Framing Practicum: Comparative Advantage

post by johnswentworth · 2021-09-09T23:59:09.468Z · LW · GW · 6 comments

Contents

  What’s Comparative Advantage?
  What To Look For
  Useful Questions To Ask
  The Challenge
None
6 comments

This is a framing practicum [? · GW] 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.

What’s Comparative Advantage?

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.

 ΔApples ΔBananas
Xenia1:0.5
Yuma1:1

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.

 ΔApples ΔBananas ΔCoconuts
Xenia1:0.5:3
Yuma1:1:2
Zion1:0.5:1

There are two ways this sort of “trade” can’t be made:

What To Look For

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

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.

Useful Questions To Ask

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? [LW · GW]) [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:

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!

6 comments

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comment by AllAmericanBreakfast · 2021-09-10T03:13:17.489Z · LW(p) · GW(p)

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.

Replies from: johnswentworth
comment by johnswentworth · 2021-09-10T16:50:39.157Z · LW(p) · GW(p)

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.

Replies from: AllAmericanBreakfast
comment by AllAmericanBreakfast · 2021-09-10T22:24:38.106Z · LW(p) · GW(p)

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.

comment by AllAmericanBreakfast · 2021-09-10T04:40:49.700Z · LW(p) · GW(p)

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?

Replies from: johnswentworth
comment by johnswentworth · 2021-09-10T17:07:01.737Z · LW(p) · GW(p)

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.

Replies from: AllAmericanBreakfast
comment by AllAmericanBreakfast · 2021-09-10T23:02:35.491Z · LW(p) · GW(p)

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?