13. Matrices and Their Applications

Elements of a matrix can be any object.

To avoid repeating ‘the same size’ hereafter I assume that vectors and matrices are conformable for multiplication.

I am using ‘material’ as a generic name for both primary and intermediate inputs.

The size of this economy is roughly \(1/20\)th of that of the US. According to the Congressional Budget Office latest report (May 2013), the size of US budget deficit is about $642 billion. Based on the latest BEA’s estimate released on June 26, 2013, the US GDP is $15,984 billion. The US deficit is, therefore, about 4 % of the GDP.

These sectors are part of a 20-sector classification known as The North American Industry Classification System (NAICS). According to the Unitaed States’ Census Bureaue “NAICS is the standard used by Federal statistical agencies in classifying business establishments for the purpose of collecting, analyzing, and publishing statistical data related to the U.S. business economy. NAICS was developed under the auspices of the Office of Management and Budget (OMB), and adopted in 1997 to replace the Standard Industrial Classification (SIC) system. It was developed jointly by the U.S. Economic Classification Policy Committee (ECPC), Statistics Canada , and Mexico’s Instituto Nacional de Estadistica y Geografia , to allow for a high level of comparability in business statistics among the North American countries. NAICS is a 2- through 6-digit hierarchical classification system, offering five levels of detail. Each digit in the code is part of a series of progressively narrower categories, and the more digits in the code signify greater classification detail. The first two digits designate the economic sector, the third digit designates the subsector, the fourth digit designates the industry group, the fifth digit designates the NAICS industry, and the sixth digit designates the national industry.” See Table 13.4 at the end of this chapter.

The closed model can include the government and foreign trade, treated as two industries.

Imports and exports are also excluded.