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Mathematics Meets Romance

A teacher in traditional chima chogori costume leading a mathematics class at the Koran high school in Tokyo. (AFP Photo)

One of the topics I teach to students in my Mathematical Economics and Business class is optimization with constraint.
 
In general, this topic talks about how we can use mathematical tools in solving economic problems such as maximization and minimization, and also use them to help solve problems that we experience in daily life as well.
 
For example, we try to maximize our utility, or the profit of the firm we work for. Meanwhile, cases of minimization problems range from reducing household budgets to minimizing a factory’s cost of production.
 
In both kinds of optimization (i.e. maximization and minimization), it is common to impose constraints. For example, we allocate a certain amount of money as our grocery budget, and with that limited money we try to maximize our utility. From a business perspective, we have to calculate the minimum cost of production needed in order to reach a certain target of production.
 
Since the lecture focusses on math, I teach about mathematical tools and how they can be applied to economic problems. In mathematical concepts, a constraint in an optimization case (e.g. budget in utility maximization) creates an important implication for the range of options that can be picked.
 
In utility maximization, this can take form of the amount of goods, X and Y, that one can consume. The implication of imposing a constraint is mutual dependency of the choice variables.
 
During the lecture, I explained an analogue of this mutual dependency concept to the class, and said we can experience mutual dependency, for example, in interpersonal relationships. This can take the form of any relationship with friends, spouses or parents. If we have mutual dependency with someone, we will consider his or her opinion in making decisions. We no longer consider only our own satisfaction; rather, we consider other people’s satisfaction with whom we feel dependent.
 
The students nodded, and I felt that they understood the concept better. They might be able to relate more easily to the concept because it is something that they faced in their daily lives.
 
This same concept crept into my mind when I met several friends on different occasions. Some of them said that the relationships they built with their partners somehow created the feeling of mutual dependency, which limited their choices. They were not complaining, but they had realized that there were things they could no longer do because of the feeling of mutual dependency.
 
Meanwhile, some other friends of mine found that this mutual dependency allowed them to have wider choices. They found that they could discover new things due to being mutually dependent.
 
Why do we find this paradox?
 
I think that this mutual dependency does impose constraints on things that we can choose. However, we should bear in mind that everything is relative. Mutual dependency may be restricting if a domain of choices shrinks after being mutually dependent with another person.
 
When there is no mutual dependency, every individual has his or her own domain of choices. These domains have different sizes and confine different choices. Hence, mutual dependency that is the construction of a new domain of choices together and mutually may impose two distinct impacts (i.e. expansion of range of individual choices or contraction of range of individual choices). This may be the reason why there are some people who feel more deprived of choices and some other people who feel they have a liberating abundance of choices.
 
Whether a relationship that restricts choices is worse than a relationship that liberalizes choice cannot be easily determined. We have to remember that every individual has his or her preference for what kinds of domain of choice he or she likes the most.

White Margin is a group of three young economists with opinionated minds and twitchy fingers. They share knee-jerk reactions, half-baked to fully-formed ideas, random musings, angry rants, and the list goes on… mainly on Jakarta and Indonesia, with an undertone of economic theory and logic. We believe that there is always room, some white margin, to fill in perspectives, even for the most rigid theories.