Capitalize on Complementarities

CAPITALIZE ON COMPLEMENTARITIES

Imagine you are running a summer tennis camp. Assume that your only important inputs are the instructors and the courts. If you start off with a single tennis court, the value of the first instructor is high, and the value of a second instructor is still positive (since you can have two instructors in a single court), but lower. A third instructor is less valuable still. Now imagine that you had two tennis courts available instead of one. All of a sudden, the value of having a second instructor has gone up: the second instructor can now go to the second court and more children can sign up for your camp.

In this situation, increasing the quantity of one input (in this case tennis courts) makes an increase in the quantity of the other input (in this case tennis instructors) more valuable. Another way to see this is that after some point hiring more instructors won’t do you much good unless you have additional tennis courts. So the value of additional instructors will be higher the more tennis courts you have.

The example above illustrates the value of capitalizing on complementarities. Courts and instructors are complements because the value of one depends on the availability of the other. The world is full of situations like this. For example, the value of fertilizer for a farmer is likely to be higher if other inputs (seeds, irrigation, farming practices, etc.) are available. The value of a blackboard in a school will depend on the availability of other school inputs (such as chalk, teachers, classrooms, etc.).

In economics terms, the situations described above exhibit positive cross-partial derivatives. In fact, when Richard teaches this maxim to his students, he refers to it as "capitalize on positive cross partial derivatives," a much more technical formulation intended to be playful and memorable.

One key application of this maxim arises when we choose a collaborator, for example in an intellectual project or in business. As Richard frequently argues, we often choose people whose skills are similar to our own. The result is that the gains from collaboration are much smaller than if we were to choose people who would bring different capabilities to the undertaking. If two engineers are planning the construction of a bridge, adding a third engineer to the team won’t help as much as adding an architect or a project manager.

Peter Schuck, Richard’s coauthor and former roommate, and now an emeritus professor of Law at Yale Law School, saw this principle in action in his collaboration with Richard: "I suspect that what I learned of Richard’s modus operandi during our first collaboration – a 1970 article in The Public Interest – has been true of many of his collaborations: Richard comes up with the idea – his comparative advantage – and then moves on to his many other projects, leaving it to the coauthor to do most of the more time-consuming fleshing out of his idea." Richard supports this view: "When you are an economic theorist, you gain more by collaborating with an empiricist than with another theorist. Similarly, if you are good at ideas and bad at follow up, you should collaborate with someone who is good at follow-up."

Richard is a living example of the benefits of following this maxim. The number of coauthors he has who were trained in different fields is astounding. As François Degeorge, former student and coauthor of Richard’s, and now professor of Finance at the Università della Svizzera Italiana and managing director of the prestigious Swiss Finance Institute, described, "The most important maxim Richard taught me is one I never heard him pronounce but always saw him practice: engage with people from different fields, interests, mindsets, countries, and ages. In the course of our research collaboration, I have enjoyed the privilege of many conversations with Richard. I was always awed by his ability to work with a prodigious number of coauthors, yet give his full attention to our exchanges. This facility stems from Richard’s intellect of course, but also from his deep love of human interaction."

The benefit of engaging with a wide range of people goes beyond professional collaborations. As Tarek Masoud, Richard’s friend and faculty colleague at the Harvard Kennedy School, colorfully put it, "Long before our leaders and institutions got wise to the importance of diversity and inclusion, Richard made a habit of seeking out and building friendships with people from backgrounds very different from his own. The diversity of the contributors to the present volume is powerful testimony to that fact. It’s also why his databank of personal stories includes such characters as Armenian clothiers, Manhattanite-coatmakers-cum-murderers, feuding Egyptian physicians, and Indian bridge players."

The maxim applies not only to professional collaborations but also to personal ones. Below, Alice Heath, a PhD student of Richard’s, describes how she used this maxim in the context of what many consider the ultimate form of collaboration: marriage. And Taran Raghuram, a student and teaching assistant of Richard’s at the Harvard Kennedy School, puts this maxim to use not only when choosing with whom to collaborate, but also in shaping how he collaborates.

Positive complementarities in marriage - Alice Heath

I took Richard’s class when I was about a year into a relationship with the person who would become my wife. My wife and I are extremely different in many ways: she likes to make decisions immediately, I like to collect more information and spend time pondering; she loves meat, I am a vegetarian; she is from the U.S., I am from the UK. Initially these differences caused a fairly large amount of difficulty, but when I learned from Richard that cross-partial derivatives are important I realized I needed to think about our differences as complementarities. When hosting a dinner party, it’s fantastic to have someone who can cook a delicious meat dish and another person who can make vegetables shine: the dinner party is much better than it would be if you had two people who could only cook meat. Similarly, it’s good to have someone to make the quick decisions for decisions where that’s suitable, and someone who can tap the brakes and make sure the important decisions have been properly analyzed. For me, the essence of cross-partial derivatives is that despite the cost of trans-Atlantic flights, marrying someone quite different from you can be an excellent choice.

Improving collaborations - Taran Raghuram

I deeply admire Richard’s ability to model successful collaboration. He identifies areas of interest where he is less knowledgeable and sees them as an opportunity to produce great value by working with experts who complement his own skills. So while positive cross-partial derivatives are of course an important analytical tool, they also serve as a personal reminder to adopt a humbler mindset and work with others to have an impact. Whenever I have a new idea, rather than stew on it endlessly to unlikely "perfection" as I used to, I now solicit feedback much sooner because of this maxim. The refrain "positive cross-partials" in my head reminds me to put aside my own ego and to seek out perspectives to more quickly converge on a better idea. This semester, I implemented a rule: spend one hour thinking about a new idea, then get feedback on it, either via a short email or a brief conversation with someone more knowledgeable. This has led to interesting and diverse work in several areas from COVID-related analysis to models of journalism.

Positive cross-partial derivatives in cities and the wider world - Ed Glaeser

This maxim is an understatement. Positive cross-partials are the hallmark of human existence. On our own, we are puny creatures who would fare poorly against any large carnivore in the wild. Our individual actions are only effective because they are supported by the actions of thousands of others – today and through history. My writing of these words required humans to invent written language, computers, the internet, the organizing of this book, and thousands of actions throughout history. My efficacy as an economist owes much to the teachers and mentors that I have had over decades, such as Richard Zeckhauser. I study cities, and positive cross-partials are the reason that people congregate together in urban areas. By acting together, we can do remarkable things. The most important of these are the cascades of collaborative brilliance that have been responsible for humanity’s greatest hits, from Athenian philosophy to the internet.