What is Coase’s Theorem?

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Coase’s theorem states that, in a situation where there is a negative externality, putting a price on the externality will have the same effect on behavior, regardless of which party bears the cost. Applies only if there are no transaction costs. The theorem is important in areas such as environmental policy because it suggests that there are several ways to deal with negative externalities such as pollution. Ronald Coase’s proposal of the theorem in his 1960 paper The Problem of Social Cost led the economic community to re-evaluate its reliance on quantitative regulation and Pigouvian taxes as the only tools to reduce negative externalities.

To understand Coase’s theorem, it may be better to illustrate with an example. Consider two college roommates, Bob and Carl. Bob is in a tough class and stays up late studying in their class. The bright light Bob uses to read gives Carl a headache and prevents him from sleeping.

If Bob uses the light for x hours at night, he gets 24x – x 2 utility units of the highest grade he gets in the class. It costs him 14x units – each hour he is awake deals 14 units of damage, an amount that represents his sleep deprivation, the actual cost of running the light, and other factors. As long as Bob gets more utility out of an hour of light use than it costs him, he won’t turn off the light.

The value he gets for each additional hour of light is called the marginal value and is found by taking the derivative of the utility function. Bob’s marginal utility is 24-2x. This value decreases with each additional hour of light, and it will only keep the light on until the marginal value of an hour of light is 14, which is after five hours.

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Carl also has a utility function, but for him light has a negative effect. If the light stays on for x hours, he takes 6x units of damage. He can handle this in two ways.

One possibility is that Carl tells Bob that he doesn’t like the light and asks Bob to compensate him for the inconvenience of having it on. If Bob agrees, he will do extra tasks that will give Carl 6 units of utility per hour he uses light, while Bob will lose 6 units per hour of light for doing them. This increases the cost to Bob of each hour of light from 14 to 20. Its marginal value now equals the marginal cost after two hours, so he uses two hours of light.

The second possibility is that Carl decides that if he wants darkness to sleep, he must give up something to get it. He finds that the maximum number of hours Bob could have the light on per day is 12 hours, which is where Bob’s marginal utility is zero, and offers to pay him 6 units of utility for every hour of those 12 hours that the light is not on. If Bob uses x hours of light, he now gets 6 * (12 – x) additional units of utility. Your new utility function is 24x – x 2 + 6 * (12 – x) = 72 + 18x – x 2 , so your marginal utility is given by 18 – 2x. It still incurs a cost of 14 per hour, so it uses two hours of light.

From a purely mathematical point of view, it doesn’t matter whether Bob pays Carl compensation for his discomfort or Carl pays Bob to turn off the light. This is the insight of Coase’s theorem. He broke with traditional theories of externality politics, which held that the only ways to contain negative externalities were to make laws against them or to force the creator of the externality to pay all the costs associated with it.

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In some cases, Coase’s theorem does not apply because of transaction costs. For example, if the light came from outside and Carl had to organize a group of students to ask the university to turn it off, the effort he made to organize would be a transaction cost. He would be willing to offer less to turn off the light, so the effect on the externality would be less than if the university paid each student.

When there are no transaction costs, Coase’s theorem presents new possibilities and also new problems. The implemented policy makes a statement about the group’s values. If Bob pays Carl, that means Carl has the right to the dark, but if Carl pays Bob, that means Bob has the right to continue studying. The prioritization of conflicting rights is a concern, although as Coase’s theorem shows, the numerical result is the same.

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