Solution Found!
[M] The consumption matrix C below is based on
Chapter 2, Problem 13E(choose chapter or problem)
[M] The consumption matrix C below is based on input– output data for the U.S. economy in 1958, with data for 81 sectors grouped into 7 larger sectors: (1) nonmetal household and personal products, (2) final metal products (such as motor vehicles), (3) basic metal products and mining, (4) basic nonmetal products and agriculture, (5) energy, (6) services, and (7) entertainment and miscellaneous products.2 Find the production levels needed to satisfy the final demand d. (Units are in millions of dollars.)
\(\left[\begin{array}{ccccccc}.1588 & .0064 & .0025 & .0304 & .0014 & .0083 & .1594 \\ .0057 & .2645 & .0436 & .0099 & .0083 & .0201 & .3413 \\ .0264 & 1506 & .3557 & .0139 & .0142 & .0070 & .0236 \\ .3299 & .0565 & .0495 & .3636 & .0204 & .0483 & .0649 \\ .0089 & .0081 & .0333 & .0295 & .3412 & .0237 & .0020 \\ .1190 & .0901 & .0996 & .1260 & .1722 & .2368 & .3369 \\ .0063 & .0126 & .0196 & .0098 & .0064 & .0132 & .0012\end{array}\right] \text {, }\)
\(\mathbf{d}=\left[\begin{array}{r}74,000 \\ 56,000 \\ 10,500 \\ 25,000 \\ 17,500 \\ 196,000 \\ 5,000\end{array}\right]\)
Questions & Answers
QUESTION:
[M] The consumption matrix C below is based on input– output data for the U.S. economy in 1958, with data for 81 sectors grouped into 7 larger sectors: (1) nonmetal household and personal products, (2) final metal products (such as motor vehicles), (3) basic metal products and mining, (4) basic nonmetal products and agriculture, (5) energy, (6) services, and (7) entertainment and miscellaneous products.2 Find the production levels needed to satisfy the final demand d. (Units are in millions of dollars.)
\(\left[\begin{array}{ccccccc}.1588 & .0064 & .0025 & .0304 & .0014 & .0083 & .1594 \\ .0057 & .2645 & .0436 & .0099 & .0083 & .0201 & .3413 \\ .0264 & 1506 & .3557 & .0139 & .0142 & .0070 & .0236 \\ .3299 & .0565 & .0495 & .3636 & .0204 & .0483 & .0649 \\ .0089 & .0081 & .0333 & .0295 & .3412 & .0237 & .0020 \\ .1190 & .0901 & .0996 & .1260 & .1722 & .2368 & .3369 \\ .0063 & .0126 & .0196 & .0098 & .0064 & .0132 & .0012\end{array}\right] \text {, }\)
\(\mathbf{d}=\left[\begin{array}{r}74,000 \\ 56,000 \\ 10,500 \\ 25,000 \\ 17,500 \\ 196,000 \\ 5,000\end{array}\right]\)
ANSWER:Solution Step 1:Let It turns out is invertible. Here for