A Structure in Parameter Space with Three Patterns Across The Wage Axis

Figure 1: Three Patterns Across The Wage Axis And One Three-Technique Pattern

This post continues the approach in this post and in this post. As previously stated, I consider the same two examples. In both examples, three processes are known for producing the numeraire, called "corn". In the example for the left panel, corn is a non-basic commodity, and a different basic commodity is used in each of the three techniques. In the example for the right panel, all three corn-producing processes require inputs of labor power, corn, and iron (in different proportions), and managers firms know of a single process for producing iron. Both commodities are basic in this second example. The examples are also parametrized differently.

In both panels, loci for three patterns of switch points on the frontier and over the wage axis terminate at a point that is also the terminus for a locus for a three-technique pattern of switch points. For the example illustrated by the right panel, a second switch point exists on the wage frontier for a larger rate of profits than the one concerned in the patterns of switch points. This structure in parameter space is also depicted as Figure 2 in my paper, 'Fluke switch points in pure fixed capital systems', for a quite different example.

This generic structure in these parameter spaces is obscured by the dotted line in the panel on the right. Along it, the wage curves for the switch point between the Beta and Gamma techniques intersect at a rate of profits of zero. But this switch point is not on the wage frontier. Below and to the right of the dotted line, the switch point between Beta and Gamma on the frontier exhibits capital-reversing, while above it that switch point has a negative real Wicksell effect. Thus, the dotted line is not associated with a change in the number of sequence of switch points along the wage frontier. But it is associated with the change of the direction of real Wicksell effects around one of these switch points.

So here is another perhaps universal structure, in some sense, in parameter spaces associated with the analysis of the choice of technique in models of prices of production.