Bio-Economics of Fishery: From Schaefer to Gordon Models

Imagine a small, coastal village. For generations, its people have lived off the sea. The ocean seems infinite, its bounty endless. But then, engines get stronger, nets get bigger, and new boats arrive, drawn by the promise of a good catch. Suddenly, the “infinite” ocean feels crowded. The fish, once abundant, are harder to find. This isn’t just a story; it’s the real-life puzzle of fishery management, a complex intersection of biology and economics. To untangle it, we need to understand not just how fish populations grow, but how human incentives drive us to harvest them. This is the heart of bio-economics, a field that charts a course from a simple biological model to a complex, dynamic economic reality.

The fish population puzzle: Schaefer’s biological model 🔗

Before we can talk about the economics of fishing, we have to understand the fish themselves. In the 1950s, a biologist named Milner B. Schaefer provided a simple but powerful way to do this. He proposed that we think of a fish population, or “biomass,” like a financial asset.

A fish population, left to itself, will grow. It has a “biological interest rate.” Our job as managers is to figure out how much “interest” we can harvest each year without touching the “principal”-that is, without making the fish population shrink. This “interest” is what Schaefer called the surplus yield.

What is logistic growth? 🔗

Schaefer’s model is built on a concept called logistic growth. It’s a fancy term for a very intuitive idea, often shown as an S-shaped curve.

• When a population is small: There’s plenty of food and space. The fish can reproduce rapidly, and the population grows quickly.
• As the population gets larger: Competition for food and resources increases. Growth starts to slow down.
• At maximum size: The population hits its natural limit, what biologists call the carrying capacity (K). At this point, the environment can’t support any more fish. The number of births is just enough to replace the number of deaths, so growth drops to zero.

The “surplus yield”-the amount of new fish added each year-changes as the population size changes. When the population is very small, the surplus is small (because there aren’t many fish to reproduce). When the population is at its maximum (K), the surplus is zero (because growth has stopped). The “sweet spot” is somewhere in the middle.

Finding the ‘sweet spot’: Maximum Sustainable Yield (MSY) 🔗

The surplus yield follows a parabolic (an inverted U-shape) curve. It’s lowest at zero population, rises to a peak, and falls back to zero at the carrying capacity (K). That peak is the single most famous-and perhaps most controversial-concept in fishery management: the Maximum Sustainable Yield (MSY).

MSY is, quite simply, the largest catch that can be theoretically taken from a fishery indefinitely. According to Schaefer’s logistic model, this sweet spot occurs when the fish population is at exactly half its carrying capacity (K/2). At this size, the population is growing at its absolute fastest rate. In theory, if you catch exactly this amount each year, the population will never shrink, and you can harvest that maximum amount forever.

[Image: A simple two-panel graph. The top panel shows the S-shaped logistic growth curve (Biomass vs. Time). The bottom panel shows the parabolic Surplus Yield curve (Yield vs. Biomass), with a clear peak labeled "Maximum Sustainable Yield (MSY)" at the biomass level "K/2".]

For decades, MSY was the holy grail for fishery managers worldwide. The goal was simple: get the fish stock to the MSY level and then harvest the surplus. It’s a biological target, pure and simple. But this purely biological view has a massive blind spot: it tells us nothing about the cost, or the profit, of catching those fish.

But what about the money? The Gordon-Schaefer economic model 🔗

In 1954, just as Schaefer’s ideas were taking hold, an economist named H. Scott Gordon published a landmark paper, “The Economic Theory of a Common-Property Resource: The Fishery.” He took Schaefer’s biological curve and laid a simple economic model right on top of it, and in doing so, he changed the conversation forever.

Introducing costs and revenues 🔗

Gordon introduced two simple economic forces to the model:

1. Total Revenue (TR): This is the total value of the fish caught. You get it by multiplying the yield (from Schaefer’s surplus curve) by the price of fish (which we’ll assume is constant). Because the yield is an inverted U-shape, the Total Revenue curve is *also* an inverted U-shape. As you apply more “fishing effort” (more boats, more time, better nets), you catch more fish, and revenue goes up… up to a point. That point, naturally, is MSY. If you apply *even more* effort past MSY, you start overfishing. The population shrinks, the next year’s yield is smaller, and your total revenue actually *goes down*.
2. Total Cost (TC): This is the cost of all that fishing effort. It includes fuel, crew salaries, boat maintenance, and a “normal profit” (the minimum needed to keep the fisher in the business). The more effort you apply, the higher your total cost. For simplicity, Gordon modeled this as a steadily rising straight line. More effort equals more cost.

The difference between these two curves-the gap between Total Revenue and Total Cost-is the most important thing in fishery economics: economic rent. You can just call it “pure profit.”

The big reveal: Maximum Economic Yield (MEY) 🔗

Gordon asked a different question than Schaefer. He didn’t ask, “What’s the *most* fish we can catch?” He asked, “Where is the *profit* the greatest?”

The answer is the Maximum Economic Yield (MEY). This is the level of fishing effort that creates the largest possible difference between total revenue and total cost. It’s the point of maximum economic rent for the fishery as a whole. It is the economic “sweet spot.”

[Image: The Gordon-Schaefer model graph. The x-axis is "Fishing Effort" and the y-axis is "Revenue/Cost". It shows the inverted U-shaped Total Revenue (TR) curve (peaking at MSY) and a rising straight Total Cost (TC) line starting from zero. Clearly label "MEY" at the point where the vertical distance between TR and TC is largest, and "MSY" at the peak of the TR curve.]

MEY vs. MSY: Why less is more (profitable) 🔗

Now, look at where MEY and MSY are on that graph. The Maximum Economic Yield (MEY) *always* occurs at a lower level of fishing effort than the Maximum Sustainable Yield (MSY).

Why? Think about it logically. As you approach MSY, you are sending out more and more boats to catch those last few tonnes of fish. Your revenue is still going up, but very, very slowly (because the TR curve is flattening). At the same time, your costs are still rising steadily. That last boat you sent out? The cost of running it was *more* than the value of the few extra fish it caught. You’re spending more to get less. It’s the law of diminishing returns, in action on the high seas.

At MEY, you catch fewer fish than at MSY, but you spend *a lot* less money to do it. The overall profit for the industry is maximized. This also has a huge biological benefit: because the fishing effort is lower, the fish population (biomass) left in the water is *larger* than it would be at MSY. It’s a win-win: a healthier, more robust fish stock and a more profitable industry.

Why do we keep getting it wrong? The tragedy of open access 🔗

If MEY is so great (more profit, healthier fish stocks), why are so many of the world’s fisheries fished far beyond both MEY *and* MSY? The answer lies in one of a single, powerful concept: the tragedy of the commons.

The ‘tragedy of the commons’ in the ocean 🔗

Most fisheries are, by default, an open-access resource. This means anyone with a boat can go out and fish. No one owns the fish until they are caught. This “no-ownership” status creates a disastrous incentive, first described by Garrett Hardin in 1968.

Let’s go back to our graph. Imagine a fishery is being managed perfectly at MEY, and the boats are all making a healthy profit (that big “economic rent”).

1. A new fisher, let’s call him Anand, sees this. He says, “Wow, they’re making a killing! I’m going to buy a boat and get a piece of that profit.”
2. Anand enters the fishery. His extra effort increases the Total Cost for the whole fishery.
3. As long as there is *any* profit to be made-as long as the Total Revenue curve is even one rupee higher than the Total Cost curve-new fishers like Anand will have an incentive to join.
4. This “race to fish” continues. More boats enter, costs rise, and the fish stock is depleted. The rush only stops when the Total Cost line finally *crosses* the Total Revenue line (where TR = TC).

This point is the open-access equilibrium. And it is a tragedy. At this point, the economic rent has been completely “dissipated,” or wasted. So many people have entered the fishery that no one makes any pure profit. The industry is bloated with too many boats, burning too much fuel, chasing too few fish. Biologically, this point is almost always *past* MSY, meaning the stock is severely overfished. It is a state of both biological and economic ruin.

A glimmer of hope: Common property management 🔗

It’s crucial to correct a common misunderstanding. “Open access” (a free-for-all where no one has rights) is *not* the same as a common property resource. A common property (or “common-pool”) resource is not un-owned; it is *collectively owned* by a well-defined group of people.

This distinction is the key to preventing the tragedy. Think of traditional fishing communities, like many along India’s coastline. For centuries, these communities have had their own rules. They may have territorial rights over a certain patch of water, restrictions on the type of gear that can be used (e.g., banning destructive nets), or seasonal closures to protect breeding fish. As studies on resource management in India highlight, these community-based systems are a form of common property management. The community has the power to exclude outsiders and, critically, to regulate its own members. By enforcing these rules, the community can collectively stop the “race to fish,” limit their effort, and manage the resource sustainably, preserving both the fish stock and the economic rent for themselves.

Thinking about tomorrow: How time and money change the ‘best’ catch 🔗

There is one final, fascinating layer to this puzzle. So far, our Gordon-Schaefer model has been “static”-it looks at a single snapshot in time. But in the real world, time matters. This brings us to the concept of discounting and dynamic optimization.

What is a discount rate? 🔗

A discount rate is the economist’s word for “impatience.” It’s based on the simple fact that a dollar today is worth more to you than a dollar a year from now. Why? Because you could take that dollar today, put it in a bank, and earn interest. The interest rate “discounts” the value of future money.

How does this apply to fish? A fisher (or a fishery manager) has a constant choice:

1. Option A: Catch a fish today, sell it, and put the money in the bank to earn interest.
2. Option B: Leave that fish in the water, where it will grow larger and reproduce, creating more fish to be caught in the future.

The fish in the water are an investment, growing at a “biological interest rate.” The money in the bank is a financial investment, growing at a “market interest rate” (the discount rate).

The fundamental rule of renewable resource use 🔗

Dynamic optimization is the process of finding the “perfect” harvest level that balances this trade-off over time. The fundamental rule it reveals is this: You should harvest the resource up to the point where its own growth rate (the return on “leaving it in”) is equal to the discount rate (the return on “cashing it out”).

The implications of this are profound and a bit scary. The “optimal” level of fishing depends entirely on the discount rate you choose.

• If the discount rate is zero (meaning we value the future exactly as much as the present), the optimal strategy is to maximize the long-term value, which leads us to MEY.
• If the discount rate is very high (meaning we are very impatient and care only about immediate profits), the market interest rate will be higher than the fish’s biological growth rate. The “optimal” economic choice becomes, disturbingly, to “liquidate” the asset. You’d be better off catching all the fish as fast as possible, driving them to extinction, and putting the money in the bank.

This reveals that managing a fishery isn’t just a biological or economic decision; it’s a social and ethical one. The discount rate we use is a reflection of how much we, as a society, value the future-and the needs of future generations-compared to our own.

From Schaefer’s simple biological curve to Gordon’s economic overlay, and from the behavioral chaos of the “tragedy of the commons” to the philosophical dilemma of the discount rate, the bio-economics of fisheries shows us that a simple fish is never just a fish. It’s an asset, a resource, a livelihood, and a legacy, all at once.

What do you think?

If you were a fishery manager, would you prioritize the biological limit (MSY) or the economic one (MEY)? Why?

When we use a high discount rate, we are essentially saying that the needs of today are more important than the needs of future generations. How much should we value the future of our oceans when making decisions today?

References

1. https://fishe.edf.org/sites/default/files/2020-12/Schaefer%20primer.docx
2. https://medcraveonline.com/JAMB/maximum-sustainable-yield-maximum-economic-yield-and-sustainability-in-fisheries.html
3. https://www.perc.org/2001/03/01/fisheries-are-classic-example-of-the-tragedy-of-the-commons/
4. https://egyankosh.ac.in/bitstream/123456789/60548/2/Unit-11.pdf
5. https://ir.library.oregonstate.edu/downloads/6395w7947