Music or Noise? Applying Economic Intuition to Roommate Relations

 

Real-Life Scenario

Living in close quarters with roommates can lead to some unexpected challenges. When it comes to living with roommates, harmony is key. But what happens when one person's idea of harmony clashes with another's?

Meet Adam and Ben, roommates sharing a flat. Adam enjoys hosting parties and often blasts music loudly in the common room, while Ben prefers peace and quiet for studying and relaxation.

It's a classic roommate dilemma:

how to balance personal preferences while respecting each other's space.

 

Analysing Economic Principles

	In this scenario, we could turn to economics for some insight first. In the dispute between Adam and Ben, we witness a classic case of market failure. Picture this – in a perfect world, everyone gets what they want without any problems. But in reality, sometimes things don't work out so smoothly. That's what we call market failure. It occurs when the allocation of goods and services by a free market is not efficient, leading to a failure to achieve Pareto optimality.
	Adam's enjoyment of loud music imposes a cost on Ben, who experiences discomfort and disturbance as a result. In Ben's eyes, the music becomes a negative externality, impacting his well-being without his consent. This externality leads to an inefficient allocation of resources, violating the principle of competitive market efficiency. In a competitive market, resources should be allocated efficiently to maximize overall welfare. However, in this scenario, the presence of externalities disrupts this efficiency, as Adam's overconsumption of music infringes upon Ben's enjoyment of the shared space. Can money help?

     

After all, economists have a knack for putting a price tag on just about anything, from the value of a human life to the cost of being law-abiding. So how can economics help shed light on Adam and Ben's situation?

We try to use the Edgeworth box in a pure exchange economy to see how Adam and Ben reaches an agreement (final equilibrium state).

Analysing Preferences

In this simplified model, we can represent Adam and Ben's preferences on a graph, with money on the x-axis and sound on the y-axis. We consider only two commodities: money (represented by the amount of currency) and sound (measured in decibels). The money can be regarded as expenditure on other goods.

For example, Adam, feeling remorseful about the disturbance his music causes Ben, seeks to compensate for the inconvenience. One approach Adam considers is to spend money to alleviate Ben's discomfort. He could invite Ben to dinner at a nice restaurant or purchase snacks and treats for them to enjoy together.

Another option on the table is for Adam and Ben to negotiate a price for Adam's music consumption. This negotiation process involves determining a monetary value that Adam would pay Ben in exchange for the right to play his music at certain times and volumes. By reaching a mutually agreeable price, Adam and Ben aim to internalize the externality and align their interests more closely. 

 Adam's utility function, u_A(m_A, s_A ), depends on his monetary endowment (m_A) and the volume of music (s_A), while Ben's utility function, u_B(m_B, s_B ), depends on his monetary endowment (m_B) and the level of noise reduction (s_B), where s_A + s_B = 1 to represent their shared environment's sound experience.

Achieving Pareto Efficiency

If we assume the possible endowment point E is half the amount of money and zero unit of music for Adam, that is, (m/2, 0), then it is half the amount of money and one unit of indoor noise reduction level for Ben, that is, (m/2,1).

The tangent points of the indifference lines are Pareto effective points. Connecting the tangent points is the contract curve, which is the Pareto effective set. These points represent Pareto-optimal allocations, such as points X and X’.

 

Challenges

However, the current model lacks conditions for competitive equilibrium because pricing and allocation of sound are not straightforward like private goods. Individuals' choices are multifaceted and influenced by a complex interplay of subjective preferences, altruism, moral considerations, and psychological factors.

For instance, how much would be enough to pay for playing music? How many meals do Adam need to take Ben out for, or perhaps to what kind of restaurant? And how should the duration of music playback be priced?

Pricing the negative externality of music consumption is inherently challenging, as it requires assigning a monetary value to subjective experiences and preferences. If sound levels could be priced continuously, a competitive equilibrium might be attainable.

In the model, if we assume that the initial endowment of music loudness is regulated by the terms of the apartment, where everyone initially has the right to reduce noise (i.e., the music sound is zero), and an equal amount of money is allocated to each person, then the initial endowment point is represented by point E. Additionally, assuming that the right to reduce noise is divisible and tradable, we can infer the existence of a competitive equilibrium. This equilibrium represents an efficient outcome where resources are allocated optimally to maximize overall welfare.

 

Is there no other way?

Overall, the most pivotal element in the negotiation and compromise between Adam and Ben lies in fostering an environment of open dialogue and genuine empathy. For example, they both could use noise-canceling headphones to respect each other's personal space and boundaries. Through respectful communication and mutual understanding, Adam and Ben can work together to foster harmony and mutual respect in their shared space.