b. 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.The augmented matrix is ?? Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 50% to Machinery andretains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 40% of its output to Chemicals and 20% to Fuelsand retains the rest. Complete parts (a) through (c) below.a. Construct the exchange table for this economy.Distribution of Output from:FuelsChemicalsMachineryPurchased by:0.20.70.4Chemicals0.30.10.3Fuels0.2(Type integers or decimals.)0.50.3Machinery c. Find a set of equilibrium prices when the price for the Machinery output is 60 units.67.1= 42.4PMachineryPChemicals60.0%3DPFuels%3D(Type integers or decimals rounded to the nearest tenth as needed.)

b. 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. The augmented matrix is ??

b. 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. The augmented matrix is ??

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...

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Question

The augmented matrix is ??

Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 50% to Machinery and
retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 40% of its output to Chemicals and 20% to Fuels
and retains the rest. Complete parts (a) through (c) below.
a. Construct the exchange table for this economy.
Distribution of Output from:
Fuels
Chemicals
Machinery
Purchased by:
0.2
0.7
0.4
Chemicals
0.3
0.1
0.3
Fuels
0.2
(Type integers or decimals.)
0.5
0.3
Machinery

c. Find a set of equilibrium prices when the price for the Machinery output is 60 units.
67.1
= 42.4
PMachinery
PChemicals
60.0
%3D
PFuels
%3D
(Type integers or decimals rounded to the nearest tenth as needed.)

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