Still More On Recurrence Of Truncation Without Reswitching

Figure 1: An Example of Structural Economic Dynamics

This post presents a diagram illustrating the effects of a particular kind of technical progress in a model with fixed capital. The example is one with two industries. Machines are produced in the machine industry and used in both the machine and corn industry. All production processes take a year to complete. Machines have a physical lifetime of two years. Managers of firms have a choice in each industry. The economic life of a machine can be one or two years in either industry.

This previous post specifies the technology at time zero. Coefficients of production for inputs and outputs are shown in Tables 1 and 2 in that post. Table 3 defines the four techniques, Alpha, Beta, Gamma, and Delta. Table 1 repeats that specification in a somewhat different format.

Table 1: Specification of Techniques

Technique	Economic Lifetime of Machines
	Machine Industry	Corn Industry
Alpha	One Year	One Year
Beta	Two Years	One Year
Gamma	One Year	Two Years
Delta	Two Years	Two Years

I consider perturbations of coefficients of production that define the amount of circulating capital needed to operate new and old machines, both in producing more new machines and in producing corn. This previous post defines the regions illustrated in the diagram at the top of this post. I repeat the definitions of the regions in Table 2 here. The cost-minimizing techniques, in each region, are listed in the order of an increasing rate of profits or decreasing wage.

Table 2: Overview of Regions

Region	Techniques	Notes
1	Alpha	No switch point.
2	Alpha, Gamma	Lower rate of profits associated with truncation in corn industry, greater output per worker.
3	Alpha, Gamma, Delta	Lower rate of profits associated with truncation, greater output per worker.
4	Alpha, Gamma, Delta, Beta	Recurrence of truncation in corn industry.
5	Alpha, Beta	Lower rate of profits associated with truncation in machine industry, greater output per worker.

I also consider the perturbations of relative markups, yielding a figure much like that at the top of this post. I conclude that both technical progress and changes in market power can have similar effects, in the large. In this example, both can bring about or eliminate the recurrence of the truncation of the economic life of the machine in one industry. This post further illustrates this claim about technical progress.

I consider further perturbations of coefficients of production in this post and this post. Although four coefficients of production decline with technical progress in Figure 1, I have not managed to specify a path through the additional regions in parameter space found in these later posts.