Multiplier Decomposition and Nonnegativity of Leontief Inverses

With the relation to the application of input-output models in a regional context; much attention has been paid to the relationships between their respective multipli ers and the methods for deriving the relationships are classified into two categories; the partition method and the multiplicative method. In Batey's comprehensive work (Batey(1985)) the former with the highest degree of completion we can find and Trigg and Madden (1990) provides us with the latter. However, a careful scrutiny of Miyazawa (1976, Chapters 1 and 2) suggests the third method which we develop here.