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Distribution of Output from: Transportation Manufacturing Services Purchased by: 0.3 0.8 Transportation 0.5 0.1 0.1 Manufacturing 0.5 0.6 0.1 Services Denote the total annual output (in dollars) of the transportation, manufacturing and services sectors by p,, PM and ps, respectively. (a) Formulate a homogeneous system of linear equations to describe the income/expenses requirements for the sectors. (b) Write (a) as a single matrix equation. (c) Solve (a) by applying Gauss-Jordan elimination method. (d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when the service sector has an annual output of $80?

Distribution of Output from: Transportation Manufacturing Services Purchased by: 0.3 0.8 Transportation 0.5 0.1 0.1 Manufacturing 0.5 0.6 0.1 Services Denote the total annual output (in dollars) of the transportation, manufacturing and services sectors by p,, PM and ps, respectively. (a) Formulate a homogeneous system of linear equations to describe the income/expenses requirements for the sectors. (b) Write (a) as a single matrix equation. (c) Solve (a) by applying Gauss-Jordan elimination method. (d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when the service sector has an annual output of $80?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 23EQ
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Given an exchange table for the economy that consists of three sectors. Distribution of Output from: Transportation Manufacturing Services Purchased by: 0.3 0.8 Transportation 0.5 0.1 0.1 Manufacturing 0.5 0.6 0.1 Services Denote the total annual output (in dollars) of the transportation, manufacturing and services sectors by p,, PM and ps, respectively. (a) Formulate a homogeneous system of linear equations to describe the income/expenses requirements for the sectors. (b) Write (a) as a single matrix equation. (c) Solve (a) by applying Gauss-Jordan elimination method. (d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when the service sector has an annual output of $80?
Transcribed Image Text:Given an exchange table for the economy that consists of three sectors. Distribution of Output from: Transportation Manufacturing Services Purchased by: 0.3 0.8 Transportation 0.5 0.1 0.1 Manufacturing 0.5 0.6 0.1 Services Denote the total annual output (in dollars) of the transportation, manufacturing and services sectors by p,, PM and ps, respectively. (a) Formulate a homogeneous system of linear equations to describe the income/expenses requirements for the sectors. (b) Write (a) as a single matrix equation. (c) Solve (a) by applying Gauss-Jordan elimination method. (d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when the service sector has an annual output of $80?
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