The total population of a tropical island is 200 people. Each person either goes fishing or gathers fruit every day. All food is shared among the islanders, and none is exchanged with anyone outside the island. Four people and one unit of fish are needed to produce five units of fish. One individual is required to produce one unit of fruit. Each islander needs 2/5 unit of fish and 3/5 unit of fruits. (a) Write the input-output matrix A for the closed Leontief economic model which describes this island. Hint: the sectors are fish, fruit and people (labour). (b) Solve the closed Leontief economic model using Gauss–Jordan elimination by hand, showing working, to find the production vector. (c) On this island, how many people go fishing and how many people gather fruit?
The total population of a tropical island is 200 people. Each person either goes fishing or gathers fruit every day. All food is shared among the islanders, and none is exchanged with anyone outside the island. Four people and one unit of fish are needed to produce five units of fish. One individual is required to produce one unit of fruit. Each islander needs 2/5 unit of fish and 3/5 unit of fruits.
(a) Write the input-output matrix A for the closed Leontief economic model which describes this island. Hint: the sectors are fish, fruit and people (labour).
(b) Solve the closed Leontief economic model using Gauss–Jordan elimination by hand, showing working, to find the production
(c) On this island, how many people go fishing and how many people gather fruit?
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