Question
Given the input matrix and the final demand vector:
a. Explain the economic meaning of the elements ,
, and
.
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.
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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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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