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Sekerka - Kyn - Hejl:  Price Calculations

3. General Formulae for Price Calculations

Every price (of any type) consists of three basic components: material costs, wages and profits. If we denote

p ..... price

c ..... materials costs

v ..... wage costs

z ..... profit

 

we can write this relation in the following way:

 

                p = c + v + z                                                       (0)

 

To this should be noted:

 

a)      in order to simplify the computation we do not take into consideration the distribution margin,

 

b)      all "non cost" components of the price are included into the profit,

 

c)      in order to attain greater accuracy a fourth component (indirect tax) should be added to the price of some commodities, but as we are interested in price calculations of uniform level, we need not take the indirect tax into account.

The substance of price calculations consists in recalculation of all prices — under the condition that technology, i.e.. e. material consumption and producti­vity of  labor does not change -- in such a way that the amount of  "z"  (profit) in all prices should correspond to a chosen uniform principle. The price calcula­tion according to a uniform base practically equals the redistribution of surplus product among the different branches of production.
The difficulty of this task consists not in the redistribution of surplus product alone (this could be computed easily) but in consequences of price interdepen­dencies; as soon as prices start to "move", the price expression of costs will change (even if a constant physical structure of output is considered), so that in order to obtain a required price, we have to add the share of surplus product calculated by the new method to the costs, the amount of which however de­pends on prices we have still in process of calculation.
In price calculations it is thus always necessary to take into account the changes in valuation of material costs. The change of wage costs could be, of course, taken into account as well; even under unchanged input of labor it could happen that the changes in prices of consumption goods will enforce the change of the amount of wages and consequently of wage costs per production unit. In order to express these changes mathematical models have been already elabo­rated. But it must be stated that these models are very complicated and, besides this, the empirical data which could make possible our computations are not yet at our disposal. Owing to this, there is no other choice than a some-what less accurate but much more simple way: to consider the component v (wage costs) of every price as constant and at the same time to make sure that the real contents of nominal wages (at least approximately) will not be subject to changes during price recalculations. This could be done, e.g. by postulating the sum of prices of consumer goods, which are purchased for wages, to be constant. We shall return to this problem in discussing the so called (n + 1)st condition.

If we sum up our considerations, we have to establish — for obtaining prices of a uniform base — the formulae and the calculation methods so that they:

 

1)  are based on the technologically given input structure, including direct labor input (expressed in wage costs);

 

2)  enable the redistribution of surplus product into the prices according to the above mentioned general rules;

 

3)   contain revaluation of material costs (in the case of production-, two channel-, and income-prices the revaluation of production funds as well) in terms of prices of a uniform base. This has to be understood as revaluation which itself is part of calculation and not an additional revaluation adjustment;

 

4)  retain the nominal amount of wage costs and real contents of wages as the only unchanging, constant element of price structure

Now we can proceed to the construction of formulae for particular types of a uniform price base.

Labor Value price.

Surplus product realized in every branch equals the produced surplus product. Therefore z = m,  where m is the produced surplus product contained in the commodity unit. At the same time it is supposed that the rate of surplus product,  m=m/v  is in all branches equal. These .two assumptions imply that the profit (z) in every price — see formula (1) — is a multiple of wage costs (v). Therefore

 

           z = m v                                                                 (1)

 

After substitution into (0) and a small adjustment we obtain the general formula of value price:

 

          p = c + v(1+ m)                                                    (2)


It is, of course, supposed that the material costs (c) are already evaluated in value prices.

Cost price.

 If  r  is the rate of profit,   r =  z /(c + v)  , then from the assumption of  a uniform rate of profit follows that  z  in every price is r multiple of the amount of costs  z  =  r (c + v) . After substituting into (1) and after some adjustment we obtain

 

           p = (c + v)(1 + r)                                             (3)

Production price.

Redistribution of surplus product according to uniform rate of profit is supposed. Let us denote the rate of profit  as  r  and the stock of produc­tion funds (evaluated in production prices) needed to produce a unit of pro­duction in a given branch as  K.   K  is also denoted as a coefficient of funds‑intensity of production. Therefore, the rate of profit is  r  =  z / K ;  the principle of a uniform rate of profit implies that the profit contained in every price is a multiple of the funds-intensity coefficient:   z  = r K.  It follows therefore that the general formula of production price is

 

              p = c + v + r K                                                      (4)

 

It has to be noted that the calculations must respect the fact that the fund coefficient of production necessarily varies with price changes; this happens not only in the case of the production price but also in the cases of the two-channel price and income price as well.

 

The two - channel price

 The two-channel price can be calculated in several alternatives: Let us assume here the following alternative: a portion of surplus product is apportioned into the prices as the so called interest on the production funds — it is pro­portionate to the production funds according to a uniform rate of interest; the rest is apportioned in relation to the wage costs. The two-channel price formula accordingly contains instead of   z  (see 1) two terms: the first one is similar to that in the value price (2), the second to that in the production price (4). The only difference is the substitution of the rate of profit r by the rate of interest   — let us denote it r* -- and of the rate of surplus product  m  by the reduced rate of surplus product  m*.  By the reduced rate of surplus product is understood the coefficient by means of which not the whole surplus product in the commu­nity, but only the part of surplus product, remaining after the deduction of the whole amount of interests on the production funds, is apportioned. The formula of the two-channel price is then as follows:

 

          p = c + v(1 + m*) +  r*K                                        (5)

 

This formula makes it clear that the price relations here are a certain "weighted average" of value relations and production prices. The greater is  m* and accor­dingly the smaller is the interest of funds r*, the nearer are the two-channel prices to the value prices (for r* = 0  they are equal to the value prices), and, on the contrary, the greater is the interest and the smaller the reduced rate of surplus product, the nearer are the two-channel prices to the production prices (for m*  = 0  they are equivalent to the production prices).

Income price

Income price is based on the idea of a uniform rate of gross income in relation to production funds. If we denote the gross income as d  where d = v + m  and the rate of gross income as   d ,   d =  d / K , then the simple formula of income price reads:

 

          p = c + d K                                                                (6)

 

The income price is peculiar, in comparison with the previously mentioned types; its calculation is not based on wage costs but only on material costs and on funds-intensity.

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