Bifurcations And Switchpoints

I have organized a series of my posts together into a working paper, titled Bifurcations and Switch Points. Here is the abstract:

This article analyzes structural instabilities, in a model of prices of production, associated with variations in coefficients of production, in industrial organization, and in the steady-state rate of growth. Numerical examples are provided, with illustrations, demonstrating that technological improvements or the creation of differential rates of profits can create a reswitching example. Variations in the rate of growth can change a "perverse" switch point into a normal one or vice versa. These results seem to have implications for the stability of short-period dynamics and suggest an approach to sensitivity analysis for certain empirical results regarding the presence of Sraffa effects.

Here are links to previous expositions of parts of this analysis:

• Variation in selected coefficients of production:
• Variation of switch points
• A bifurcation diagram
• A model of prices of production under oligopoly:
• The model
• Variation of switch points with markups
• A bifurcation diagram
• Bifurcations with variations in the rate of growth

In comments, Sturai suggests additional research with the model of oligopoly. One could take the standard commodity as such that it has no markup. What I am calling the scale factor for the rate of profits would be the rate of profits made in the production of the standard commodity. Markups for individual industries would be based on this. I have identified a problem, much like the transformation problem, in comparing and contrasting free competition and oligopoly. I would have to think about this.