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Sekerka - Kyn - Hejl:  Price Systems Computable from Input-Output Coefficients

 

1. Assumptions of the model

 

 Consider an input-output model in physical terms in very detailed breakdown.

 LET
     
X  be  the column vector of total production in physical terms;
     
Y  be  the column vector of final production in physical terms;
     
A  be   the matrix of input-output coefficients;
     
B  be   the matrix of capital-output coefficients;
     
C  be   the matrix of coefficients of workers' consumption

Vectors X, Y and matrices A, B, C, are defined so that the following equations hold

AX  +  Y

 =

X

(1)

 

BX^

 =

F

(2)

 

     CX^     

 =

 (3)

 

 where

X^ is a diagonal matrix formed from the vector X;
F is a matrix whose element  fij is the stock of capital of the kind i in the branch j
D is a matrix whose element dij is the quantity of goods i consumed by workers in the branch j.

Matrices A, B, C are the three basic characteristics of the economic system from which we shall derive our price systems. Note that these matrices represent the requirements of productive factors per unit of production in various branches: matrix A represents requirements of intermediate products, matrix B of the stock of physical capital, and matrix C requirements of labor, expressed in subsistence (real) wages. We shall assume that matrices A, B, C are non-negative, that they have positive maximum characteristic roots, and that the maximum characteristic root of matrix A is less than one. These are the only assumptions laid down. In a normal economy, these assumptions are always fulfilled.

 

 

 

 

 

 

 

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