5. Consider the production model x = Cx+d for an economy with two sectors, where C c = [ 2] .0 .6 d= 50 30 Use an inverse matrix to determine the production level necessary to satisfy the final demand.
5. Consider the production model x = Cx+d for an economy with two sectors, where C c = [ 2] .0 .6 d= 50 30 Use an inverse matrix to determine the production level necessary to satisfy the final demand.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
5
![2005 018 0
bban mi
10
Exercises 1-4 refer to an economy that is divided into three
sectors-manufacturing, agriculture, and services. For each unit
of output, manufacturing requires .10 unit from other companies
in that sector, .30 unit from agriculture, and .30 unit from services.
For each unit of output, agriculture uses .20 unit of its own output,
.60 unit from manufacturing, and .10 unit from services. For each
unit of output, the services sector consumes .10 unit from services,
.60 unit from manufacturing, but no agricultural products.
1. Construct the consumption matrix for this economy, and de-
termine what intermediate demands are created if agriculture
plans to produce 100 units.
2. Determine the production levels needed to satisfy a final
demand of 18 units for agriculture, with no final demand for
the other sectors. (Do not compute an inverse matrix.)
3. Determine the production levels needed to satisfy a final
demand of 18 units for manufacturing, with no final demand
for the other sectors. (Do not compute an inverse matrix.)
4. Determine the production levels needed to satisfy a final de-
mand of 18 units for manufacturing, 18 units for agriculture,
and 0 units for services.
5. Consider the production model x = Cx+d for an economy
with two sectors, where
.0
.5
c = [82]
C
.6
.2
50
30
d =
Use an inverse matrix to determine the production level
necessary to satisfy the final demand.
[.1
c = [/
.5
6. Repeat Exercise 5 with C =
.6
18
[2], and d= [1]
.2
7. Let C and d be as in Exercise 5.
a. Determine the production level necessary to satisfy a final
demand for 1 unit of output from sector 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6bb2273-ae71-4436-8787-039b32bc3b2f%2F82ac936f-a0af-4460-8d18-225881e30d67%2Fb5lz6z7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2005 018 0
bban mi
10
Exercises 1-4 refer to an economy that is divided into three
sectors-manufacturing, agriculture, and services. For each unit
of output, manufacturing requires .10 unit from other companies
in that sector, .30 unit from agriculture, and .30 unit from services.
For each unit of output, agriculture uses .20 unit of its own output,
.60 unit from manufacturing, and .10 unit from services. For each
unit of output, the services sector consumes .10 unit from services,
.60 unit from manufacturing, but no agricultural products.
1. Construct the consumption matrix for this economy, and de-
termine what intermediate demands are created if agriculture
plans to produce 100 units.
2. Determine the production levels needed to satisfy a final
demand of 18 units for agriculture, with no final demand for
the other sectors. (Do not compute an inverse matrix.)
3. Determine the production levels needed to satisfy a final
demand of 18 units for manufacturing, with no final demand
for the other sectors. (Do not compute an inverse matrix.)
4. Determine the production levels needed to satisfy a final de-
mand of 18 units for manufacturing, 18 units for agriculture,
and 0 units for services.
5. Consider the production model x = Cx+d for an economy
with two sectors, where
.0
.5
c = [82]
C
.6
.2
50
30
d =
Use an inverse matrix to determine the production level
necessary to satisfy the final demand.
[.1
c = [/
.5
6. Repeat Exercise 5 with C =
.6
18
[2], and d= [1]
.2
7. Let C and d be as in Exercise 5.
a. Determine the production level necessary to satisfy a final
demand for 1 unit of output from sector 1.
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