Sekerka - Kyn - Hejl:   Price Calculations


8. Program and Calculation Procedure


To solve the set of price equations we can use either inversion of matrices method, or alternatively process of iterations.

We now turn back to our considerations on the (n + 1)st condition. Because  of this condition some non-linearities sneaked into the price calculations (with the exception of the value type price). Also the question arises whether a solution exists and, if so, whether it is unique. But the analysis of existence and uniqueness of desired price vectors is outside the scope of this article.


With regard to the (n + 1)st condition it would be of little use to solve the equations (11) to (20) by the matrix inversion; therefore, it was decided to use the  procedure of iterations. When writing the program we wanted to allow that the calculation of all price typTwo methods are possible in computing price indices: either a matrix inversion method or an iteration could be possible even with change in the form of the (n + 1)st condition, as well as in the case, when the (n + 1)st variable is in fact a priori given  constant (e. g. 3% profitability in the case of the cost prices.)

The iteration method chosen proved to be adequate. Its full description for each type of prices would require introduction of too many confusing symbols.  Therefore we limit ourselves here only to characterization of the basic principles of the program.


On the basis of parameters (i.e.. e. of constants determining the type of calcu­lation) and on the basis of information inserted into the computer directly (from the control desk) the price type, the demanded accuracy of computation and some other data are determined.

We start from some basic price indices (as a rule from unity indices) and compute the "revaluated" material costs; in the case of the value- and cost type the wage costs are added, and after this in the case of other types the revaluation of production funds has to be undertaken in addition. Further, the program tests whether in the process of computa­tion the (n + 1)st condition has to be used (if in the case e. g. of the cost type the profitability is determined in advance, e. g. 3%, it is superfluous to take this condition into consideration).


If the condition is to be taken into account, then, on its base, the "approximation" of the sought (n -j- 1)st variable is deter-mined (one of the variables such as u, r, ,u*, o O is in question). On the basis of this "approximation" a new set of n price indices is additionally computed. [The (n, + 1)st variable is — in the case of the value type — determined additio­nally after all iterations have been finished. This procedure is repeated until the demanded accuracy is attained.

In the case of value- and cost- price types, the net computation (without input and output) on the computer NE 803 B lasted approximately 15 minutes, in the case of production- and two-channel price the time — span was longer; the postulate for maximum difference between two values of the same price index corresponding to two successive iterations not to exceed 0,0001 was respected in all these computations.














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