Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met.

Question

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met. ​  ​

Quizplus · Accepted Answer

We need to find the output of each industry so that the demands of both industries and the open sector are met.
Let's find the total output necessary to meet the demand vector D:
Total Output = AD + D
Total Output = 
[2 1.2;
1.6 3][60;
40]
+ [50;
30]
= [130;
130]
To meet the demands of both industries and the open sector, the output vector should be equal to the total output vector. To find the output of each industry, we look at the columns of the output vector. Thus, the output of the first industry is 43.33 million and the output of the second industry is 46.67 million.
Therefore, the answer is C.

Matrix a Is an Input-Output Matrix Associated with an Economy