Fish or Fruit: Production Possibilities and Trade
An island economy uses all its land and labour to produce two goods, fish and fruit. Its daily production possibilities are: 0 fish and 100 tonnes of fruit; 20 fish and 90 tonnes of fruit; 40 fish and 70 tonnes of fruit; 60 fish and 40 tonnes of fruit; 80 fish and 0 tonnes of fruit. At present, poor organisation and seasonal unemployment mean the island produces 30 tonnes of fish and 70 tonnes of fruit. A neighbouring island offers a standing trade: it will give 2 tonnes of fruit for every 1 tonne of fish received. The island's fishermen say they can catch more fish, but fruit growers fear losing sales. The government wants to know whether the island should produce at full capacity, and whether the trade offer is worth accepting. You are asked to advise.
1. Calculate the opportunity cost of fish at each segment of the frontier and explain why it changes.
Read the worked answer
Moving along the frontier:
- From 0 fish to 20 fish, fruit falls from 100 to 90 tonnes. Opportunity cost = 10 / 20 = 0.5 tonnes of fruit per tonne of fish.
- From 20 to 40 fish, fruit falls from 90 to 70. Opportunity cost = 20 / 20 = 1.0 tonne of fruit per tonne of fish.
- From 40 to 60 fish, fruit falls from 70 to 40. Opportunity cost = 30 / 20 = 1.5 tonnes of fruit per tonne of fish.
- From 60 to 80 fish, fruit falls from 40 to 0. Opportunity cost = 40 / 20 = 2.0 tonnes of fruit per tonne of fish.
The opportunity cost rises because resources are not equally suited to both activities. The first fishermen are likely to be those with the best boats and fishing grounds; as more fish are produced, land and labour better suited to fruit are diverted. This gives the frontier its bowed-out shape and illustrates increasing opportunity cost.
2. Is the current production combination efficient? Explain what moving to the frontier would require and what it would cost.
Read the worked answer
The current combination is 30 tonnes of fish and 70 tonnes of fruit. At 30 fish, the frontier would allow 80 tonnes of fruit, because the segment between 20 fish and 40 fish implies that each extra 10 fish costs 10 tonnes of fruit. The island is therefore inside its frontier: it could have 10 more tonnes of fruit without giving up any fish.
The combination is inefficient. The cause is poor organisation and seasonal unemployment, not a shortage of resources. Moving to the frontier would require using idle labour and land better, improving transport or storage, and reducing seasonal gaps in work. If the move uses otherwise unemployed resources, the opportunity cost in terms of forgone fruit may be low or zero. But there may still be costs: training, management time, or investment in equipment. The government should compare those costs with the 10 tonnes of fruit gained.
3. Should the island accept the trade offer? Show the gains from specialisation and trade with a numerical example.
Read the worked answer
The trade offer is 1 tonne of fish for 2 tonnes of fruit. Compare this with the domestic opportunity cost of fish. Up to 60 fish, the opportunity cost of fish is at most 1.5 tonnes of fruit, which is less than the trade price of 2. So the island has a comparative advantage in fish and should specialise in fish, not fruit.
A numerical example: suppose the island moves to 60 fish and 40 fruit on its frontier. It then exports 20 fish and receives 40 fruit in return. Consumption after trade is 40 fish and 80 fruit. Before trade, it produced 30 fish and 70 fruit. The gain is 10 fish and 10 fruit. Compared with the frontier combination of 40 fish and 70 fruit, it gains 10 fruit with the same fish.
The fruit growers' fear is understandable, but the island can consume more of both goods by specialising where its opportunity cost is lower. The judgement is to accept the offer, while managing the adjustment for fruit growers through retraining or a gradual shift. The offer is beneficial as long as the trade price stays above the domestic opportunity cost of fish.