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"Price Systems Computable from Input-Output Coefficients,"

3. Extensions of a Price Model

It follows from the preceding section that comparability of East European statistical data with Western data can be improved if they are recalculated into artificially computed “production prices”. Of course, a total elimination of the price bias cannot be expected, but even a small improvement would be valuable.

The reevaluation of East European statistics by prices comparable to market prices is not the only feasible way. It is also possible to recalculate Western statistics into prices comparable with the East European price systems, or to recalculate both sets of statistics into artificial prices. In all of those cases, international comparability can be improved and some very interesting information can be gained.

Let us first increase the number of price models by two. These two models are totally artificial and inapplicable to any real economy, nevertheless, they are theoretically interesting and useful. They correspond, in a certain way, to “labor-value prices”, but reflect the dependence of prices on capital and material inputs respectively, rather than on labor inputs. We can, therefore, label them “capital-value prices” and “material—value prices” 6).

“Labor-value prices” (la) cover material costs and distribute value-added in proportion to direct wage costs. Let us, therefore, construct “capital-value prices” as prices covering material costs and distributing value-added in proportion to capital stock tied in the production of each commodity.

 “Capital-Value Prices”

(14a)                p’   =   p'A + r* p'B

(14b)               p'b   =   1.

 The subsistence wage equation p'c = w is redundant in this case, because wage costs do not enter the price equations. The numeraire equation (14b), as before, serves only to fix price level and has no effect on relative prices. If the system is productive, (i.e. if the dominant characteristic root of the matrix A is less than one) , as originally assumed, then (14a) can be rearranged to read:

 (15a)                            p   =   r* p'B(I - A) -1

 The matrix   B(I - A) -1  is semipositive, therefore, there exists a semipositive vector p, associated with the dominant characteristic root  l B(I - A) -1      of the matrix   B(I - A) -1  The parameter r* is determined by:

 (15b)         r*  =   1/ l B(I - A) -1      

  If the matrix B (I-A) -1 is indecomposable, then uniqueness and strict positivity of p is guaranteed. In a similar way, we can construct “material-value prices” by distributing value-added proportionally to material costs. 

“Material—Value Prices”

      (16a)     p'   =   p'A  + n* p'A,

     (16b)     p'b  =   1

 No subsistence wage equation is needed in this case either, and the numeraire (16b) has no impact on relative prices.

A simple rearrangement of (16a) gives:

      (17)                p'  =   (1 + n*) p'A,

 

We can immediately see from (17) that p' is semipositive (strictly positive if A is indecomposable) and

            (18)                             n*    = 1/ lA

 where  lA  is the dominant characteristic root of the matrix A. Because    lA  < 1   by assumption,  n* is always positive. 

What is the purpose of introducing these two models of purely artificial prices ? First of all, it can be demonstrated that “production prices” are an “intermediate case” between “labor-value prices” and “capital-value prices”. Certainly it is clear from (10a) and (11) that

(a) if real wage is raised enough to make the dominant characteristic root of the matrix A + C equal to 1, the rate of profit will fall to 0, and “production prices” will become “labor-value prices”;

(b) If, on the contrary, real wage is pressed down to 0 the rate of profit will reach r* and “production prices” will be transformed into “capital-value prices”.

Reasoning along these same lines shows that “cost-prices” (2a)  are a certain intermediate case between “labor—value prices” and “material-value prices”.

Still more interesting is the property of artificial prices to measure various macroeconomic indicators without bias.

 

 

 

 

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