Saturday, May 25, 2019

All Combinations of Real Wicksell Effects, Substitution of Labor

Figure 1: A Pattern Diagram

Consider an example of the production of commodities, in which many commodities are produced within capitalist firms. Suppose two techniques are available to produce a given net output. These techniques use the same set of capital goods, albeit in different proportions. They differ in process in use for only one industry. Given the qualification about the same capital goods, generic (non-fluke) switch points are the intersection of the intersection of the wage curves for two techniques that differ in exactly one process.

Suppose that, due to technological progress, some coefficients of production decrease in the process unique to the Alpha technique. Figure 1 shows a possible pattern diagram for this generalization of a previous example. Here, switch points and the maximum rate of profits are plotted against the rate of profits. As time goes by, a reswitching pattern leads to a reswitching example. The switch point created at the larger rate of profits exhibits, after t = 1/2, a negative real Wicksell effect and a reverse substitution of labor. A pattern over the axis for the rate of profits then results in the existence of another switch point at an even higher rate of profits. Technological progress can bring about, in a single example, the combination of both non-zero directions of real Wicksell effects with both non-zero directions of the substitution of labor.

The regions in Figure 1 in which reswitching occurs also illustrate process recurrence. Process recurrence is more general, inasmuch as it can arise even without reswitching.

Since all four possible combinations, of nonzero-real Wicksell effects and the substitution of labor, are possible, the direction of real Wicksell effects and the direction of the substitution of labor are independent of one another. The choice of technique results in variation in gross outputs in multiple industries, for given net outputs. (The question of returns to scale is of interest in this context.) These variations in gross outputs also result in variation in the amount of labor firms want to employ. Around a switch point with a positive real Wicksell effect, firms want to employ more labor, per unit of net output, in the aggregate across all industries. A necessary consequence is that they want to employ more labor in at least one industry. This variation in aggregate employment is consistent with any direction in the variation in the labor coefficient of production in the industry with the varying process.

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