Question

K

Find the production matrix for the following input-output and demand matrices
using the open model.
A =
0.3 0.2
0.35 0.4
3
-[³]
6
D=
The production matrix is
(Round the final answer to the nearest hundredth as needed. Round all
intermediate values to four decimal places as needed.)

Answer 1

`\displaystyle\\Answer:\ \left [ {{\boxed{2.1}} \atop {\boxed{3.45}}} \right]`

Explanation:

`\displaystyle\\A=\left [ {0.3\ \ \ \ 0.2} \atop {0.35\ \ \ 0.4}} \right]\ \ \ \ \ D=\left [ {{3} \atop {6}} \right]\\\\A*D=\left [ {{c_(11)} \atop {c_(21)}} \right] \\\\c_(11)=a_(11)*b_(11)+a_(12)*b_(21)\\\\c_(11)=0.3*3+0.2*6\\\\c_(11)=0.9+1.2\\\\c_(11)=2.1\\\\c_(21)=a_(21)*b_(11)+a_(22)*b_(21)\\\\c_(21)=0,35*3+0,4*6\\\\c_(21)=1.05+2.4\\\\c_(21)=3.45\\\\Thus,\ A*D=\left [ {{2.1} \atop {3.45}} \right]`

Answer 2

The production matrix, obtained using the open model formula, is [2.1, 3.45] after rounding to the nearest hundredth.

Given matrices:

A = [0.3 0.2; 0.35 0.4]

D = [3; 6]

The identity matrix I is:

I = [1 0; 0 1]

Now, compute X = (I - A)^(-1)D:

(I - A) = [0.7 -0.2; -0.35 0.6]

Taking the inverse:

(I - A)^(-1) = [1.4286 0.5714; 0.7143 1.4286]

Finally, multiply by D:

X = [1.4286 0.5714; 0.7143 1.4286] * [3; 6]

X = [2.1; 3.45]

The correct production matrix is [2.1, 3.45], rounded to the nearest hundredth.