Worksheet #9 Section 2.6(1)
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George Mason University *
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Course
111
Subject
Mathematics
Date
Apr 3, 2024
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MATH 111 Worksheet #9 Section 2.6 Input-Output Analysis (15 Points-SHOW WORK) Name____________________________________________________________________________ Submit on Gradescope
1.
The economy of a small island nation is based on two sectors, agriculture and tourism. Production of a dollar’s worth of agriculture requires an input of $0.20 from agriculture and $0.15 from tourism. Production of a dollar’s worth of tourism requires an input of $0.40 from agriculture and $0.30 from tourism. Find the output from each sector that is needed to satisfy a final demand of $60 million for agriculture and $80 million for tourism. a)
Find the input-output matrix A. b)
Find the consumer demand matrix D. c)
Find the production matrix 𝑿 = (𝑰 − 𝑨)
−𝟏
∗ 𝑫
(Show each step - you may use MatLabs.) d)
Answer the question.
2.
A town has a merchant, a baker, and a farmer. To produce $1 worth of output, the merchant requires $0.15 worth of baked goods and $0.35 worth of the farmer's products. To produce $1 worth of output, the baker requires $0.40 worth of the merchant's goods, $0.10 worth of his own goods, and $0.35 worth of the
farmer's goods. To produce $1 worth of output, the farmer requires $0.20 worth of the merchant's goods, $0.15 worth of baked goods, and $0.20 worth of his own products. How much should the merchant, baker, and farmer produce to meet a demand for $16,000 worth of output from the merchant, $14,000 worth of output from the baker, and $11,000 worth of output from the farmer? a.
Find the input-output matrix A. b.
To produce $1 worth of output, how much does the merchant require of itself? c.
To produce $1 worth of output, how much does the baker require of the farmer? d.
Find the consumer demand matrix D. e.
Find the production matrix X where 𝑿 = (𝑰 − 𝑨)
−𝟏
∗ 𝑫
(Show each step –
you may use MatLabs) f.
Answer the question.
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