The Economic Theory of the Heart

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Translated on February 8, 2009

Stripping romanticism from Romance: An Introduction

When asked “What is the field of study of economics”, the average person’s reply will probably involve inflation, GNP, the exchange rate and taxes. Despite the validity of all these examples, this typical point of view rests merely on phenomena produced by the central concern of the economic discipline: The scientific analysis of human choice.

The second half of the 20th century brought about a wave of “unorthodox” economic research, focusing on subject matter not commonly discussed in standard economics. Gary Becker, now a Nobel laureate, analyzed crime, leisure, education, housework and many other aspects of human life by employing the tools of classical economics. Anthony Downs and James Buchanan (another Nobel prize winner) took the economic approach to the foundation of political systems, while Milton Friedman developed a new approach to macroeconomics through insights on people’s behavior towards the future. Even the role of religion has been taken into account in the work of Robert Barro.

A field of research which remains relatively unattended, however, is that of interpersonal relationships – in particular, “romantic” relationships. A plausible answer for this void is the perception of the subject as irrelevant, or beyond the reach of the tools of economic analysis. Yet after a brief survey of the amount of resources that we, as a society, allocate to amorous relationships, the scarcity of economic research on the subject is puzzling.

This article attempts an informal, exploratory approach to the application of several economic tools to the romantic relationship. Independent of the validity of these specific applications, I believe the underlying assumption – that the decision-making mechanism of human beings is essentially the same for all subject matter – to be worthwhile.

Just like Everything Else: Love in the Utility Function

The feeling commonly described as love, regardless of its composition or variance amongst individuals, is a subjective appraisal of the value of certain variables. As such, it can be expressed within the classic format of the utility function. To verify this result we can check if said preferences show the necessary properties to be expressed in a standard function. Note that reflexivity is given if the following properties are met (continuity is not discussed for its empirical implications):

  • Completion: Given two sets of attributes (regarding a particular instance of physical appearance, sense of humor, etc.) A and B that are portrayed in two different subjects, the individual is able to specify if he prefers one over the other, or is indifferent between the two. This is equal to saying that this person can decide if he prefers one girl’s looks over another’s, or if he’s equally well off with either.
  • Transitivity: If a set of personality traits A is preferred to set B, and set B is in turn preferred to set C, the individual will also prefer set A to set C. This is essentially the individual’s consistency in her valuation of certain personality traits.

The utility function may be useful to express that which the individual values in the potential mates that surround him. A simple way to include the individual’s existing relationships in his preference set is to insert the other person’s utility function inside the original individual. The function’s positive or negative sign would imply affection or enmity. This function could also be weighted to show the relative importance of this person’s welfare to the individual, or the individual’s misconception of what brings welfare to the second person.

Another relevant implication of this approach is that, even in “matters of the heart”, the individual will continue to behave in a rational manner, attempting to maximize his utility function. Rationality is not necessarily expressed in the individual’s preference set, but rather in his attempt to achieve these preferred states. Naturally the function can be adjusted for a limited rationality – the idea is not that the individual will always avoid mistakes, but that he will at least seek to avoid them.

Some further insights can be obtained if we work with a specific form of the utility function. Taking the classic example of a n-goods Cobb-Douglas function.

Cobb-Douglas Function

Cobb-Douglas Function

Where U is the individual’s utility function, A is a non-negative parameter, xi represents a certain personality trait and the sum of all αi equals one. Within the function xi may represent characteristics which are valued by the individual, such as a potential mate’s IQ, body mass index, education or income. Note that these preferences may be independent of what the individual himself believes them to be, ex-ante empirical testing.

An implicit conclusion in this function is the negation of the formal concept of there being only one true love for each person. When more than a few traits are valued in a potential mate, this specification implies countless combinations of personality traits (and people) which maximize the individual’s welfare. More realistic scenarios would include a proposed distribution of these desired traits in the “market”, a price mechanism, and substantial search costs. Intuitively, one can say that the concept of “one true love” works despite potentially infinite combinations as a result of significant cost restrictions.

Another implication comes from the Cobb-Douglas form’s convexity- the case for diminishing marginal returns in romance. When considering a potential mate, it is easy to concede that one’s welfare does not increase with a prospect’s beauty or intelligence in a linear fashion. A more complex scenario emerges when we speak of a specific mate (a wife or husband, perhaps), and nest the welfare derived from this relationship inside a more general utility function.

The Old Ball and Chain: Satiety in Love

After happily accepting the romantic notion that love is free, one must accept that to experience love one must continue to live and therefore employ various scarce resources. By thinking about how the existence of a romantic bond requires resources from those involved in it, we may reach some conclusions about this interaction. In particular, if we look at how “expensive” a relationship is in the context of all the individual’s activities and resources, we could reach some conclusions about how sustainable the liaison really is.

Without indulging too much in the philosophy of the matter, love is generally considered to mean that two people enjoy spending time with one another, and desire each other’s welfare. The former variable could be considered the “consumption” of love (e.g the company of an individual portraying the individual’s desired traits). Of interest in this case is that the benefits obtained by this consumption are limited by a temporal satiety horizon.

An example of what is mean by this horizon is easily available in nourishment: If approached in a simplistic manner, diminishing marginal returns in food would imply that each meal after our first would bring us less and less utility (something which is easily refutable). If we apply a time limit to our satiety (and therefore to our diminishing marginal returns), however, the proposed model begins to resemble reality and is able to explain why eating three hamburgers may be too much for a time span of two hours but not enough for two days. Formally, this would imply a “decay” factor in the utility function which would depend on the time interval between meals.

In essence, how quickly the individual has had “enough” of his mate (and when he will choose to do something else with his resources) in the short term only describes the old adage that “the dosage makes the poison”. All that would be required for a successful relationship would be a match in the desired frequency (similar satiety horizons). This is in accordance with conventional wisdom about codependence.

For a relationship to succeed in the long term, however, the marginal returns for the individual must remain, at least, positive. This suggests a relationship between the different instances of the short-term marginal return functions, dictated by their discrete temporal horizon. Graphically, this approach is similar to the conventional depiction of a firm’s short-run marginal utility/cost versus its long-run counterpart. The following diagram depicts the blissful case of that husband which loves his wife more “with the dawn of each day”:

The discussion of the benefits an individual obtains from a relationship necessarily brings us to the question of whether she will continue to partake in it. We have seen that her satiety horizon will determine if she will choose other activities in the immediate term, and that the relationship between these short-run curves will dictate her long-run involvement. However, there are several additional considerations (externalities) in the analysis of this decision.

The Ties that Bind: Relationship Hold-Up

According to renowned economist Oliver Williamson, one of the more relevant problems in administrative economics is that of asset specificity. This problem is at the root of the phenomenon termed hold-up. In their Economics, Organization and Management, Milgrim and Roberts define hold-up as “The business problem in which each part held to a written contract is concerned with being forced to accept unattractive terms further ahead after it has already sunk an investment”.

For example, let us suppose that Ford, the auto maker, wishes to begin production of its new Mustang sports car. For this model, Ford requires an unusually powerful engine, and approaches Shelby Motors, small manufacturer known for its expertise in high-performance engines. The companies sign a deal for all Mustang production, and Shelby takes out a big loan to build the machines they will require to produce such a large amount of engines according to Ford’s specification.

After “sinking” or making this one-time investment, Ford’s manager contacts Shelby to inform him that due to market changes he will no longer be able to reach the agreed price and can pay only 10% less. Now Shelby is in a fix: To accept this new deal would represent a significant profit reduction, but since he has invested in being able to produce exactly the product that Ford specified, they will have a hard time selling that engine at full price to other clients. Shelby Motors is in a classic case of the hold-up dilemma.

A romantic relationship is essentially a contract between two parties and is therefore subject to this kind of problem. When starting a relationship with another person, a series of “investments” (particularly of time and effort with their corresponding opportunity costs, but certainly of other resources as well) are made that will only yield benefits for the participants of that specific relationship.

Examples for this abound: The initial dating effort, the memorization of anniversary and birthday dates, the learning of tastes in meals, music, films, the attempt to get along with the partner’s friends and family, etc. All these activities, which are certainly valuable for the relationship’s continuation (and as we have seen, for the participants utility functions), are relatively useless outside of this partnership.

As a relationship continues through time, the size of this sunk investment continues to grow (although at a decreasing rate). As we have seen, the rational individual continually evaluates his welfare within the partnership, gauging the costs and benefits of remaining as opposed to all other potential mates. Without the existence of these sunk costs, the individual would seek to dissolve the relationship as soon as his costs outweighed his benefits. With time, these investments become so significant, however, as to prevent the relationships’ end even after long periods of short-term cost.

For this reason, the individual will accept a sub-optimal short-run situation until the added losses outweigh the value of these sunk investments. This assumes that the individual cannot scale down his short-term involvement in the relationship (IE, he cannot move out and visit his wife to chat every now and then).

The holdup concept is therefore of value in describing the nature of the individual’s preferences regarding his relationships in the long run. As a cost for leaving the relationship, it must be weighed against the potential benefits of this action. Assuming a monogamous relationship, the most significant benefits for the individual of dissolving the relationship regard his opportunity cost.

We Need to Talk: The Market for Relationships and Divorce

As we have seen, the concept of hold-up becomes useful in interpreting the individual’s decision to stay or leave her partner. Another useful model for this cost-benefit scenario is that of the market for relationships. This is a peculiar market structure, as each individual in the market both supplies and demands the product in question – not dissimilar from the financial options markets.

When analyzing one of the greater costs of being in a monogamous relationship, the market concept becomes useful. The individual’s opportunity cost, as expressed in the utility she would receive from being in a relationship with any other mate, can only be estimated when referring to the current market. In this particular case, since the individual is looking at other potential suitors, she must look at his “purchasing power”, in this case his own desirable traits or market value.

In a manner analogous to the labor market, the individuals’ “market-value” decreases with age, ceteris paribus, due to the nature of aging on the human body (and some very generalized preferences). For this reason, the individual’s opportunity cost for staying in a relationship decreases as time goes on. This would suggest why, in most countries, the divorce rate tends to drop as the divorcees’ age increases. Two interpretations of this can be offered:

In the first scenario, the value of the couple’s sunk investments grows while their market value (and thus their opportunity cost) decreases at a greater rate. This generates a long-term optimal state where the participants stay in the relationship, despite continuous short term costs. The “happily ever after” interpretation takes these factors into account, but the couple’s long term marginal return curve is positively sloped and their short-term marginal returns are increasing while holding their temporal horizon constant.

In more practical terms, the hold-up concept may generate noxious behavior in relationships when, taking his partner’s sunken investments into account, the individual decides to take advantage of the situation by reducing the resources he allocates to the joint effort. This would explain a reputed tendency of males to stop exercising or investing in their wardrobe after they have married.

One way in which firms deal with this issue is by writing and agreeing to complex contracts that clarify the norms of behavior given several contingencies. Romantically, people have dealt with the problem in a similar way, but in a much less explicit and effective fashion. The widespread social customs of dating, courtship, marriage and engagement are essentially tacit contracts between those involved. These agreements are usually implicit and follow standard operating procedure dictated by social norms, such as monogamous behavior, cohabitation and resource sharing.

The efficiency of these contracts, in contrast to the mentioned industrial ones, is seriously undermined by their lack of formality and explicitness. Recently, the pre-nuptial agreement has become increasingly popular, reflecting recognition of these shortcomings.

The romantic notions involved represent a significant obstacle for the realm of personal relationships to achieve a solution similar to that of firms: The concept of unconditional love, besides being contrary to the previously discussed utility-function approach, reinforces the conditions for hold-up (through psychological costs of exit for those involved) which lead to sub-optimal results.

These concepts are easily applicable without going to the full extent of writing a hundred-page pre-nuptial agreement. Simply discussing all the likely scenarios that could follow an engagement, and refusing to accept previously established conventions (which may not apply to the particular case) is likely to reduce the likelihood of the hold-up problem arising.


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