[M] The demand vector in Exercise 13 is reasonable for 1958 data, but Leontief’s discussion of the economy in the reference cited there used a demand vector closer to 1964 data:

Find the production levels needed to satisfy this demand.

Reference Exercise 13:

[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.)

Solution

Step 1:

Let

It turns out is invertible.

Here for the final demand ,the solution to is easy with computer software such as Matlab.

Rounded to 4 places,matlab gives

So,