6. The Impact of Changes in Relative Prices
The changes in relative prices can be studied apart from the “two-levelness” of prices, if we introduce two new price systems which imply the same relative prices as two-level “cost prices” or two-level “production prices”, but do not contain turnover tax.
Such systems are known as “two-channel prices”8). Let us define them:
“M - Two Channel Prices”
(70a) p' = (1 + n) p'A + (1 + m)w l',
(70b) p'c = w
(70c) p'b = 1.
“C - Two-Channel Prices”
(71a) p' = p’A + (1 + m )w1' + r p'B,
(71b) p'c = w
(71c) p'b = 1.
As before, we can proceed to:
(72) p' = (1 + n)p'[A + (1 + m)C],
(73) p' = r p'B[I - A - (1 + m)C ]-1
A comparison of (72) and (73) with (62) and (69) shows that relative “M-two channel prices” are equal to relative two level “cost prices” and that relative “C-two channel prices” are equal to relative two-level “production prices”, provided m = d.
If we assume:
(74) n ³ 0, m ³ 0, r ³ 0
then, the following upper limits can be derived for n, m and r:
(75) n £ = 1/lA+C - 1 , m £ = 1/lC(I-A)-1- 1 , r £ = 1/lB(I-A)-1.
When m = 0 “M-two channel prices” become “cost prices”, and when v = 0 they become “labor-value prices”. The gradual increase in m from 0 to its upper limit (75) will result in a gradual decline in n from its upper limit to 0. Relative prices will be also gradually changed. The direction and the degree of changes in relative prices will depend on the particular coincidence of matrices A and C. If these matrices are known, the whole spectrum of “M-two channel prices” can be empirically computed by solving the equation (72) with various values of the parameter m. It is important to stress that the gradual increase in m would not cause any random shifts in the price vector; they would rather result in very systematic and predictable changes.
The same can be said about “C-two-channel prices” (73). The gradual increase in m from 0 to its upper limit, will cause a gradual decline in r from its upper limit to 0, and also smooth and predictable changes in relative prices from “production prices” to “labor-value prices”. The direction and the degree of these changes depend on the particular coincidence of matrices A, C and B.
Clearly, if the “physical content” of a certain macroeconomic indicator is given, then the changes in its nominal value are explainable from the changes in parameters m, n, and r.
The concept of “two-channel prices” may be extended to include “capital value prices” and “material value prices”. In order to do that, it is sufficient to move the lower limit of m from 0 to -1:
(76) n ³ 0, m ³ -1, r ³ 0
which implies the new upper limits for v and r
(77) n £ (1/lA) - 1 , m £ (1/lC(I-A)-1) - 1 , r £ 1/lB(I-A)-1
The pushing of m down from 0 to -1, will cause a further increase in n towards its new upper limit, and, “M-two-channel prices” will be pushed beyond “cost prices” towards “material value prices”.
A similar effect is achieved in “C-two channel prices” by depressing m down to -1.
Diagrams 1 and 2 show the effect of changing parameters m, n and r on both types of two-channel prices. It is based on Czechoslovak price calculations for 1966.9)
It is obvious that the movement along the spectrum of two-channel prices brings about systematic and predictable changes in relative prices. It is not surprising, therefore, that such a movement results also in systematic and clearly explainable changes in the ratios: a , b, and g.
Table 3 shows the values of some macroeconomic indicators for “C-two-channel prices”.
Let us now return to the two - level price systems. The previous exposition laid the groundwork for a decomposition of the price bias into two parts: (i) an effect of changed relative prices and (ii) an effect of differences in the levels of wholesale and retail prices.
Suppose, for example, that we want to estimate the impact of turnover tax with the rate levied on “production prices”.
We shall use the following notations
ao, bo, go - the respective ratios measured at one-level “production prices”
a*, b*, g* - the ratios measured at one-level “C-two-channel prices” with m = d* a**, b**, g** - the ratios measured at two-level “production prices”.
The imposition of turnover tax d* on “production prices" does change relative prices because the uniform rate of profit in the two - level system, is smaller than r in the one-level system. The rates r and r* are determined in the following manner: (78) r = 1/ l B(I-A-C)-1 r* = 1/ l B[I-A- (1+d*)C]-1
The formula (73) can be used to calculate “C-two-channel prices” corresponding to the parameters r = r* and m = r* . Relative prices of such a price system are the same as if the tax d* were imposed, however, there is no difference between the levels of wholesale and retail prices. The differences between a* , b* and g* measured at above-described prices and ao , bo and go measured at original “production prices”, represent the price bias caused purely by changes in relative prices.
Once the bias resulting from changed relative prices is determined, the rest of the bias is very easy to find. From (41), (42) and (43), it follows directly that:
(79a) a** = a* /(1 + d*g* )
(79b) b** = b* /(1 + d*g* )
(79c) g** = (1 + d*) g* /(1 + d*g* )
The differences between just defined a**, b**, g** and the previously obtained parameters a*, b*, g*, represent the second part of the price bias. This part has its origin purely in the “two-levelness” after elimination of the “relative price” effect.
If d* > 0 then a** - a* < 0, b** - b* < 0 and g** - g* > 0. It is, therefore, obvious that the “two-levelness” alone causes always undervaluation of a and b and overvaluation of g. This effect resulting from the “two-levelness” of prices can be either increased or diminished by the “relative-price” effect.
This will depend on the values and signs of differences a* - ao , b* - bo , and g* - go .
Let us illustrate the decomposition of the price bias using the data from the Table 3. The values of parameters a , b and g measured at one level “production prices” (m = 0) are:
ao = 1.458 , bo = 2.618 , go = .403.
Suppose that the turnover tax with the rate d* =.511 is levied on consumer goods. The “relative-price" effect of such turnover tax can be read directly from the Table 3. We find a* , b* and g* as the value of parameters a , b and g measured at one-level “C-two-channel prices” with the parameter m equal to .511:
a* = 1.412 , b* = 2.726 , g* = .391
The “relative-price” effect leads to slight under valuation of a and g and to overvaluation of g . The values a** , b** and g** corresponding to two-level “production prices” with turnover tax d* = .511, can be now calculated from (79a,b,c):
a** = 1.177 , b** = 2.272 , g** = .492
The pure “two-level” effect is much stronger than the “relative-price” effect and causes considerable under valuation of a and b and overvaluation of g .
Table 4 summarizes the decomposition of the price bias for all three parameters.