginal cost (MC) of production and the marginal external cost (MCE) of pollution. In this case, the marginal cost of production is given by MCp=0.5Q and the MCE is a constant $5 per unit of production.

If the court refuses an injunction, the pulp mill will produce where its marginal cost equals the market price, as this is where it maximizes profit without considering the pollution externality.

The quantity (Q) produced is found by setting MCp equal to the market price, resulting in 0.5Q = $20, giving us Q = 40 units. However, this level is not economically efficient because it does not account for the external cost of pollution. The social marginal cost (SMC) is the sum of the MCp and the MCE, which becomes SMC = 0.5Q + 5. Economic efficiency is achieved where SMC equals the market price, which is 0.5Q + 5 = $20, solving for Q gives us 30 units. Thus, 40 units is not efficient, as it exceeds the socially optimal output level of 30 units due to the negative externality.

An agreement between the homeowners and the pulp mill can lead to both groups being better off by reaching the socially optimal level of production. A possible agreement could involve payments to the mill for reducing its output from the private optimum (40 units) to the socially optimum (30 units). The total amount of payments that can make both parties better off lies between $0 and $150, which is the cost the mill incurs from reducing the last 10 units of production. These payments internalize the external cost and lead to a reduction in production that aligns with the social optimum.

A graph would illustrate the initially rising MCp, the constant MCE, and the SMC, which is the vertical addition of MCp and MCE. The SMC curve intersects the market price at the economically efficient quantity (30 units), which is less than the quantity produced when ignoring the externality (40 units). The area between the SMC curve and the market price for the output reduction from 40 to 30 units would represent the range of possible payments that could be used to incentivize the mill to reduce pollution.