Price systems computable from input-output coefficients

Input-Output models of various types of prices. Prices are derived as characteristic vectors of certain kinds of matrices and price parameters as their characteristic roots. The most general are the three-channel prices that are characteristic vectors of the linear combination of matrices of the full material input coefficients, full capital-output coefficients and full workers consumption coefficients. From the general three-channel prices two types of two-channel prices are derived. The special 'extreme' cases or the 'singe-channel' prices are the labor- value prices that are proportional to full labor costs, the N-income prices that are proportional to full material costs and the F-income prices that are proportional to full capital-output ratios. The special intermediate cases are the cost-prices and the production-prices. It is shown that all these types of prices make some linear combinations of certain macroeconomic indicators invariant to changes in output vectors. The results of experimental calculations of some of these types of prices from the Czechoslovak data are presented. The price model was also used for the Czechoslovak price reform of 1960's, when 25 thousands of price indices were calculated by iterative solution of the simultaneous equations.