Problem 4: Externalities and the Coase Theorem. A frat house throws loud parties

Question

Problem 4: Externalities and the Coase Theorem. A frat house throws loud parties. It has two neighbors. On one side is professor 1 who hates the parties since he can not sleep. The damage to him is 500. On the other side is professor 2 who enjoys listening to the music. Her value for listening to the music is 200. The frat house is willing to pay at most 1000 to be able to keep partying. Professor 1 or the frat house can install soundproof windows at their houses, with costs of 350 and 300, respectively. If the frat house builds the windows in its house, neither professors will be able to hear the music anymore.

(a) What outcome maximizes the economic efficiency? Should soundproof windows be installed? If so, where should they be installed?

(b) Assume that a court decides that professor 1 has the right to not be bothered by the music. So without a deal, the frat house should either stop partying or build windows. What should it do? Now what if the three parties can get together to make a deal? Will there be a deal? If so, provide an example of the deal that is acceptable to all groups.

(c) Assume that the court decides that the frat house has the right to produce noise. Without a possibility of a deal, what would happen? If the groups can negotiate, will they be able to make a deal?

Explanation / Answer

Externalities refers to a situation where an act by an individualor a group affect the other party , either positively or negatively without its impact being reflected in the market prices. For example , planting a tree by individual do good to the entire society ( positive externality) or smoking by a person can have adverse effect on others ( negative externality).

The coarse theorem states that if trade in externality is possible and its transactions costs is low,bargaining will lead to a Pareto optimum situation (that is one is made better off without making anyone worse off).

In the example that has been stated in the question there is a party that plays loud music. This is creating both positive and negative externality. The professor who loves music is receiving positive externality and the professor who is not able to sleep and hates music is the part of negative externality. According to the coarse theorem if the party who plays music is able to compensate the other party without making anyone worse off , he may continue with the loud music.

The above compensation scheme is described as follows:

Damage to professor 1= 500

Value to professor 2= 200

Compensation frat is ready to make =1000

Cost of installing sound proof wall in the frat home itself=300

Cost of installing sound proof wall in professor 1 home=350

a)The output that maximises the efficiency will be a situation of installing a sound proof wall in professor 1 house. It is so because it will cost 350 which the frat is ready to pay. Though the cost of installing a sound proof wall in his own home costs him only 300. However if he does so the professor 2 will not be able to receive any music and made worse off. So the rational decision would be to install a sound proof system in professor 1 house until the cost of compensation is less or equal to what the compensator is willing to pay.

b) If by the court of law , the professor 1 should not be disturbed, the frat would continue playing music but after installing a sound proof system at his home. It is so because the frat can enjoy the music without harming anyone. Professor 2 will not be receiving any music ( positive externality) but he isnt either made worse off ( negative externality). However if all the three party come together to make a mutual decision , there can be two deals that they can end up with . First that professor 2 can come and enjoy the music at the party home. The other that professor 1 is made a maximum (1000) compensation which is more than the loss (500) to convince him to install sound proof system.

c)If the court allows the frat house to play music than in that case there is two possibility. First the loud music will be played without making any compensation to professor 1 , as he cant do anything because its the decision of the court. The other can be a scheme of compensation where the frat house is convinced to pay a minimum compensation(350) to allow professor 1 to install a sound proof system.

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