FORMAL ANALYSIS OF PRICES

Prices

Surplus Value

Apparent System and Apparent Creative Value

FORMAL ANALYSIS OF PRICES

In order to study the structural properties of the system and those of the firms in relation to it, we hypothesize various kinds of distribution caused by different relationships between capital and income and between wages and profits, in the perfect competition hypothesis.
If there is no capital, as it would be in a primitive barter economy, the whole economic value is distributed as income. If capital is high, the system is in an advanced stage of the process of industrialization. If we suppose a zero profit, as in a primitive or in a socialistic distribution, the income is composed only by wages. If capital exists and wage is zero, the workers would all be slaves or shareholders of the firms.
A system which produces only final consumer goods may have existed at the beginning of economics, in the barter relationships, but the use of money, along with the freedom of buying and selling (essential for the formation of prices), implies the existence of capital and profit, therefore this kind of distribution, as the socialistic distribution, is concretely impossible. The same applies for the zero wage, or the equal composition of capital and the perfect competition hypothesis.

Prices

Using the relationships among the previously determined economic categories, the price of the commodity I:

P_i = [w l_i + c_i (1- e)] (1+r)

can be expressed this way:

P_i = p_i l_i = l_i + (c_i - l_i) [(1+r) / (1+R)]

We have indeed:

P_i = l_i w (1+r) + c_i (1- e) (1+r)

(1- e) = 1 - w - π,
(1- e) = 1 - w - [r / (1+r)]
(1- e) = [1+r - w (1+r) - r] / (1+r)
(1- e) (1+r) = 1 - w (1+r)

w (1+r) = 1 - (1- e) (1+r)

and since (1- e) = 1/(1+R)

w (1+r) = 1 - [(1+r) / (1+R)]

P_i = l_i - l_i [(1+r) / (1+R)] + c_i [(1+r) / (1+R)]

from which:

P_i = l_i + (c_i - l_i) [(1+r) / (1+R)]

p_i = 1 + (c_i / l_i -1) [(1+r) / (1+R)]

From this we can see that the quantity of social labor indicated by the price of a commodity is equal to its own creative value, l_i L_t, plus or minus a certain quantity of social labor for the equilibrium of the exchanges depending on the characteristics of the firm (l_i and c_i) and those of the system (r and R).
In an economic system without means of production, profit unlikely would exist; the economic value is distributed only as 'wage', w = e, and upon exchange everyone obtains different commodities whose average total value coincides with the quantity of time of labor employed to produce a single kind of commodity, that is: P_i = l_i and p_i = 1. But even if profit exists, it is e = 1 = 100%, the maximum rate of profit is R = e / (1- e) = infinite, and 1 / (1+R) = 0, and price would always coincide with the creative value.
If in the system there are means of production, it is E < L_t, e < 1, [1 / (1+R)] > 0, and prices normally indicate a quantity of social labor differing from that which produces them. If the means of production do exist in some firms, the quantity of social labor expressed by the price of the commodity produced by a firm which does not use them, being equal only to wages, would be smaller than the quantity of labor which produces it even in the case of socialist distribution, with r = 0; it decreases with the increasing of the rate of profit, and become zero for r = R.
Only in the hypothetical case of equal composition of capital in every firm, c_i = l_i, for no matter what the variation of rate of profit, social value coincides with the creative value: P_i = l_i, and p_i = 1.
In general, if the composition of capital of a firm is greater than the average, ci > li, then the quantity of social labor indicated by the price is greater than the applied quantity of labor, and vice versa in the opposite situation. By increasing the rate of profit, the difference between price and creative value also increases and, when it reaches the maximum admitted by the technology of the system, r = R, and therefore, (1+r) / (1+R)=1, it implies a price coinciding with a fraction of social value directly determined by the fraction of capital of that firm, that is P_i L_t = c_i L_t (not c_i (1- e) L_t). The magnitude of the social value, expressed by the price of a commodity, therefore, is always included between l_i L_t and c_i L_t, that is:

li < Pi < ci,

li = Pi = ci,

li > Pi > c,i

When the compositions of capital are different, a variation of distribution implies such a variation of prices that the various c_i magnitudes, the price of the net product and the magnitude of e and R, also vary.
There is one theoretical case for which, even with different composition of capital, and therefore variable prices, the magnitudes of the monetary efficiency and the maximum rate of profit remain constant with the variation of the relationship between wages and profits, that is, when the commodities composing the net product and those composing the gross product are in the same physical proportion. In this case, indeed, every commodity of the gross product would be contained y times into the net product, and e, which is a relationship between monetary magnitudes, would coincide with y which is a relationship between physical quantities. Varying distribution, and therefore the price of commodities, the price of the net product, like that of the gross product, remains constant, and e does not change. In this case, though, the variation of prices is accompanied by the variation of the magnitude of the various c_i and of the composition of capital of the firms.

Surplus Value

Since money is commanded labor, profit is surplus-value, directly coinciding with the surplus-labor, understood as a quantity of social labor exceeding the value of the consumer goods for the workers, which is obtained not in exchange for the labor given to the society but for the freedom of buying and selling.
Let's consider the profit of the firm I:

∏_i = [w l_i + c_i (1- e)] r L_t,
∏_i = [l_i w r + c_i (1- e) r] L_t,

being:
w (1+r) = 1 - (1- e) (1+r)
w + w r = 1 - 1 + e - (1- e) r
w r = (e - w) - (1- e) r

with:
(e - w) = π
w r = π - (1- e) r

∏_i = [l_i [π - (1- e) r] + c_i (1- e) r] L_t,
∏_i = [l_i π - l_i (1- e) r + c_i (1- e) r] L_t,
∏_i = [π l_i (c_i - l_i) (1- e) r] L_t,

with: (1- e) = 1 / (1 + R)

∏_i = {π l_i (c_i - l_i) [r / (1+R)]} L_t

In the case of equal composition of capital in every firm, that is c_i = l_i and c_i - l_i = 0, and also in the case of absence of capital in the system, therefore with c_i = 0, but also r / (1+R) = 0 because R = infinite, profit directly indicates a fraction of the creative value of the firm:

∏_i = π l_i L_t

Apparent System and Apparent Creative Value

Marx is also correct in considering the variation of the prices of equilibrium as the effect of the redistribution of social surplus value-labor.
Mathematically, the variation of prices caused by a variation of the relationship wage/profit can be considered as the effect of a redistribution of the labor applied in every firm; as if in a socialist distribution there was an apparent variation of the creative value of commodities. Namely, we can imagine that the same commodities are produced with the same means of production and by the same global labor which, though, is apparently distributed among the firms in such a way that if distribution were socialist, the price of the commodities would coincide exactly with the prices of the capitalist distribution which actually has decided them.
In order to calculate the distribution of the apparent workers, then, we must impose the condition that the apparent wage W_i given by the product of the apparent workers £_i L_t for the monetary efficiency e, which is now the apparent rate of wage, is equal to the sum of the real wages and profits of that firm.

W_i = e £_i L_t = w l_i L_t + [w l_i L_t + c_i (1- e) L_t] r

e £_i = w l_i + [w l_i + c_i (1- e)] r
e £_i = w l_i + w l_i r + c_i (1- e) r
e £_i = w (1+r) l_i + c_i (1- e) r

w (1+r) = 1 - (1+r) (1- e)
w (1+r) = 1 - (1- e + r - er)
w (1+r) = 1 - 1 - r + e + er
w (1+r) = e - (1- e) r

e £_i = l_i [e - (1- e)] + c_i (1- e) r
e £_i = e l_i - l_i (1- e) r + c_i (1- e) r
e £_i = e l_i + (c_i - l_i)(1- e) r
£_i = l_i + (c_i - l_i)[(1- e) / e] r

And since R = e / (1- e)

£_i = l_i + (c_i - l_i)(r / R)

If the rate of profit is zero and the distribution is really socialistic, then £_i = l_i.
Even when the composition of capital is identical in every firm, c_i = l_i and c_i - l_i = 0, with the existence and variation of profit the apparent creative value coincides with the actual creative value.
In the general case of different compositions of capital, it is possible that for some firms, on a given level of rate of profit, it is c_i = l_i and therefore £_i = l_i, but that can not continue to subsist on other levels because a variation of prices implies a variation of the magnitude of c_i and R. If w = 0, and therefore r = R, then £_i = c_i, and the apparent workers coincide with the fraction of capital.
When both w and r are positive, both price and apparent creative value are included between real creative value and capital, but we notice that, when profit is zero, in a firm where the composition of capital is, let's suppose, higher than the average, the apparent creative value coincides with the real one because r / R = 0, while the price indicates an higher quantity of social labor because (1+r) / (1+R) > 0. By increasing the rate of profit, both magnitudes increase until they converge at the proportion of capital for r = R. The apparent creative value, therefore, is always between actual creative value and the price.

November 2001 R.A.M.