1. The total population of a tropical island is 200 people. Every day each person either goes fishing or gathers fruit. All food is shared between the islanders and none is traded outside the island. The production of 5 units of fish requires four people and one unit of fish. The production of 1 unit of fruit requires one person. Each person in the island requires 2/5 units of fish and 3/5 units of fruit.
2. (a)Write the input-output matrixAfor the closed Leontief economic model which describes this island.Hint: the sectors are fish, fruit and people (labour).
3. (b)Solve the closed Leontief economic model using Gauss-Jordan elimination by hand, showing working, to find the production vector.
4. (c)On this island, how many people go fishing and how many people gather fruit?