Technological Progress In The Production Of Type II Tractors

Figure 1: Variation in the Choice of Technique with Technical Progress

This post is a continuation of an analysis of an example in the corn-tractor model.

An analysis of technical change is another application of this partitioning of parameter space by fluke switch points. In this context, the change in properties of the wage frontier is the result of structural economic dynamics (Pasinetti 1993). A movement from the upper right to the lower left in Figure 2 reflects a specific kind of technical progress in producing tractors of type II. The quantity of type II tractors needed to manufacture a new type II tractor decreases with a movement to the left. The maximum rate of profits for the technique with type II tractors increases. The quantity of type II tractors needed to make a bushel corn decreases with a downward movement. The maximum wage increases.

Figure 1 depicts the variation in the analysis of the choice of technique along a specific line in Figure 2. The coefficients of production for inputs of type II tractors, in both industries, fall together in travelling from the upper-right to the lower-left in the graph. Switch points and the maximum wage are plotted. Four fluke switch points provide vertical divisions in the diagram. The cost-minimizing technique is labeled among ranges of the wage. From right to left, the diagram shows how technical progress in producing type II tractors results in the corresponding technique ultimately replacing the technique with type I tractors.

Region 6, with triple-switching, arises in the midst of this transition. It can be preceded by a region with a single switch point, as it is in this diagram. Or triple-switching can be preceded by region 3, in which double-switching occurs. The region with triple-switching can be followed by region 7, with a single switch point, or by region 5, with double-switching. A region with triple-switching might not occur at all, as in a path through regions 3, 2, and 5. The appendix provides an example in which double-switching can occur, but not triple-switching. Double-switching might also not occur at all, with a path from region 4, through region 2, and into region 1.

This example therefore suggests that a technology in which the corresponding prices of production exhibit triple-switching will appear only as a transient phenomenon, as one technique replaces another due to technical change. This conclusion also applies to double-switching. Presumably, the same result applies to multiple switching with four or more switch points.

How multiple switching manifests in market prices depends on many determinations not considered in this article. The speed at which coefficients of production evolve with technical change, compared to the speed at which market prices approach prices of production, if they do, seems of some importance. Robinson (1975) argues the latter process should be analyzed in historical time, not with a mechanical process in logical time. The stability of wages and the rate of profits is another issue. Accounting conventions for depreciation and for allocating overhead costs might impact these processes. The size of extra profits obtained by being first to adopt a new process or technique is another consideration. Nevertheless, no theoretical basis seems to exist for the idea, for example, that a rise in wages or a fall in the interest rate is associated with a drop in employment due to the adoption of a less labor-intensive or more capital-intensive technique of production, out of a given and known book of blueprints.