Tag Archives: Example in Mathematical Economics

Figure 1: A Bifurcation Diagram1.0 Introduction I have been looking at how bifurcation analysis can be applied to the choice of technique in models in which all capital is circulating capital. In my sense, a bifurcation occurs when a switch point appears or disappears off the wage frontier. A question arises for me about how to apply or visualize bifurcations in models with land, fixed capital, and so on. This post starts to investigate this question by looking at a numerical example of...

Coefficients for First Column in Leontief Input-Output Matrix I have uploaded a draft paper with the post title to my SSRN site. Abstract:This note demonstrates that the special case condition, needed for a simple labor theory of value (LTV), of equal organic compositions of capital does not suffice to determine technology. A model of the production of commodities, with circulating capital and all commodities basic, is analyzed. Given direct labor coefficients and labor values, an...

Figure 1: A Bifurcation Diagram This post expands on this previous post. The technology is the same, but the rates of decrease of the coefficients of production in the Beta and Gamma corn-producing processes are not fixed. Instead, I consider the full range of parameter values. (I find the graphs produced by bifurcation analysis interesting for this case, but I think a two-commodity example can be found with more pleasing diagrams.) Anyways, Figure 1 shows a bifurcation diagram for the...

Figure 1: A Bifurcation Diagram This post presents another example of bifurcation analysis applied to structural economic dynamics with a choice of technique. This example illustrates: Two reswitching examples appear and disappear without a restitching bifurcation ever occurring, at least on the wage frontier. Two bifurcations over the wage axis arise. At the time each bifurcation of this type occurs, another switch point for the same techniques exhibits a real Wicksell effect of zero....

Variation of Switch Points with Technical Progress in Two Industries I have a new working paper - basically an update of one I have previously described. Abstract: This article illustrates the application of bifurcation analysis to structural economic dynamics with a choice of technique. A numerical example of the Samuelson-Garegnani model is presented in which technical progress is introduced. Examples of temporal paths through the parameter space illustrate variations of the wage...

Coefficients for Iron-Production in the Leontief Input-Output Matrix I have uploaded a working paper with the post title. Abstract: This note demonstrates that the special case condition, needed for a simple labor theory of value, of equal organic compositions of capital does not suffice to determine technology. Prices do not vary across techniques for both techniques in a numeric example of a two-commodity linear model of production, and they are proportional to labor values. Both...

Figure 1: Fluke Switch Points on Each Axis1.0 Introduction I have developed an approach for finding examples in which either two fluke switch points exist on the wage frontier or a switch point is a fluke in more than one way. This post presents a numerical example with two fluke switch points on the frontier. Not all examples generated by this approach are necessarily interesting, although I find the approach of interest. I don't think the example in this approach is all that...

A Bifurcation Diagram with Two Temporal Paths I have a working paper with the post title. Here's the abstract: This article illustrates the application of bifurcation analysis to structural economic dynamics with a choice of technique. A numerical example of the Samuelson-Garegnani model is presented in which technical change is introduced. Examples of temporal paths through the parameter space illustrate variations of the wage frontier. A single technique is initially uniquely...

Figure 1: A Bifurcation Diagram I have previously illustrated a case in which real Wicksell effects are zero. I wrote this post to present an argument that that example is not a matter of round-off error confusing me. Consider the technology illustrated in Table 1. The managers of firms know of three processes of production. These processes exhibit Constant Returns to Scale. The column for the iron industry specifies the inputs needed to produce a ton of iron. Two processes are known for...