Input Output model

[Neel Tulsan]

Need some help with this homework. I don't want the solution to the problem, but the steps to solve the problem.

Assuming X =AX + D
or X = inverse(I-A).D

should I use matrix A to solve the Cramer's rule, or should I use (I-A)?

The input output model for the following sectors have been input below.​
		in Millions$​
​	Agriculture​	Manufacture​	Energy​
Agriculture​	11​	3​	0​
Manufacture​	1​	13​	4​
Energy​	0​	1​	10​
Total​	12​	17​	14​
Find the technology matrix A​
Assuming a rise in external demand for agriculture of $3million and Manufacture $2million, find:​
(ii) the system of linear equation that would give the change in production?​
(iii) the change in production using Cramer's Rule​
(iv) the change in production using Gauss Jordan Elimination​

 

[Deleted member 4993]

Need some help with this homework. I don't want the solution to the problem, but the steps to solve the problem.

Assuming X =AX + D
or X = inverse(I-A).D

should I use matrix A to solve the Cramer's rule, or should I use (I-A)?

The input output model for the following sectors have been input below.​
		in Millions$​
​	Agriculture​	Manufacture​	Energy​
Agriculture​	11​	3​	0​
Manufacture​	1​	13​	4​
Energy​	0​	1​	10​
Total​	12​	17​	14​
Find the technology matrix A​
Assuming a rise in external demand for agriculture of $3million and Manufacture $2million, find:​
(ii) the system of linear equation that would give the change in production?​
(iii) the change in production using Cramer's Rule​
(iv) the change in production using Gauss Jordan Elimination​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem.

 

[HallsofIvy]

Need some help with this homework. I don't want the solution to the problem, but the steps to solve the problem.

Assuming X =AX + D
or X = inverse(I-A).D

should I use matrix A to solve the Cramer's rule, or should I use (I-A)?

The input output model for the following sectors have been input below.​
		in Millions$​
​	Agriculture​	Manufacture​	Energy​
Agriculture​	11​	3​	0​
Manufacture​	1​	13​	4​
Energy​	0​	1​	10​
Total​	12​	17​	14​
Find the technology matrix A​
Assuming a rise in external demand for agriculture of $3million and Manufacture $2million, find:​
(ii) the system of linear equation that would give the change in production?​
(iii) the change in production using Cramer's Rule​
(iv) the change in production using Gauss Jordan Elimination​

Well, what is your understanding of "Cramer's rule" and "Gauss Jordan Elimination" to solve an equation like Ax= b?

 

[Neel Tulsan]

1 unit for each item gives me a technology matrix of

11/12	3/17	0
1/12	13/17	4/14
0	1/17	10/14

From there I can do the gauss jordan and cramer's. There's no problem with that. I;ve got the answers for all the parts. Please understand my question: for (iii) and (iv), I am not sure if I should do the Gauss Jordan / Cramer's using my technology matrix (A) where D = 3 ,2 and 0, or with the inverse, that is (I-A).

Here's my Cramer's when I use technology Matrix A. - x for agriculture, y for manufacture and z for energy.

A	0.92​	0.18​	0.00​		Ax	3​	0.18​	0.00​		x	2.79​
	0.08​	0.76​	0.29​			2​	0.76​	0.29​
	0.00​	0.06​	0.71​			0​	0.06​	0.71​		y	2.42​
Det A	0.4702​					Det Ax	1.3110​			z	-0.20​
Ay	0.92​	3​	0.00​		Az	0.92​	0.18​	3​
	0.08​	2​	0.29​			0.08​	0.76​	2​
	0.00​	0​	0.71​			0.00​	0.06​	0​
Det Ay	1.1360​					Det Az	-0.0960​

So the change in production when I use A is 2.79, 2.42 and -0.20. (Wondering how energy can be negative by the way)

Got the same change in production with the Gauss Jordan so no problem with that one too.

 

[Neel Tulsan]

1 unit for each item gives me a technology matrix of

11/12	3/17	0
1/12	13/17	4/14
0	1/17	10/14

From there I can do the gauss jordan and cramer's. There's no problem with that. I;ve got the answers for all the parts. Please understand my question: for (iii) and (iv), I am not sure if I should do the Gauss Jordan / Cramer's using my technology matrix (A) where D = 3 ,2 and 0, or with the inverse, that is (I-A).

Here's my Cramer's when I use technology Matrix A. - x for agriculture, y for manufacture and z for energy.

A	0.92	0.18	0.00		Ax	3	0.18	0.00		x	2.79
	0.08	0.76	0.29			2	0.76	0.29
	0.00	0.06	0.71			0	0.06	0.71		y	2.42
Det A	0.4702					Det Ax	1.3110			z	-0.20
Ay	0.92	3	0.00		Az	0.92	0.18	3
	0.08	2	0.29			0.08	0.76	2
	0.00	0	0.71			0.00	0.06	0
Det Ay	1.1360					Det Az	-0.0960

So the change in production when I use A is 2.79, 2.42 and -0.20. (Wondering how energy can be negative by the way)

Got the same change in production with the Gauss Jordan so no problem with that one too.

Thanks