# 13

This is a framing practicum post. We’ll talk about what comparative advantage is, how to recognize applications of comparative advantage in the wild, and what questions to ask when you find it. Then, we’ll have a challenge to apply the idea.

Today’s challenge: come up with 3 examples of comparative advantage which you have not seen before. For each one, say what the different objectives are, and what the different components/subsystems are. They don’t need to be good, they don’t need to be useful, they just need to be novel (to you).

("What do different objectives and subcomponents have to do with comparative advantage?" I hear you ask, "I don't remember anything about that from econ 101." This is framing practicum - we want to apply the frame of comparative advantage to new kinds of systems, not just trade-between-nations or whatever. So, we're going to present it a bit differently from what you're used to.)

Expected time: ~15-30 minutes at most, including the Bonus Exercise.

Suppose we’re running a fruit-growing company, Fruit Co, with many different orchards which can each grow apples or bananas. Each farm has different soil, different weather, different initial conditions, etc, and therefore faces different opportunity costs for growing each fruit. For instance, the Xenia site might be able to grow 1 extra unit of apples/yr at the cost of 0.5 units of bananas (by replacing their least-effective banana grove with apple trees) or vice versa, while the Yuma site may be able to grow 1 extra unit of apples/yr at the cost of 1 unit of bananas or vice versa.

Claim: given these numbers, the company can achieve a pareto increase in their fruit production. How? Well, they can produce one more unit of apples at the Xenia site (missing out on 0.5 units of bananas), and produce one less unit of apples at the Yuma site (using those resources to produce 1 extra unit of bananas). Overall, the amount of apples produced stays the same, but the amount of bananas produced increases by 0.5 units.

Intuitively: each site specializes a little more in whatever fruit they have a comparative advantage (aka relative advantage) in growing. We have multiple goals (growing more apples, and growing more bananas), and multiple subsystems which we can independently adjust to contribute to those goals (Xenia and Yuma orchards). Each subsystem faces different trade offs between the different goals, so we can make "trades" between subsystems with different trade off ratios in order to achieve pareto gains. Each subsystem specializes a little more in whatever goal their trade off ratio favors, relative to the other subsystem.

We can also add more subsystems (e.g. Zion orchards), and more goals (e.g. coconut-growing). Maybe Xenia can trade off production in ratios of 1:0.5:3 (apples:bananas:coconuts), Yuma can trade off in ratios of 1:1:2, and Zion can trade off production in ratios of 1:0.5:1. We can pick any two sites, then pick any two fruits whose ratios differ between the sites, and do exactly the same sort of “trade” as before: each site specializes a bit more in whichever of the two fruits their ratio favors, compared to the other site. For instance, we could pick Xenia/Zion and apples/coconuts: Xenia could produce 3 more units of coconuts at the cost of 1 unit of apples, and Zion could replace those apples at the cost of just 1 unit of coconuts, so overall there’s a gain of 2 coconuts.

• One site is already maximally specialized. For instance, if Zion is already fully specialized in growing apples, then there are no further banana or coconut groves to replace with apple trees.
• The two sites trade off in exactly the same ratios. For instance, Xenia and Zion both trade off apples:bananas at a ratio of 1:0.5, so we can’t achieve a pareto gain with a little more specialization in those two fruits between those two sites.

## What To Look For

In general, comparative advantage should come to mind whenever we have an optimization problem with both

• Multiple goals/objectives (i.e. pareto optimality)
• Components/subsystems whose parameters can vary (approximately) independently

Note that “multiple goals” might really mean “multiple sub-goals” - e.g. Fruit Co might ultimately want to maximize profit, but producing more apples is a subgoal, producing more bananas is another subgoal, etc.

In the Fruit Co example, the key question is: what are the ratios at which different sites can trade off between production of different fruits? As long as those ratios are different, we can achieve a pareto gain.

More generally, we should ask: what are the ratios at which different components/subsystems can trade off between different objectives?

Another example: suppose we’re designing a car. We have many objectives: speed, handling, cost, noise, comfort, etc. We have many subsystems which we can adjust approximately-independently: engine, transmission, body, seats, air conditioner, etc. So, we look at the ratios at which we can trade off speed:cost:noise by adjusting the engine, or the body, or the air conditioner. Can we achieve a 1-unit decrease in noise more cheaply by adjusting the engine or the air conditioner? Can we gain a bit of speed at the least noise-cost by adjusting the engine or the body? If these ratios differ, it often means we can achieve a pareto gain - e.g. maybe we can give the air conditioner team a bit of extra noise-budget (to make the air conditioner cheaper), and in exchange the engine team spends a little extra to cut back on engine noise, and that works out to a net decrease in both cost and noise.

## The Challenge

Come up with 3 examples of comparative advantage which you have not seen before. For each one, say what the different objectives are, and what the different components/subsystems are. They don’t need to be good, they don’t need to be useful, they just need to be novel (to you).

Any answer must include at least 3 to count, and they must be novel to you. That’s the challenge. We’re here to challenge ourselves, not just review examples we already know.

However, they don’t have to be very good answers or even correct answers. Posting wrong things on the internet is scary, but a very fast way to learn, and I will enforce a high bar for kindness in responses to other peoples' answers. I will personally default to upvoting every complete answer, even if parts of it are wrong, and I encourage others to do the same.

Post your answers inside of spoiler tags. (How do I do that?) [EDIT: I accidentally made this a normal post rather than a question post, and now there's responses so it's a bit late to switch. Ignore the spoiler requirement for this one.]

Celebrate others’ answers. This is really important, especially for tougher questions. Sharing exercises in public is a scary experience. I don’t want people to leave this having back-chained the experience “If I go outside my comfort zone, people will look down on me”. So be generous with those upvotes. I certainly will be.

If you comment on someone else’s answers, focus on making exciting, novel ideas work — instead of tearing apart worse ideas. Yes, And is encouraged.

I will remove comments which I deem insufficiently kind, even if I believe they are valuable comments. I want people to feel encouraged to try and fail here, and that means enforcing nicer norms than usual.

If you get stuck, look for optimization problems with both:

• Multiple goals/objectives (i.e. pareto optimality)
• Components/subsystems whose parameters can vary independently

Bonus Exercise: for each of your three examples from the challenge, what are the ratios at which different components/subsystems can trade off between different objectives? I’m not looking for numerical values here, just a statement of what those “ratios” mean within the context of your particular example. How might you measure the ratios?

This bonus exercise is great blog-post fodder!

New Comment

When thinking about comparative advantage, I find it helpful to frame it in terms of the lowest opportunity cost. I think this points attention in the most useful way to explain the concept.

If Xenia can produce 1 unit of apples or 0.5 units of bananas, this is just saying that the amount grown of one fruit is the opportunity costs of growing the other fruit. Xenia has a lower opportunity cost of growing apples than Yuma.

Also, it would be nice to do one of these for market size as well.

I have at least two practicum posts planned for markets, looking at them from different angles.

One is a direct follow-up to this post: we say two "subsystems" (of the sort used in this post) are in "equilibrium" when they can't make any "trade" which would yield a pareto gain on the objectives. In this post, we saw that that means the two subsystems have the same trade off ratios (aka opportunity costs). Those ratios are prices - specifically, the prices at which any of the equilibrated subsystems can "trade" with any other subsystems or the external world. The equilibrated subsystems are a "market", and their shared prices are the defining feature of that market.

Under that angle, market size isn't particularly relevant. Markets are about pareto optimality and trade-equilibrium.

The other angle is markets as a limit in games with many identical players. As the number of players grows, identical players compete to make deals, and only the best bids/offers win. So, we end up with a "shared price" for whatever deals are made.

Under that angle, market size is a central question.

Market size is central in other cases as well. It is what permits specialization of labor. Comparative advantage is a mechanism for permitting this development even when one of the producers has an absolute advantage, such as Yuma in this example. However, the most important factor in specialization is sheer market size. This is why I’m excited to consider this frame further in the future.

General system components:

• Two or more producers
• Two or more products with differing costs for each producer
• Consumption
• A coordinating mechanism

Scientific hierarchy and specialization. When a new graduate student does wet lab work for a PI in a large and well-funded lab, they're generally foregoing only an opportunity to do wet lab work somewhere else. They don't have the resources, scientific knowledge base, or position to pursue their own high-level research strategy, even if they had one. If a well-funded PI were to do wet lab work, they'd be giving up time they could be devoting to high-impact strategy work. Hence, even though the PI might be better at the bench than any of their graduate students, they nevertheless don't actually do any wet lab work themselves. On occasion, though, they might step in to perform a critical procedure in a crunch if the assigned grad student isn't able to do it.

Furthermore, successful labs probably specialize not only to advance the state of the art in their field, but also in order to be able to provide services to other labs. If lab A is run by a highly competent PI who has a large but limited supply of labor and capital, they could develop competency in any of a wide range of advanced skills and techniques. But if lab B, even if run by a modestly competent PI, can specialize in a component of work relevant to lab A, then they might have a comparative advantage in that area. Lab A will let them have it, so that they can produce more of the things lab B is not able to do.

Hibernation vs. winter foraging. Ground squirrels hibernate; hares do not. One speculative explanation is that, in energy-sparse environments, species specialize not only in different particular food sources, but in different seasons. Hares specialize in exploiting winter food sources; ground squirrels specialize in maximally exploiting summer resources through more complex patterns of behavior. In a sense, they're finding different comparative advantages. They may evolve with these patterns in a way that reflects a sort of "evolutionary trade." Hares focusing on a pattern of energy consumption and expenditure that can run at a uniform moderate level, sustainable in summer against competition from lots of hungry squirrels, and also in winter when food sources are scarce. Squirrels focus on a pattern that maximally exploits abundant summer resources, and then shuts down during the winter, "leaving the rest" for the hares. This isn't symbiosis, and it's not just "specialization" in the narrow sense of, say, growing a beak adapted to a particular flower shape. Beak specialization is equivalent to a firm producing better tools for its workers to do the job it's focused on; hibernation vs. winter foraging lifestyles are equivalent to the process by which firms choose which jobs to focus on in the first place.

Can we apply other economic principles to understand evolution and predict or explain patterns in our observations? We might use "market size" to understand the evolution of multicellular organisms. The more cells we have in the body, the more they're able to specialize. This predicts that we'd find increased cellular diversity in larger organisms, even within analogous organs.

Cellular differentiation. Pluripotency and mature function are two different cell "products." Stem cells can offer cheap pluripotency, but it's expensive for them to differentiate all the way to maturity. Partially differentiated cells can reach maturity in a narrower set of endpoints cheaply, but cannot naturally revert to pluripotency (as far as I know). The body uses these cells, and coordinates their reproduction, differentiation, and maturation.

This makes me curious about the extent to which cellular proliferation and differentiation is controlled vs. incentivized. The body is certainly heavily controlled by intercellular signaling, which controls the behavior of cells. This is analogous to a command economy. When, if ever, is the body regulated (in a healthy way, i.e. not cancer) by creating "rewards" of energy or oxygen to select for cells maximally able to exploit that reward?

I like the insights on research specialization.

On cellular signalling: "control by intercellular signalling" is not necessarily analogous to a command economy. After all, even in a market economy, we have lots of interagent signalling in the form of e.g. prices. Indeed, many hormones function quite similarly to prices (i.e. they signal abundance or scarcity of an associated resource), and biological signalling is largely decentralized - different organs specialize in different signals and their associated functions. The "rewards" need not be energy or oxygen or even growth of a cell population; indeed, we don't necessarily need a "reward" signal at the cellular level at all in order for the economic analogy to apply. That's part of the idea of this post: we can apply comparative advantage (and opportunity cost, markets, etc) even when the "subsystems" are not themselves optimizers which "want" anything. There can be just one "central" set of pareto-optimization objectives, but the optimization is implemented in a decentralized way by "trading" until the opportunity costs of different subsystems equilibrate.

Yes, the market analogy seems like a valuable one to lean into. Textbooks tend to focus on a control systems approach to describing protein and cellular regulation and action. The body is viewed as an intricate machine, which is not designed, but has a design determined by evolutionary forces which acts to achieve functions conducive to reproduction. This tends to make me frame cells and proteins as components of a machine, which only gain an independent "agency" of their own in the case of cancer.

I can see two broad strategies for incorporating this into our understanding.

One is for communication and study purposes. By using familiar and vivid frames, we might be able to teach about biology in a more compelling manner.

This seems useful, but even better would be to use economic frames to derive truly novel insights. In my lab, control systems are the dominant framework for understanding the systems under study. It's a large, old, world-class lab populated by scientists who are smarter and more experienced than me, so I find it likely that this tradition has resulted at least in part from its massive, sustained, demonstrated utility.

What sort of predictions or strategies can we make by using economic frames, beyond simply repackaging known mechanisms into novel language and analogies? How can economic frames lead us to concrete experimental techniques in order to test and build on these novel insights? What are the challenges and limitations of an economic framing of cellular biology?

Example One: Good Cop / Bad Cop

The classic interrogation trope involves a suspect who is being interrogated by two police officers - one who is friendly and tries to offer to help the suspect, and one who is aggressive and threatens them with the consequences of not cooperating. We can think of the two cops as components of the Police Agent, and they are pursuing two goals: Trust and Fear. Both Trust and Fear are sub-goals for the ultimate goal which is likely a confession, plea deal or something of that nature, but the officers have uncertainty about how much Trust or Fear might motivate the suspect towards this ultimate goal, so they want to maximize both. Here, Trust is built by the "Good Cop" while Fear is built by the "Bad Cop". Imagine both cops start out pretty evenly split between pursuing Trust and Fear, but the the first cop is naturally a bit more aggressive (this is the "Bad Cop") and so he is following a slightly aggressive strategy (i.e. geared towards Fear). Vice versa for the second cop ("Good Cop"). Now because the suspect is already afraid of the Bad Cop, the Bad Cop gets more Fear from increasing their aggression than the Good Cop would, as it's taken more seriously. Similarly, because the suspect is already slightly friendly towards the Good Cop, the Good Cop gets more Trust from increasing their friendliness than the Bad Cop would, because they've built rapport and it's seen as more genuine. Thus, in order to maximize the total amount of Trust and Fear, the Good Cop should completely specialize in friendliness and the Bad Cop should completely specialize in aggression, due to their comparative advantages.

Example Two: Multi-Party Systems

In a multi-party system, you might have three political parties that are all broadly on the same side of the spectrum, with little doubt they'd form a governing coalition if they could. Let's say there are n groups that these three parties can possible draw votes from, with each group representing a certain policy goal that all three parties would be happy or indifferent towards implementing (example for the left: unions, immigrants, students, renters). So we have three subsystems (each party) and n goals they are try to maximize. Now note that rhetoric / messaging is generally tied to what goals you focus on, and that a given voter may find different rhetoric more or less persuasive for a given political goal. If all three parties attempt to solve all n goals equally, they will likely have very similar rhetoric / messaging due to similar goal focus and composition of their political coalition. This means any given voter will likely be hearing only one version of a message, but hearing it from three different sources, which minimizes the chance of the message landing and maximizes confusion & conflict. If instead, each of the three parties focuses on a different subset of groups and policy goals (based on whatever they are randomly currently inclined towards) , any given voter will hear three distinct messages on similar goals and so will be likelier to be persuaded by one of them - furthermore the messaging is likelier to be more direct and less confused. So to maximize the likelihood of achieving any of the n goals - by maximizing the likelihood of these three parties winning a majority of seats - these parties should specialize in different types of rhetoric. The key aspect of comparative advantage here is that there's a negative interaction term between all the different groups/goals (representing confusion of rhetoric and wasted messaging) so parties can achieve Pareto-optimal gains by focusing on a specific group/goal and leaving another to a different party. This may seem like a poor explanation for party specialization given the historical ways in which parties have formed, but parties are a revolving door of new members and a system where each party pulls in members from a subset of the n groups and those members then push that party towards advocating for that subset of n groups is stable and maximizes any one group's chances of success. Friendly party leaders can also talk to each other to achieve some version of this coordination - I've seen this in practice in my own country. Note: this idea is not novel to me but the framing of it as comparative advantage is.

Example Three: Student Debt

Here the two sub-systems are you and future you. The multiple goals are money and time. As a student you might be able to get a \$15/hr part-time job whereas in the future you could get a job where you expect to be paid twice that. Clearly to maximize money and time in a pareto-optimal way, you'll refrain from working while being a student, and instead work slightly more when you're older. This would generally entail taking on a lot of student debt. In this example there are costs since money is not fungible through time and taking on debt incurs interest, but if the comparative advantage is big enough, those can be overcome.