(a) Suppose NationLand has 5 sectors: agriculture (A), energy (N), real estate (R), education (E), and entertainment (T). The following table represents the number of units of goods from other sectors used to produce one unit with a given sector. The table also lists the demand for each good from NationLand's trading partners. Internal and External Unit Demand Levels Internal Consumption Rates A NR E T 0.15 0.05 Agriculture (A) Energy (N) Real Estate (R) 0.01 0.025 0.1 0.05 0.025 0.01 0.02 0.0 1 0.3 0.1 0.05 0.125 0.4 0.25 0.1 0.2 0.15 Entertainment (T) 0.01 0.05 0.15 0.25 0.05 Education (E) 0.1 Outside Demand (total) 40 10 0 15 25 Let A, N, FR, E, and aT denote the number of units produced by the agri- culture (A), energy (N), real estate (R), education (E), and entertainment (T) sectors respectively. Write a system of equations that defines the number of units each sector should produce to satisfy both internal and external demand (total units). (b) Rewrite your system of equations in the form Ma= d' where M is a matrix of coefficients. What do a and d' represent in this model? (c) Does the system have a solution? In other words, is there a set of production levels that would satisfy both internal and external demand? Is this solution unique?
(a) Suppose NationLand has 5 sectors: agriculture (A), energy (N), real estate (R), education (E), and entertainment (T). The following table represents the number of units of goods from other sectors used to produce one unit with a given sector. The table also lists the demand for each good from NationLand's trading partners. Internal and External Unit Demand Levels Internal Consumption Rates A NR E T 0.15 0.05 Agriculture (A) Energy (N) Real Estate (R) 0.01 0.025 0.1 0.05 0.025 0.01 0.02 0.0 1 0.3 0.1 0.05 0.125 0.4 0.25 0.1 0.2 0.15 Entertainment (T) 0.01 0.05 0.15 0.25 0.05 Education (E) 0.1 Outside Demand (total) 40 10 0 15 25 Let A, N, FR, E, and aT denote the number of units produced by the agri- culture (A), energy (N), real estate (R), education (E), and entertainment (T) sectors respectively. Write a system of equations that defines the number of units each sector should produce to satisfy both internal and external demand (total units). (b) Rewrite your system of equations in the form Ma= d' where M is a matrix of coefficients. What do a and d' represent in this model? (c) Does the system have a solution? In other words, is there a set of production levels that would satisfy both internal and external demand? Is this solution unique?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Opening the model
In Session 2 you explored a simple Closed Leontief Exchange Model with five in-
terdependent industries. In the closed exchange model no goods or services enter
or leave a national economy. However, most nations import and export goods. For
this problem you will develop an open exchange model for the newly formed nation,
NationLand, then generalize the model to an economy with n sectors.
(a) Suppose NationLand has 5 sectors: agriculture (A), energy (N), real estate
(R), education (E), and entertainment (T). The following table represents the
number of units of goods from other sectors used to produce one unit with a
given sector. The table also lists the demand for each good from NationLand's
trading partners.
Internal and External Unit Demand Levels
Internal Consumption Rates
A N R
0.1 0.05 0.025 0.15
E
T
0.05
Agriculture (A)
Energy (N)
Real Estate (R)
0.01 0.025
0.1
0.25
0.01 0.02 0.0 1
0.4 0.3 0.1
Education (E) 0.1 0.05 0.15
Entertainment (T) 0.01 0.05 0.15 0.25 0.05
0.2
0.15
Outside Demand (total)
40
10
0
15
25
Let A, EN, R, E, and aT denote the number of units produced by the agri-
culture (A), energy (N), real estate (R), education (E), and entertainment (T)
sectors respectively. Write a system of equations that defines the number of
units each sector should produce to satisfy both internal and external demand
(total units).
(b) Rewrite your system of equations in the form M = d' where M is a matrix of
coefficients. What do a and d represent in this model?
(c) Does the system have a solution? In other words, is there a set of production
levels that would satisfy both internal and external demand? Is this solution
unique?
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