Input-Output Analysis, Linear Programming and Modified Multipliers



where I is the n × n identity matrix. The (I - A) matrix is called the Leontief matrix and
(I
- A)-1 is called the Leontief inverse matrix which shows the total-requirements matrix
for the economy. Equation (1) can be interpreted as
X = (I -A)-1Y , which means
changes in total industry output are predicted using the Leontief inverse matrix. Thus the
column sum of (I
- A)-1 is interpreted as the total changes in output from the changes in
final demand, which is called output multiplier

(2) α = i'(I - A)-1,
where
α is the output multiplier column vector and i is an n × 1 column vector of ones.
Thus kth element in
α implies there is exogenous change in final demand for kth sector
total industry output change by
αk. Likewise, the employment multiplier can be defined
as follows
(3) e
' = i'N(I - A)-1,
where N is the matrix with diagonal of n1,n2,..., nnand off diagonal all zeros, where

Employmenti

ni =----—------i- (i = 1, 2, ... n). Hence, the kth element in e implies there is an

Outputi

exogenous change in employment for kth sector, total industry output change by ek.

Similarly, the income multiplier can be defined as

(4)     h' = i'H(I - A)-1,
where H is the symmetric matrix with diagonal of h
1, h2, ., hn and off diagonal all zeros,

where hi =


household incomei
outputi


(i = 1, 2, . n).


Again, the kth element in h implies there




More intriguing information

1. Publication of Foreign Exchange Statistics by the Central Bank of Chile
2. The name is absent
3. Dual Inflation Under the Currency Board: The Challenges of Bulgarian EU Accession
4. SOME ISSUES IN LAND TENURE, OWNERSHIP AND CONTROL IN DISPERSED VS. CONCENTRATED AGRICULTURE
5. The name is absent
6. Changing spatial planning systems and the role of the regional government level; Comparing the Netherlands, Flanders and England
7. Wounds and reinscriptions: schools, sexualities and performative subjects
8. Using Surveys Effectively: What are Impact Surveys?
9. The Role of Land Retirement Programs for Management of Water Resources
10. The name is absent
11. The name is absent
12. The Impact of Optimal Tariffs and Taxes on Agglomeration
13. Developments and Development Directions of Electronic Trade Platforms in US and European Agri-Food Markets: Impact on Sector Organization
14. The name is absent
15. Analyse des verbraucherorientierten Qualitätsurteils mittels assoziativer Verfahren am Beispiel von Schweinefleisch und Kartoffeln
16. The name is absent
17. Cancer-related electronic support groups as navigation-aids: Overcoming geographic barriers
18. Strengthening civil society from the outside? Donor driven consultation and participation processes in Poverty Reduction Strategies (PRSP): the Bolivian case
19. Rent-Seeking in Noxious Weed Regulations: Evidence from US States
20. A THEORETICAL FRAMEWORK FOR EVALUATING SOCIAL WELFARE EFFECTS OF NEW AGRICULTURAL TECHNOLOGY