Optimal Fishing Management Under Emission Cost in Korean Fisheries

During my master's course ARE 275 (Environmental and Resource Economics) at UC Davis, I tackled a simple but unaddressed question: What happens when fishing fleets must pay for their carbon emissions? And what policy recommendations follow?

1. The Problem: Old Boats, Big Emissions

Nearly half of Korea's fishing fleet is over 15 years old—essentially the gas-guzzling pickup trucks of the sea. The Anchovy Tow Net Fishery, producing 90% of domestic anchovy, emits 152,000 tons of $\text{CO}_2\text{eq}$ annually. Yet nobody was asking: What if they had to pay for these emissions?

2. The Model: Where Biology Meets Economics

I started with the logistic growth model for fish population growth:

where $r$ is the intrinsic growth rate, $K$ is the carrying capacity (maximum sustainable population), and $X_t$ is the fish stock at time $t$. This shows populations grow fastest at medium levels—nature's "everything in moderation."

The harvest function is straightforward:

where $q$ is the catchability coefficient (e.g., how efficiently you catch fish), and $E_t$ is fishing effort (measured in horsepower). Your catch depends on fish stock and fishing effort.

3. Finding Equilibrium

At sustainable equilibrium, growth equals harvest:

Solving for equilibrium stock:

Substituting back into the harvest equation:

With $a = qK$ and $b = \frac{q^2K}{r}$:

This quadratic function is linear in parameters $a$ and $b$—perfect for OLS estimation with harvest and effort data!

4. Adding Economics

Profit ($\pi$) equals revenue minus cost:

where $p$ is the price per ton of fish and $c$ is the cost per unit of fishing effort.

Maximizing profit:

This yields Maximum Economic Yield (MEY):

Compare to Maximum Sustainable Yield where $E_{MSY} = \frac{a}{2b}$: clearly $E_{MEY} < E_{MSY}$. Profit-maximizing fishermen should fish less than catch-maximizing fishermen.

5. The Carbon Cost Twist

Adding emission costs transforms total cost to:

where $e$ is the emission cost per unit of effort (emission rate × carbon price). The new optimal effort becomes:

Emission costs reduce optimal fishing by exactly $\frac{e}{2pb}$—nature charging rent for atmospheric carbon storage.

6. The Results: Everyone Wins

Table 1 reveals the stunning outcomes:

Table 1: ATNF Performance Under Different Management Scenarios

Key findings:

• 38% effort reduction → 60% profit increase
• 58,000+ tons less $\text{CO}_2$ annually
• ₩1.48 billion saved in emission costs

7. Why It Works

The tragedy unfolds daily: Each fisher thinks "If I don't catch these fish, someone else will." Everyone overfishes, depleting stocks and raising costs—individually rational but collectively insane. Reducing to MEY levels achieves:

• Stock recovery → higher catch per effort
• Less fuel use → lower emissions and costs
• Internalized emission costs → further effort reduction → healthier stocks

8. Policy Recommendations

Korea should:

1. Buy back 37% of the fleet—expensive but doubly effective
2. Set catches at MEY—let markets allocate effort
3. Include fisheries in carbon trading—internalize the externality
4. Subsidize engine upgrades—cleaner remaining boats

9. The Bottom Line

Environmental economics isn't tree-hugging versus profit-making—it's finding where they align. The math confirms ancient fishing wisdom: moderation is profitable, and sometimes the best fishing strategy is leaving the boat docked, not only for your profits, fish stocks, but also emissions.

In Korean fisheries, the path to higher profits literally runs through lower emissions. Doing well by doing good isn't just possible—it's mathematically optimal.