# PP/DP trajectories, fixed capital model I

We repeat the same experiment using this time fixed capital model I in which we construct the matrix of capital stock coefficients by multiplying the row vector of capital stock per unit of output times the column vector of investment shares. In Figure 7.3, we display the paths of prices consequent upon changes in the relative rate of profit. As expected, the paths of relative prices are linear going either in the upward or downward direction.

The capital—output ratios, as shown in Figure 7.4, remain the same regardless of the changes in the rate of profit, a result explained by the way in which the matrix of the capital stock coefficients matrix is constructed. The rank of such a matrix is equal to one and imposes its form when multiplied from the right by the Leontief inverse. In effect, the column norms of the matrix display little variability, a result that has to do with the process of vertical integration.

*Figure 7.3* Price trajectories and the relative rate of profit, fixed capital model I, USA 2014.

*Figure 7.4* Capital intensities and relative rate of profit, fixed capital model I, USA 2014.

# PP/DP trajectories, fixed capital model II

The above findings are contrasted to those derived from a fixed capital model in which we use the matrix of capital stock coefficients proper, that is, through the capital flow or investment matrix with the aid of which we construct new shares and the resulting matrix we multiply element by element by the capital—output vector. The so derived matrix of capital stock coefficients is then multiplied by the Leontief inverse also augmented by the matrix of workers consumption coefficients.

The movement of relative prices is quite similar to that of the model I with some minimal differences lending support to the suggested treatment of the matrix capital stock employed in constructing the capital stock matrix in model I. The price trajectories are shown in Figure 7.5 while the capital intensities are shown in Figure 7.6.

*Figure 7.5* Price trajectories and the relative rate of profit, fixed capital model II, USA 2014.

*Figure 1.6* Capital intensities and relative rate of profit, fixed capital II.

A cursory consideration of the price trajectories in the fixed capital models I and II shows that the ranking of prices is exactly the same. Furthermore, the differences in price trajectories are minimal, as we can see in industries

- 2 and 3, which almost coincide in the two models, whereas industries 1, 4 and 5 are in the same ranking and do not differ in any empirically significant way over the entire range of the relative rate of profit. Such price trajectories indicate that the movement of capital—output ratios does not show variability. In fact, in Figure 7.4, they are moving parallel to the horizontal axis and nearly parallel is their movement in the model II (Figure 7.6). Sectors 2 and
- 3 in both models have a capital—output ratio close to the standard ratio (in model I slightly higher and model II slightly lower) and so their trajectories are near one in both models. One could reasonably argue that the capital intensities of these industries are not far from the Sraffian standard product, in a sense, to the Ricardian practical invariable measure of value.