Leontief Inverse

The overall impact on gross income of advances of capitalist money is captured by the Leontief inverse (I - At)-1. To explore this relationship in more detail the Leontief inverse can be expressed as a series of impacts,... 

The purpose of this appendix is to clarify the role of surplus value in the interindustry model of the circuit of money in Chapter 4. The elements of the Leontief inverse in... 

Step 4 Use the Leontief Inverse matrix (7 — A ) and the following formulas are used to assess the quantity of CO2 emissions in a given region ... 

The 10 model includes an lO table, a technical coefficients table, and a Leontief inverse matrix as described in Sect. 26.3.1. The case uses the input coefficients table of producers prices [34] shown in matrix A. The LQ method is then used to estimate Penghu s technical coefficients matrix A Finally, Penghu s Leontief inverse matrix (/ A ) is calculated. 

Table 26.4 Penghu s total Leontief inverse matrix (I—A ) ...

Penghu, we multiply the national coeflhcients by LQ, LQc, LQ/. After acquiring the technical coefiicient table of Penghu, the Leontief inverse matrix (/ — A ) is calculated as shown in Table 26.4. 

In addition to Penghu s Leontief inverse matrix (/ - A ) , the final demand vector for tourism F is estimated for Penghu. In this paper, we estimate the final demand vector of tourism F (Table 26.5) based on the statistical reports of the number of visitors to principal scenic spots in Taiwan in 2006 and the travel time data of Taiwan residents in 2007. Afterward, the Leontief inverse matrix (/ — A ) , the final demand vector of tourism F, and the formula X = I — A ) f are used to estimate the direct vector (X) of required economic inputs for all sectors are computed as shown in Table 26.6. 

We further note that Equation 8.1 can be rewritten to its simplified form, where L = (I - A)-l is the Leontief inverse matrix ... 

The Leontief inverse matrix is also called the total requirements matrix since each element, /, represents the increase in the output for sector i that is required for every unit of increase in the final demand of sector j. Note that, as a result of convention that has been established among users of I-O over the past decades, flows in Equations 8.1-8.3 are expressed in terms of economic value, which facilitates use of I-O for economic planning purposes. Nevertheless, it has been clearly established that the same general... 

For this example, we can compute for the Leontief inverse matrix, L, as ... 

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