Question

After graduation you read an article about overfishing in the South China Sea. The article states that at the current rate of fishing, the population of fish in the South China Sea will be depleted in the near future. You write a post about it on social media and the next day you are hired by the Permanent Court of Arbitration to help solve the conflict between a number of countries that fish in the South China Sea.

a) Assume that all fish in the South China Sea are exactly the same, and each fish can be sold in international markets at $1 per fish. Assume also that fishing companies (as a whole) have a marginal cost of 0.1Q, where Q is the quantity of fish (in millions). How many fish will be fished? As always, explain your answers and show your calculations.

b) A prestigious economic consulting firm estimates the damage that fishing companies do to each other due to overfishing. In particular, assume that the social marginal cost of fishing is estimated to be 0.2Q, where Q is the quantity of fish (in millions). How many fish should be fished?

c) Assume that there are 20 million fish in the South China Sea, and at the beginning of every year 10 million fish are born and 5 million fish die of old age. If the Permanent Court of Arbitration is not able to solve the problem of overfishing, what will happen to fish in the South China Sea? How many years will it take for that to happen?

d) Assume the Permanent Court of Arbitration is able to issue binding mandates to all countries in the South China Sea. Propose TWO ways to implement the optimal amount of fishing, and show how they would work and why they would achieve the desired result.

e) Suppose instead that the Permanent Court of Arbitration cannot enforce any mandates, and is only able to make recommendations to prevent overfishing. Will the countries in the South China Sea want to follow your recommendations?

Answer 1

a.) Here, the market of fish is perfectly competitive. Hence, the per unit price is also the marginal revenue of the fish market. The per unit marginal cost is given. Hence, using the laws of perfect competition, we can find the quantity of fish as follows -

0.1Q = 1

Q = 1/0.1 = 10

Hence, 10 million fish will be fished.

b.) If the social marginal cost is 0.2Q, then this should be equated with the price of fish to find the socially efficient quantity of fish that should be fished. We get -

0.2Q = 1

Q = 1/0.2 = 5

Hence, 5 million fish will be fished.

c.) If the Permanent Court of Arbitration is not able to solve the problem, then the fish in the South China Sea will deplete.

If there are 20 million fish in the sea, and 10 million are added every year, and 5 million die, that means only around 5 million are added every year. Total fish are 20+5 = 25 million. According to the equilibrium conditions, if 10 million are fished out, then only 15 million remain at the end of the first year.

Similarly, at the beginning of the 2nd year,  here are 15 million fish in the sea, and 10 million are added, and 5 million die. Total fish are 15+5 = 20 million. According to the equilibrium conditions, if 10 million are fished out, then only 10 million remain at the end of the second year.

Similarly, at the beginning of the 3rd year,  here are 10 million fish in the sea, and 10 million are added, and 5 million die. Total fish are 10+5 = 15 million. According to the equilibrium conditions, if 10 million are fished out, then only 5 million remain at the end of the third year.

Finally, at the beginning of the 4th year,  here are 5 million fish in the sea, and 10 million are added, and 5 million die. Total fish are 5+5 = 15 million. According to the equilibrium conditions, if 10 million are fished out, then no fish remain at the end of the third year.

Hence, at the present rate, in 4 years, all the fish will get depleated.

d.) Two ways to prevent overfishing can be as follows -

Taxing: Imposing a tax on the quantity fished can help prevent overfishing as the more they fish, the more tax they will have to pay.

Penalty: The government can fix the quantity of fish that can be fished, and can impose a corrective penalty on every violation of that quantity.

e.) The countries will be reluctant to follow the recommendations and hence preventive measures have to be adopted like taxes and penalties. This is because given the fact that overfishing has a negative externality, the society always has a tendency of producing more than the socially optimum quantity.