Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 50% of its output 'to Chemicals and 30% to Fuels and retains the rest. Complete parts (a and (b) below.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 6EQ: Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of...
icon
Related questions
icon
Concept explainers
Question

linear hw, please show ALL WORK AND LABEL PARTS A AND B

Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and
Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and
retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery
and retains the rest. Machinery sells 50% of its output to Chemicals and 30% to
Fuels and retains the rest. Complete parts (a and (b) below.
Distribution of Output from:
Chemicals
Fuels
Machinery
Purchased by:
0.1
0.7
0.5
Chemicals
0.3
0.1
0.3
Fuels
0.6
0.2
0.2
Machinery
a. Develop a system of equations that leads to prices at which each sector's income
matches its expenses. Then write the augmented matrix that can be row reduced to
find these prices. The first, second, and third columns of the matrix should
correspond to Chemicals, Fuels, and Machinery, respectively.
b. Find a set of equilibrium prices when the price for the Machinery output is 100
units.
Transcribed Image Text:Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 50% of its output to Chemicals and 30% to Fuels and retains the rest. Complete parts (a and (b) below. Distribution of Output from: Chemicals Fuels Machinery Purchased by: 0.1 0.7 0.5 Chemicals 0.3 0.1 0.3 Fuels 0.6 0.2 0.2 Machinery a. Develop a system of equations that leads to prices at which each sector's income matches its expenses. Then write the augmented matrix that can be row reduced to find these prices. The first, second, and third columns of the matrix should correspond to Chemicals, Fuels, and Machinery, respectively. b. Find a set of equilibrium prices when the price for the Machinery output is 100 units.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Points, Lines and Planes
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage