Question

Given the input matrix and the final demand vector:
 

A = \begin{bmatrix} 0.05 & 0.25 & 0.34 \\ 0.33 & 0.10 & 0.12 \\ 0.19 & 0.38 & 0 \end{bmatrix}, \quad d = \begin{bmatrix} 1800 \\ 200 \\ 900 \end{bmatrix}


a. Explain the economic meaning of the elements 0.330, and 200.
b. Explain the economic meaning (if any) of the third column sum.
c. Explain the economic meaning (if any) of the third row sum.
d. Write out the specific input-output matrix equation for this model.
e. Find the solution output levels of the three industries using Cramer’s rule.

11 Jan 2025
Answer :
Word Count : 436
Let's go step by step through this problem. --- ## Given Data We are given the input-output matrix \( A \) and the final demand vector \( d \): \[ A = \begin{bmatrix} 0.05 & 0.25 & 0.34 \\ 0.33 & 0.10 & 0.12 \\ 0.19 & 0.38 & 0 \end{bmatrix} \] \[ d = \begin{bmatrix} 1800 \\ 200 \\ 900 \end{bmatrix} \] ### (a) Economic Meaning of Certain Elements 1. \( A_{2,1} = 0.33 \) This means that industry 2 requires 0.33 units of input from industry 1 to produce 1 unit of its output. 2. \( A_{3,3} = 0 \) This means that industry 3 does not _________ ______ _______ _______ _____ ____ _____ ___ ______ ___ ___.
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