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 $0.39 from agriculture and $0.44 from tourism. Production of a​ dollar's worth of tourism requires an input of $0.43 from agriculture and $ 0.28 from tourism. Find the output from each sector that is needed to satisfy a final demand of $40 million for agriculture and $74 million for tourism.is 47420000 and 38320000 correct?

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Asked Nov 16, 2019
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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 $0.39 from agriculture and $0.44 from tourism. Production of a​ dollar's worth of tourism requires an input of $0.43 from agriculture and $ 0.28 from tourism. Find the output from each sector that is needed to satisfy a final demand of $40 million for agriculture and $74 million for tourism.

is 47420000 and 38320000 correct?

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Expert Answer

Step 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 $0.39 from agriculture and $0.44 from tourism. Production of a​ dollar's worth of tourism requires an input of $0.43 from agriculture and $ 0.28 from tourism. Find the output from each sector that is needed to satisfy a final demand of $40 million for agriculture and $74 million for tourism.

Step 2

Let x be the output from Agriculture

Y be the output from Tourism.

According to given information we get

Total output from agriculture
...()
x 0.39x 0.44y + 40
Total output from tourism
..i)
y 0.48.x 0.28y 74
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Total output from agriculture ...() x 0.39x 0.44y + 40 Total output from tourism ..i) y 0.48.x 0.28y 74

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Step 3

Write in matrix f...

X= MX+ D
Where X -output matrix
Mtechnolog y matrix
D= final demand matrix
039 0.44x
0.43 0.28
40
70
X-(I-M) D
10.39-0.44
-0.43 1-0.28
40
70
0.61-0.44T[40
70
-0.43 0.72
T0.72 0.4440
1
0.4392-0.1892 0.43 0.61|70
10.72 0.44 40
0.25 0.43 0.61 70
2.88 1.76 40
| 1.72 2.44 70
2.88 (40)+1.76(70)
|1.72 (40)+2.44(70)
115.2+123.2
68.8+170.8
238.4
239.6
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X= MX+ D Where X -output matrix Mtechnolog y matrix D= final demand matrix 039 0.44x 0.43 0.28 40 70 X-(I-M) D 10.39-0.44 -0.43 1-0.28 40 70 0.61-0.44T[40 70 -0.43 0.72 T0.72 0.4440 1 0.4392-0.1892 0.43 0.61|70 10.72 0.44 40 0.25 0.43 0.61 70 2.88 1.76 40 | 1.72 2.44 70 2.88 (40)+1.76(70) |1.72 (40)+2.44(70) 115.2+123.2 68.8+170.8 238.4 239.6

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