image source

Okay, I’m a psychologist and an economist, not a mathematician. But even still, we know more about romance and “that kind of” love from poets than scientists. Sure, when mothers look at pictures of their children there’s an increase in activity in various regions of the hypothalamus, oxytocin and vasopressin are released at orgasm and during other physical acts (e.g. petting), and animal studies show the correlation between monogamy and neural structures in the limbic system, but what does that mean? You can’t reduce romantic love into receptors, transporters, neurotransmitters, agonists, antagonists, ligands, IPSPs, EPSPs, or action potentials.

Likewise, relationships clearly have some level of utility, the cost of which can be derived from the aggregated sum of costs (gifts, time, stress, etc.). So we can figure out how much we value the person based on what we spend to gain the utility derived from the relationship. Rationally, if we found someone or something else that gave us more utility we would abandon our partners to gain the more cost-effective good, service, or person, which/who has a higher benefit:cost ratio.

Does the fact that people pass up excellent jobs in order to spend more time with loved ones show that Love is a Giffen Good? Is it the result of myopia that people enter into legally binding, monogamous matrimony? Furthermore, the phrase, “bicker like an old married couple,” connoting aged love, suggests that Love exhibits increasing marginal utility rather than the more common decreasing marginal utility. If such is the case, why do we insist on practicing monogamy?

What proxy variable can we use to get an econometric estimation of the price (i.e. benefit) of Love? What sort of market is Love? there are certainly many agents, but who is the buyer, who is the seller? What are the barriers to entry? Not all people (and therefore their love) are the same, so competitive seems to go out the window, but it lacks the typical barriers to entry of an oligopoly. Are social constraints and Hercleic definitions barriers to entry, and if so, why do we even bother paying lip service to diversity? Is there perfect information? What are the metric units?

Dabbling into Statistics

What’s the expected value of a relationship?

• Let H denote value if together and healthy
• Let U denote value if together and unhealthy
• Let B denote the pain of the breakup

Then E(L) = P(H)H – P(B)B, but what about unhealthiness? Since it’s obvious that an unhealthy relationship increases stress, which has real economic costs, it would be safe to assume it would add negatively to the equation we get E(L) = P(H)H – P(U)U – P(B)B

But girls who date tools have shown us clearly that often staying in an unhealthy relationship is sometimes the better option to breaking up.
Add in a “it depends variable,” d, ranged [-1,1] and we get E(L) = P(H)H + dP(U)U – P(B)B

Easy enough, but how do we derive H, U, and B? Integrals of utility over time? Seems valid enough, but once again how do we calculate utility? Foregone nights with the guys, foregone job opportunities (wages discounted to present value), summed costs of dates/gifts, etc.?

Is spending a night together on the couch watching a movie really only worth 3 hours * $10/hour in foregone wages + $3.50 for the movie? $33.50? Add in economic’s “feel good utility” (as in what we buy when we “give” to charity), F, and a night is worth $33.50 + $F. How does H related as a function, H = H(F, t, c, s) where t = time, c = cost, and s = stress? What are the inputs to functions U and B?

How do we calculate the probabilities P(H), P(U), P(B)? Clearly if we thought P(B) > P(H) we would never enter the relationship in the first place, but people break up all the time. Myopia? We typically assume P(U) = 0, but once again, I know lots of people in unhealthy relationships (or who were), and doesn’t the cost of a breakup, B, vary depending on the values of H and U?

So B=B(H, U, friends, social standing, boredom, sex)
U=U(motives, sex, incompatibility, randomness variable)

Where can we find a metric for motives? Is the value of sex the average going wage (easily found from prostitutes) – CbP(con), where Cb = cost of a baby, and P(con) = probability of conception?

My head hurts. What is Love anyway?