### Economic Input-Output Model: Energy and Transportation SectorAn economy is based on Energy (E) and Transportation (T). To produce a dollar's worth of output from the energy sector, an input of $0.20 from energy and $0.35 from transportation is needed. For a dollar’s worth of output from the transportation sector, an input of $0.30 from energy and $0.15 of transportation is required. The input-output matrix representing this economy is:\[ \begin{bmatrix} E & T \\ \hline0.20 & 0.30 \\ 0.35 & 0.15 \end{bmatrix} \]In this matrix:- The first row represents the input requirements for the energy sector. - To produce $1 in the energy sector, $0.20 energy from itself and $0.35 of transportation is needed.- The second row represents the input requirements for the transportation sector. - To produce $1 in the transportation sector, $0.30 energy and $0.15 of transportation is required.To find the total output required to meet a consumer demand of $80 million worth of Energy and $100 million worth of Transportation, we need to solve this linear system using the given matrix.This input-output model can be used in economics to determine how different sectors are interconnected and to predict the total production requirements to meet certain levels of consumer demand across various sectors.

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An cconomy is based on Energy (E) and Transportation (T). In order to produce a dollar's worth of output from the energy sector, input of $0.20 form energy and $0.35 from transportation is needed. For a dollar's worth of output from the transportation sector, input of $0.30 from energy and $0.15 of transportation is needed. The input output matrix describing this economy is E E0.20 0.30 Т 0.35 0.15 Find the total output, to satisfy a consumer demand of $80 million worth of Energy and $100 million worth of Transportation.

An cconomy is based on Energy (E) and Transportation (T). In order to produce a dollar's worth of output from the energy sector, input of $0.20 form energy and $0.35 from transportation is needed. For a dollar's worth of output from the transportation sector, input of $0.30 from energy and $0.15 of transportation is needed. The input output matrix describing this economy is E E0.20 0.30 Т 0.35 0.15 Find the total output, to satisfy a consumer demand of $80 million worth of Energy and $100 million worth of Transportation.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

### Economic Input-Output Model: Energy and Transportation Sector

An economy is based on Energy (E) and Transportation (T). To produce a dollar's worth of output from the energy sector, an input of $0.20 from energy and $0.35 from transportation is needed. For a dollar’s worth of output from the transportation sector, an input of $0.30 from energy and $0.15 of transportation is required. The input-output matrix representing this economy is:

\[
\begin{bmatrix}
E & T \\
\hline
0.20 & 0.30 \\
0.35 & 0.15
\end{bmatrix}
\]

In this matrix:
- The first row represents the input requirements for the energy sector.
- To produce $1 in the energy sector, $0.20 energy from itself and $0.35 of transportation is needed.
- The second row represents the input requirements for the transportation sector.
- To produce $1 in the transportation sector, $0.30 energy and $0.15 of transportation is required.

To find the total output required to meet a consumer demand of $80 million worth of Energy and $100 million worth of Transportation, we need to solve this linear system using the given matrix.

This input-output model can be used in economics to determine how different sectors are interconnected and to predict the total production requirements to meet certain levels of consumer demand across various sectors.

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