Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ:
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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Question
How would I go about answering this maths question
![(a)
In the simple model of a national economy:
Y=C+I+G
I= 25; G = 25
T = 0.2Y
C = 0.6 Yd
where Y is income, Y₁ is disposable income, T is tax, C is consumption.
G and I are not variables of the model but are values set by Government and other
non-governmental sectors.
(i)
What type of variables are G and I?
(ii)
Write Y in terms of C by substituting for I and G.
(iii)
(iv)
Find C in terms of Y only using the Tax and Consumption equations.
Use your answers to (ii) and (iii) to write the system of two simultaneous
equations in Y and C in matrix form. [Do not solve the equations].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7b7d550-5791-43d9-ad03-e8d2a5e38b61%2Fd1cfcab6-2b03-43a7-8228-f7d0c3e3e01b%2Fhu91h0a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a)
In the simple model of a national economy:
Y=C+I+G
I= 25; G = 25
T = 0.2Y
C = 0.6 Yd
where Y is income, Y₁ is disposable income, T is tax, C is consumption.
G and I are not variables of the model but are values set by Government and other
non-governmental sectors.
(i)
What type of variables are G and I?
(ii)
Write Y in terms of C by substituting for I and G.
(iii)
(iv)
Find C in terms of Y only using the Tax and Consumption equations.
Use your answers to (ii) and (iii) to write the system of two simultaneous
equations in Y and C in matrix form. [Do not solve the equations].
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