Answered: Consider a simple economic system…

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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Question

Consider a simple economic system consisting of three industries: electricity, water, and coal. Production, or output, of one unit of electricity requires 0.5 unit of itself, 0.25 unit of water, and 0.25 unit of coal. Production of one unit of water requires 0.1 unit of electricity, 0.6 unit of itself, and 0 units of coal. Production of one unit of coal requires 0.2 unit of electricity, 0.15 unit of water, and 0.5 unit of itself. Find the input-output matrix for this system.

Expert Solution

Step 1: Given information:

Production, or output, of one unit of electricity, requires 0.5 unit of itself, 0.25 unit of water, and 0.25 unit of coal.

Production of one unit of water requires 0.1 unit of electricity, 0.6 unit of itself, and 0 units of coal.

Production of one unit of coal requires 0.2 unit of electricity, 0.15 unit of water, and 0.5 unit of itself. F

To find: the input-output matrix for this system.

Step 2: Explanation

The input-out matrix is shown below:

$table row blank cell left parenthesis O u t p u t right parenthesis end cell blank row E W C end table open square brackets table row cell 0.5 end cell cell 0.1 end cell cell 0.2 end cell row cell 0.25 end cell cell 0.6 end cell cell 0.15 end cell row cell 0.25 end cell 0 cell 0.5 end cell end table close square brackets table row E row W row C end table space left parenthesis I n p u t right parenthesis$

Column entries indicate the amounts required by each industry from others and from itself to produce one unit of output whereas the row entries indicate the amounts supplied by each industry to others and to itself to produce one unit of output

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