Prices of production in circulating and fixed capital models I and II
In this section, we estimate the prices of production (PP) defined as prices that incorporate the economy’s general rate of profit. The estimation of PP is carried out in both circulating and fixed capital models. The capital stock matrix used in the fixed capital model is estimated through two alternative ways. The first is the product of the column vector of investment shares times the row vector of capital—output ratio. The second way is based on the capital flows matrix, which has been aggregated into five sectors. The so aggregated capital flow matrix is multiplied by the diagonal matrix of capital—output ratios. The resulting by the second method capital stock matrix is considered a better estimate, although the results of the two estimating methods are not so much different, as we show below.
Prices of production in a circulating capital model
For the estimation of PP, we use the vector of real wage, that is, the basket of goods that workers spend their money wage on, that is
where w is the money wage, p stands for the PP and b is the (nxl) vector of wage goods estimated by aggregating the column of the consumption expenditures to form five shares that are then multiplied by the economy-wide average wage:
Alternatively, we could use the minimum instead of the average wage, but experience has shown that the average wage gives more stable results over the years for the same country and across countries.
Having estimated the basket of wage goods normally consumed by workers with their money wage, we can proceed with the estimation of the non- normalized prices of production, It, in the circulating capital model defined as follows:
where bl is a new matrix that represents the quantity of commodity i, which is required for the consumption of workers in order to produce commodity j. The above relation after some manipulation gives the following eigenequation:
Using the above realistic example of five sectors, we get the following maximal eigenvalue whose reciprocal gives us the rate of profit r = 1/2.7853774 = 0.359 and the normalized absolute eigenvalues are the following:
We observe, once again, that the subdominant eigenvalues are quite small relative to the maximal and the ratio of the subdominant to the dominant eigenvalue is 18.17%. A result that lends support to the view that the subdominant eigenvalues do not add or subtract much in the overall motion of the economy. In the last two of the subdominant eigenvalues, the imaginary parts (not shown) are three times lower than their real part and their module combined is nearly 2% of the maximal eigenvalue. The matrix H is as follows:
The maximal eigenvalue associated with the unique positive left-hand-side (l.h.s.) eigenvector gives the vector of relative prices and in terms of our numerical example, we get the normalized standard commodity vector of PP
Once again, we invoke our usual statistics of deviation of PP from MP, and we get the following:
The MAD is 0.0936 or 9.36%.
The MAWD is 0.047 or 4.74%.
The d-statistic is 0.158 or 15.8%.
Linear model of production 179