For a good introduction to Marxist and non-Marxist economics including a discussion of value theory, I strongly recommend:
http://www.econ.jhu.edu/people/fonseca/het/hethome.htm
As far as the Okishio theory is concerned, this should clarify everything:
1. THE STATIC-NOMINAL RATE OF PROFIT Throughout the following presentation, it will be assumed that prices =3D values; the inclusion of divergences between values and production prices complicates the exercise but adds nothing to the results. This framework also shows that the Okishian calculation fails to represent the dynamic of the rate of profit for reasons which are not linked with the so-called "transformation = problem".
In this section, a two-department economy -means of production and means of consumption- is considered in a condition of stationary reproduction, i.e. having no technical change. This economy is depicted by the following matrices and vectors:
Xt =3D=20
960=20
960=20
At =3D=20
0.25=20
0.25=20
0=20
0=20
Bt =3D=20
0=20
0.1=20
Lt =3D [2.5 2.5]
Mt =3D At + BtLt =3D=20
0.25=20
0.25=20
0.25=20
0.25=20
Yt =3D (I - At)Xt =3D=20
480=20
960=20
Xt is the physical output vector, measured in units; At is the matrix of unit means of production coefficients; Lt is the vector or unit living labor coefficients and Bt is the vector of real wage, means of consumption per working day. The irreducible matrix Mt is formed by the unit coefficients of means of production (first row) and means of consumption (second row). Under static conditions, total physical net product is Yt.=20 It is known that the static rate of profit pt) of this economy is given by pt =3D (1/et) -1,, where et is the maximum eigenvalue of matrix Mt. In the example, et =3D ½ (< 1; the economy is "productive"), and thus pt =3D 100%. Relative prices (=3D values) are obtained by the following system of homogeneous equations: [1] Pt [Mt - etI] =3D 0 where Pt is the vector of relative prices. This system may be normalized by P2 =3D 1, thus defining the physical exchange proportion between the two commodities: [2] Pt =3D [1 1] It is important to say that the above procedure for obtaining the rate of profit through et, as well as the calculation of relative prices by means of equation [1], is not a general method for calculating these magnitudes. It is valid only under two special conditions: either when there is no technical change, or when there is technical change but, over time, prices =3D values. The latter is the condition considered in this article. Now then, in capitalist society, exchanges are carried out by means of money, and not by barter relations, as equation [2] suggests. In Capital I, Marx distinguishes three functions of money: money as measure of value, money as means of circulation and "money-as-money". Money considered "as money" functions as an instrument of hoarding, means of payment and world money. These functions are actually performed under some set of socially valid rules and institutions, i.e. a under a monetary system. In this article, it is considered a monetary system in which the form of value is constituted by two closely related aspects or kinds of money, symbol-money and reserve-money. Commodities are compulsorily exchanged by means of symbol-money -the pound, £- paper money without intrinsic value issued by a national monetary authority which has "objective social validity... [acquired by] its forced currency". Side by side with symbol-money, there is also a commodity-money -gold- which has a parity with the £ sanctioned by the monetary authority. Hence, in this framework, reserve-money is a commodity with intrinsic value and, then, it contains, represents and can conserve a given amount of social labor-time. The monetary authority can only issue paper money; so, it has no influence, for example, on the rate of interest. The monetary system is thus organized by means of paper money endowed with forced currency and guaranteed by gold, the reserve-money. Additionally, it is assumed that, under certain circumstances, symbol-money can perform any monetary function. In particular, the possibility of a continuous use of symbol-money instead of gold is given by the stability of the parity £/gold. Contrarily, a rise in this relation would provoke the lost of monetary functions by symbol-money and, consequently, an increase in the use of gold as money. So, the first relation defining the monetary system is the parity pound/gold (Gt). This relation is defined as the amount of pound notes freely exchangeable with one ounce of gold in a given period. The dimension of this ratio is: [3] Gt =3D £/ o.g. where o.g. means "ounces of gold". In period t, the specific parity pound/gold sanctioned by the monetary authority is £1 =3D 1 ounce of gold. As already was noted, in this monetary system, because reserve-money is a commodity (gold), it contains and represents a certain amount of labor-time. However, it will be supposed that gold is not produced in this economy. The labor-time contained in, and represented by, one ounce of gold defines a second relation of the monetary structure: the parity labor-time/gold (gt), which has the dimension: [4] gt =3D w.d. /o.g where w.d. means "working days". This is a relation between the substance of value -labor-time- and one specific aspect of the form of value -reserve-money. Frequently, Marx calls it "value of money", which is an ambiguous designation for two reasons: Firstly, because it is a relation between = labor-time and reserve-money, not between " value" and " money". Secondly, because it can be confused with another relation, that between labor-time and symbol-money, which will be examined below. It is, thus, convenient to establish a special designation for gt, the relation between labor-time and reserve-money. Concerning gt, it will be supposed, firstly, that, in period t, the labor-time contained in one ounce of gold is equal to that contained in each of produced commodities and, secondly, that this relation is constant over time, i.e. gt =3D gt+1. The latter is an important assumption of Marx in Capital III, made in order to analyze the dynamic of profit rate: "Firstly, the value of money. This we can take as constant = throughout." The explicit consideration of = symbol-money permits one to establish a third relation in the monetary system: the monetary expression of labor (MELt), a ratio between the pound (£) and the substance of value = (labor-time): [5] MELt =3D £/ w.d. Since there is forced currency of paper money, labor-time is necessarily expressed through pounds. This defines the MELt as the amount of symbol-money which represents one unit of labor-time in a given period. (In section 3, it will be shown that the equation MELt =3D Gt/gt is valid only under static conditions.) Because, in period t, the labor-time contained in one ounce of gold is the same that that contained in each of the produced commodities and Gt =3D £1/1 ounce of gold, the vector of = symbol-money prices -i.e. the exchange ratios of commodities [2] expressed in paper money- is Pt£ =3D [£1 £1]. Then, using the above-presented data, it is possible to construct the following scheme of reproduction: Table 1
C V=20 C+V SV=3DPR VA=3DPP I 240 240=20 480 480 960=20 (800) (800)=20 (1.600) (1.600)=20 (3.200) II 240 240=20 480 480 960=20 (800) (800)=20 (1.600) (1.600)=20 (3.200) S 480=20 480 960 960=20 1920 (1.600) (1.600)=20 (3.200) (3.200)=20 (6.400)
In Table 1, numbers in the first line of each department are measured in £, while numbers in parentheses are measured in working days. The calculation of the latter will be explained below. Since prices =3D values, in each department the surplus value (SV) produced is equal to the appropriated profit (PR) and objectified value (VA) is equal to production price (PP). The static rate of profit is pt =3D 100% and the rate of surplus value st =3D = 200%.
For reproduction to be accomplished, a mass of symbol-money (mt) must exist. Assuming that only current output is exchanged, this mass is defined by the following equation: [6] mt =3D P£ = tXt/Vt
where scalar Vt is the velocity of circulation of symbol-money. It will supposed that Vt =3D 1, so the mass mt introduced by the monetary authority is mt =3D £1920.
The MEL corresponding to the living labor can be defined as the ratio between the value-product (£-prices multiplied by physical net product) and total living labor = LtXt. Under the static conditions prevailing in period t, this quotient is equal to the MEL corresponding to the whole labor-time objectified in the economy. Therefore, MELt can be calculated as: [7] MELt =3D P£ t = Yt/LtXt =3D £1440/4800w.d. =3D £0.3/w.d
(In section 2, a more general calculation of the MEL will be presented.) Thus, in period t, one working day is expressed through £0.3, or, in other words, £1 expresses 1/0.3 =3D 3.33 working days. Always taking into account that, in period t, static conditions prevail and prices =3D values, it is easy to calculate the vector of labor-times contained in commodities, either by = P£ t =3D P£ t = (1/MELt) =3D [3.33 w.d. 3.33 w.d.], or by P£ t =3D Lt [I-At]-1. By means of vector P£ t, labor-time magnitudes in Table 1 (numbers in parentheses) are worked out. For instance, labor time contained in constant capital is = (P£ tAt)j = (Xt)j; so, for Department I the calculation is 3.33*0.25*960 =3D 800 w.d. Since the labor-time contained in one ounce of gold (relation [4]) is assumed to be equal to that contained in each of the produced commodities, the parity = labor-time/gold is gt =3D 3.33 working days per ounce of gold.
Louis Proyect
(http://www.panix.com/~lnp3/marxism.html)